Journal articles: 'Mathematical modelling - Epidemiology'

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Michael, E. "Mathematical modelling of disease epidemiology." Parasitology Today 9, no. 11 (November 1993): 397–99. http://dx.doi.org/10.1016/0169-4758(93)90042-e.

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Gubernov, Vladimir, Sergey Minaev, Hong G. Im, Nam Il Kim, and Kaoru Maruta. "Modelling in Ecology, Epidemiology and Evolution." Mathematical Modelling of Natural Phenomena 13, no. 6 (2018): E2. http://dx.doi.org/10.1051/mmnp/2018066.

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Yanchevskaya, E. Ya, and O. A. Mesnyankina. "Mathematical Modelling and Prediction in Infectious Disease Epidemiology." RUDN Journal of Medicine 23, no. 3 (December 15, 2019): 328–34. http://dx.doi.org/10.22363/2313-0245-2019-23-3-328-334.

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Mathematical modeling of diseases is an urgent problem in the modern world. More and more researchers are turning to mathematical models to predict a particular disease, as they help the most correct and accurate study of changes in certain processes occurring in society. Mathematical modeling is indispensable in certain areas of medicine, where real experiments are impossible or difficult, for example, in epidemiology. The article is devoted to the historical aspects of studying the possibilities of mathematical modeling in medicine. The review demonstrates the main stages of development, achievements and prospects of this direction.

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Huppert, A., and G. Katriel. "Mathematical modelling and prediction in infectious disease epidemiology." Clinical Microbiology and Infection 19, no. 11 (November 2013): 999–1005. http://dx.doi.org/10.1111/1469-0691.12308.

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Mindell, J. "Mathematical modelling of health impacts." Journal of Epidemiology & Community Health 59, no. 8 (August 1, 2005): 617–18. http://dx.doi.org/10.1136/jech.2005.034355.

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de Jong, Mart C. M. "Mathematical modelling in veterinary epidemiology: why model building is important." Preventive Veterinary Medicine 25, no. 2 (December 1995): 183–93. http://dx.doi.org/10.1016/0167-5877(95)00538-2.

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Morozov, A. "Preface." Mathematical Modelling of Natural Phenomena 13, no. 3 (2018): E1. http://dx.doi.org/10.1051/mmnp/2018041.

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VYNNYCKY, EMILIA. "13. The application of reproduction number concepts to tuberculosis Vynnycky E, Fine PEM. Epidemiol Infect 1998; 121: 309–324." Epidemiology and Infection 133, S1 (October 2005): S45—S47. http://dx.doi.org/10.1017/s0950268805004334.

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Epidemiology & Infection probably attracts more papers on mathematical modelling of infectious diseases than does any other epidemiology journal. The most important modelling papers published in the journal were probably those of Anderson and May during the 1980s, which laid the foundations for much of the subsequent modelling work carried out by themselves and their colleagues. Since the start of their partnership, they authored 17 articles between them in the journal, including work quantifying the effect of different vaccination strategies against measles and rubella [1, 2], on the epidemiology of rubella in the United Kingdom [3], and on the effect of age-dependent contact between individuals on the critical level of vaccination coverage required for control [4]. The latter work, published in 1985, was particularly important, since it described methods for incorporating realistic assumptions about (heterogeneous) mixing between individuals into models, an issue which was beginning to be addressed in the mathematical literature but which had not yet reached many epidemiological journals. Other important modelling work published in Epidemiology and Infection includes that of McLean et al. (reproduced in this edition) on the control of measles in developing countries [5, 6], and by Garnett and Grenfell on the epidemiology of varicella zoster in developed countries [7, 8].

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Groner, Maya L., Luke A. Rogers, Andrew W. Bateman, Brendan M. Connors, L. Neil Frazer, Sean C. Godwin, Martin Krkošek, et al. "Lessons from sea louse and salmon epidemiology." Philosophical Transactions of the Royal Society B: Biological Sciences 371, no. 1689 (March 5, 2016): 20150203. http://dx.doi.org/10.1098/rstb.2015.0203.

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Effective disease management can benefit from mathematical models that identify drivers of epidemiological change and guide decision-making. This is well illustrated in the host–parasite system of sea lice and salmon, which has been modelled extensively due to the economic costs associated with sea louse infections on salmon farms and the conservation concerns associated with sea louse infections on wild salmon. Consequently, a rich modelling literature devoted to sea louse and salmon epidemiology has been developed. We provide a synthesis of the mathematical and statistical models that have been used to study the epidemiology of sea lice and salmon. These studies span both conceptual and tactical models to quantify the effects of infections on host populations and communities, describe and predict patterns of transmission and dispersal, and guide evidence-based management of wild and farmed salmon. As aquaculture production continues to increase, advances made in modelling sea louse and salmon epidemiology should inform the sustainable management of marine resources.

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Blance, Andrew, Yu-Kang Tu, and Mark S. Gilthorpe. "A multilevel modelling solution to mathematical coupling." Statistical Methods in Medical Research 14, no. 6 (December 2005): 553–65. http://dx.doi.org/10.1191/0962280205sm418oa.

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Williams, Gail, Don McManus, Yuesheng Li, and Zheng Feng. "COMPARISON OF ENVIRONMENTAL APPROACHES TO CONTROL SCHISTOSOMIASIS JAPONICA: A MATHEMATICAL MODELLING APPROACH." Epidemiology 15, no. 4 (July 2004): S135—S136. http://dx.doi.org/10.1097/00001648-200407000-00351.

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TEMIME, L., G. HEJBLUM, M. SETBON, and A. J. VALLERON. "The rising impact of mathematical modelling in epidemiology: antibiotic resistance research as a case study." Epidemiology and Infection 136, no. 3 (September 4, 2007): 289–98. http://dx.doi.org/10.1017/s0950268807009442.

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SUMMARYMathematical modelling of infectious diseases has gradually become part of public health decision-making in recent years. However, the developing status of modelling in epidemiology and its relationship with other relevant scientific approaches have never been assessed quantitatively. Herein, using antibiotic resistance as a case study, 60 published models were analysed. Their interactions with other scientific fields are reported and their citation impact evaluated, as well as temporal trends. The yearly number of antibiotic resistance modelling publications increased significantly between 1990 and 2006. This rise cannot be explained by the surge of interest in resistance phenomena alone. Moreover, modelling articles are, on average, among the most frequently cited third of articles from the journal in which they were published. The results of this analysis, which might be applicable to other emerging public health problems, demonstrate the growing interest in mathematical modelling approaches to evaluate antibiotic resistance.

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Zwerling, Alice, Sourya Shrestha, and David W. Dowdy. "Mathematical Modelling and Tuberculosis: Advances in Diagnostics and Novel Therapies." Advances in Medicine 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/907267.

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As novel diagnostics, therapies, and algorithms are developed to improve case finding, diagnosis, and clinical management of patients with TB, policymakers must make difficult decisions and choose among multiple new technologies while operating under heavy resource constrained settings. Mathematical modelling can provide helpful insight by describing the types of interventions likely to maximize impact on the population level and highlighting those gaps in our current knowledge that are most important for making such assessments. This review discusses the major contributions of TB transmission models in general, namely, the ability to improve our understanding of the epidemiology of TB. We focus particularly on those elements that are important to appropriately understand the role of TB diagnosis and treatment (i.e., what elements of better diagnosis or treatment are likely to have greatest population-level impact) and yet remain poorly understood at present. It is essential for modellers, decision-makers, and epidemiologists alike to recognize these outstanding gaps in knowledge and understand their potential influence on model projections that may guide critical policy choices (e.g., investment and scale-up decisions).

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ACEDO, L., J. DÍEZ-DOMINGO, J. A. MORAÑO, and R. J. VILLANUEVA. "Mathematical modelling of respiratory syncytial virus (RSV): vaccination strategies and budget applications." Epidemiology and Infection 138, no. 6 (December 15, 2009): 853–60. http://dx.doi.org/10.1017/s0950268809991373.

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SUMMARYWe propose an age-structured mathematical model for respiratory syncytial virus in which children aged <1 year are especially considered. Real data on hospitalized children in the Spanish region of Valencia were used in order to determine some seasonal parameters of the model. Weekly predictions of the number of children aged <1 year that will be hospitalized in the following years in Valencia are presented using this model. Results are applied to estimate the regional cost of paediatric hospitalizations and to perform a cost-effectiveness analysis of possible vaccination strategies.

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Mulenga, Justina. "Mathematical Modelling of Epidemiology of Malaria: A Case Study of Luapula Province of Zambia." American Journal of Applied Mathematics 4, no. 6 (2016): 289. http://dx.doi.org/10.11648/j.ajam.20160406.15.

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Coen, PG, K. Cartwright, and J. Stuart. "Mathematical modelling of infection and disease due to Neisseria meningitidis and Neisseria lactamica." International Journal of Epidemiology 29, no. 1 (February 2000): 180–88. http://dx.doi.org/10.1093/ije/29.1.180.

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GAYTHORPE, K. A. M., C. L. TROTTER, B. LOPMAN, M. STEELE, and A. J. K. CONLAN. "Norovirus transmission dynamics: a modelling review." Epidemiology and Infection 146, no. 2 (December 22, 2017): 147–58. http://dx.doi.org/10.1017/s0950268817002692.

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SUMMARYNorovirus is one of the leading causes of viral gastroenteritis worldwide and responsible for substantial morbidity, mortality and healthcare costs. To further understanding of the epidemiology and control of norovirus, there has been much recent interest in describing the transmission dynamics of norovirus through mathematical models. In this study, we review the current modelling approaches for norovirus transmission. We examine the data and methods used to estimate these models that vary structurally and parametrically between different epidemiological contexts. Many of the existing studies at population level have focused on the same case notification dataset, whereas models from outbreak settings are highly specific and difficult to generalise. In this review, we explore the consistency in the description of norovirus transmission dynamics and the robustness of parameter estimates between studies. In particular, we find that there is considerable variability in estimates of key parameters such as the basic reproduction number, which may mean that the effort required to control norovirus at the population level may currently be underestimated.

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MASSIN, L., J. LEGRAND, A. J. VALLERON, and A. FLAHAULT. "Modelling outbreak control for pneumonic plague." Epidemiology and Infection 135, no. 5 (November 23, 2006): 733–39. http://dx.doi.org/10.1017/s0950268806007345.

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SUMMARYAlthough pneumonic plague is listed by the Centers of Disease Control in the leading ‘critical biological agents’, very few studies exist on this subject. In this study, a mathematical compartment model was used to describe the geographical and temporal spread of an epidemic of pneumonic plague following its use as a biological weapon. Univariate and multivariate analyses were performed in order to assess the key parameters for the control of an outbreak in France. If interventions were taken 10 days after an attack, a reference scenario of 1000 index cases in Paris would lead to 2500 deaths. The results of the study indicate that the rapidity of onset of interventions has the largest effect on the final size of the epidemic, followed by wearing masks, treating contacts preventively and quarantine. Limiting inter-regional mixing does little to reduce casualties, although it does confine them to a single region.

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Lu, Xiaoshu, and Esa-Pekka Takala. "A novel mathematical approach for modelling time-dependent musculoskeletal outcomes for office staff." Statistics in Medicine 27, no. 22 (September 30, 2008): 4549–68. http://dx.doi.org/10.1002/sim.3291.

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AZEVEDO, R. S., and M. AMAKU. "Modelling immunization strategies with cytomegalovirus vaccine candidates." Epidemiology and Infection 139, no. 12 (March 14, 2011): 1818–26. http://dx.doi.org/10.1017/s0950268811000343.

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SUMMARYIn order to analyse the impact of vaccination against cytomegalovirus (CMV) on congenital infection incidence using current vaccines tested in phase II clinical trials, we simulated different scenarios by mathematical modelling, departing from the current vaccine characteristics, varying age at vaccination, immunity waning, vaccine efficacy and mixing patterns. Our results indicated that the optimal age for a single vaccination interval is from 2 to 6 months if there is no immunity waning. Congenital infection may increase if vaccine-induced immunity wanes before 20 years. Congenital disease should increase further when the mixing pattern includes transmission among children with a short duration of protection vaccine. Thus, the best vaccination strategy is a combined schedule: before age 1 year plus a second dose at 10–11 years. For CMV vaccines with low efficacy, such as the current ones, universal vaccination against CMV should be considered for infants and teenagers.

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MORGAN-CAPNER, PETER. "12. Mathematical modelling: a key to control of infectious diseases in man and animals McLean AR, Anderson RM. Epidemiol Infect 1988; 100: 419–442." Epidemiology and Infection 133, S1 (October 2005): S41—S43. http://dx.doi.org/10.1017/s0950268805004322.

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Predicting the impact of infectious diseases on the well-being of the community is a cornerstone of identifying effective prevention, control and support. One only has to reflect on the last few years in the United Kingdom to see the impact mathematical modelling has had on public and government, with controversy around the likely numbers of sufferers from new-variant Creutzfeld–Jakob disease, human immunodeficiency virus, and continuing debate as to whether to use vaccine to support control of foot-and-mouth disease. Over the last 20–25 years, Epidemiology and Infection, and before it the Journal of Hygiene, have published many of the sentinel papers in the mathematical modelling of infectious disease, both in humans and animals. The discipline has advanced from relatively simple analyses to the most complex assessments whose underlying mathematics and statistics almost certainly exceed the comprehension of all but a few microbiologists and public health specialists. The depth of the analysis does not obscure the key messages, however, for the epidemiology of infectious disease and its control, and a Special Article in the journal in 1988 overviewed its contribution [1].

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LIU, W. C., C. JENKINS, D. J. SHAW, L. MATTHEWS, M. C. PEARCE, J. C. LOW, G. J. GUNN, H. R. SMITH, G. FRANKEL, and M. E. J. WOOLHOUSE. "Modelling the epidemiology of Verocytotoxin-producing Escherichia coli serogroups in young calves." Epidemiology and Infection 133, no. 3 (February 4, 2005): 449–58. http://dx.doi.org/10.1017/s0950268804003644.

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We investigate the epidemiology of 12 Verocytotoxin-producing Escherichia coli (VTEC) serogroups observed in a calf cohort on a Scottish beef farm. Fitting mathematical models to the observed time-course of infections reveals that there is significant calf-to-calf transmission of VTEC. Our models suggest that 40% of all detected infections are from calf-to-calf transmission and 60% from other sources. Variation in the rates at which infected animals recover from infection by different VTEC serogroups appears to be important. Two thirds of the observed VTEC serogroups are lost from infected calves within 1 day of infection, while the rest persist for more than 3 days. Our study has demonstrated that VTEC are transmissible between calves and are typically lost from infected animals in less than 1 week. We suggest that future field studies may wish to adopt a tighter sampling frame in order to detect all circulating VTEC serogroups in similar animal populations.

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BRISSON, M., W. J. EDMUNDS, N. J. GAY, B. LAW, and G. DE SERRES. "Modelling the impact of immunization on the epidemiology of varicella zoster virus." Epidemiology and Infection 125, no. 3 (December 2000): 651–69. http://dx.doi.org/10.1017/s0950268800004714.

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The objective of this study was to develop and apply a dynamic mathematical model of VZV transmission to predict the effect of different vaccination strategies on the age-specific incidence and outcome of infection. To do so a deterministic realistic age-structured model (RAS) was used which takes account of the increased potential for transmission within school aged groups. Various vaccine efficacy scenarios, vaccine coverages and vaccination strategies were investigated and a sensitivity analysis of varicella incidence predictions to important parameters was performed. The model predicts that the overall (natural and breakthrough) incidence and morbidity of varicella would likely be reduced by mass vaccination of 12-month-old children. Furthermore, adding a catch-up campaign in the first year for 1–11 year olds seems to be the most effective strategy to reduce both varicella incidence and morbidity (in the short and long term), though with the possible detrimental effect of increasing the incidence of zoster.

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Lampl, Michelle. "Perspectives on modelling human growth: Mathematical models and growth biology." Annals of Human Biology 39, no. 5 (July 27, 2012): 342–51. http://dx.doi.org/10.3109/03014460.2012.704072.

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van Nes, A. "Epidemiology: Mathematical modelling of pseudorabies virus (Syn. Aujeszky's disease virus) outbreaks aids eradication programmes: A review." Veterinary Quarterly 23, no. 1 (January 2001): 21–26. http://dx.doi.org/10.1080/01652176.2001.9695070.

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KARHUNEN, M., T. LEINO, H. SALO, I. DAVIDKIN, T. KILPI, and K. AURANEN. "Modelling the impact of varicella vaccination on varicella and zoster." Epidemiology and Infection 138, no. 4 (October 2, 2009): 469–81. http://dx.doi.org/10.1017/s0950268809990768.

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SUMMARYIt has been suggested that the incidence of herpes zoster may increase due to lack of natural boosting under large-scale vaccination with the varicella vaccine. To study the possibility and magnitude of such negative consequences of mass vaccination, we built a mathematical model of varicella and zoster epidemiology in the Finnish population. The model was based on serological data on varicella infection, case-notification data on zoster, and new knowledge about close contacts relevant to transmission of infection. According to the analysis, a childhood programme against varicella will increase the incidence of zoster by one to more than two thirds in the next 50 years. This will be due to increase in case numbers in the ⩾35 years age groups. However, high vaccine coverage and a two-dose programme will be very effective in stopping varicella transmission in the population.

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Ghosh, A. "Dynamics of Japanese encephalitis - A study in mathematical epidemiology." Mathematical Medicine and Biology 16, no. 1 (March 1, 1999): 1–27. http://dx.doi.org/10.1093/imammb/16.1.1.

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Unwin, H. Juliette T., Isobel Routledge, Seth Flaxman, Marian-Andrei Rizoiu, Shengjie Lai, Justin Cohen, Daniel J. Weiss, Swapnil Mishra, and Samir Bhatt. "Using Hawkes Processes to model imported and local malaria cases in near-elimination settings." PLOS Computational Biology 17, no. 4 (April 1, 2021): e1008830. http://dx.doi.org/10.1371/journal.pcbi.1008830.

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Developing new methods for modelling infectious diseases outbreaks is important for monitoring transmission and developing policy. In this paper we propose using semi-mechanistic Hawkes Processes for modelling malaria transmission in near-elimination settings. Hawkes Processes are well founded mathematical methods that enable us to combine the benefits of both statistical and mechanistic models to recreate and forecast disease transmission beyond just malaria outbreak scenarios. These methods have been successfully used in numerous applications such as social media and earthquake modelling, but are not yet widespread in epidemiology. By using domain-specific knowledge, we can both recreate transmission curves for malaria in China and Eswatini and disentangle the proportion of cases which are imported from those that are community based.

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Hou, Jiawen, Jie Hong, Boyun Ji, Bowen Dong, Yue Chen, Michael P. Ward, Wei Tu, et al. "Changed transmission epidemiology of COVID-19 at early stage: A nationwide population-based piecewise mathematical modelling study." Travel Medicine and Infectious Disease 39 (January 2021): 101918. http://dx.doi.org/10.1016/j.tmaid.2020.101918.

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Zheng, Qinyue, Xinwei Wang, Chunbing Bao, Zhongren Ma, and Qiuwei Pan. "Mathematical modelling and projecting the second wave of COVID-19 pandemic in Europe." Journal of Epidemiology and Community Health 75, no. 6 (February 16, 2021): 601–3. http://dx.doi.org/10.1136/jech-2020-215400.

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BASU, S., and A. P. GALVANI. "The transmission and control of XDR TB in South Africa: an operations research and mathematical modelling approach." Epidemiology and Infection 136, no. 12 (July 7, 2008): 1585–98. http://dx.doi.org/10.1017/s0950268808000964.

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SUMMARYExtensively drug-resistant tuberculosis (XDR TB) has emerged as a threat to TB control efforts in several high-burden areas, generating international concern. XDR TB is now found in every region of the world, but appears most worrisome in the context of HIV and in resource-limited settings with congregate hospital wards. Here, we examine the emergence and transmission dynamics of the disease, incorporating the mathematical modelling literature related to airborne infection and epidemiological studies related to the operations of TB control programmes in resource-limited settings. We find that while XDR TB may present many challenges in the setting of resource constraints, the central problems highlighted by the emergence of XDR TB are those that have plagued TB programmes for years. These include a slow rate of case detection that permits prolonged infectiousness, the threat of airborne infection in enclosed spaces, the problem of inadequate treatment delivery and treatment completion, and the need to develop health systems that can address the combination of TB and poverty. Mathematical models of TB transmission shed light on the idea that community-based therapy and rapid detection systems may be beneficial in resource-limited settings, while congregate hospital wards are sites for major structural reform.

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Glagolev, Mikhail V., Aleksandr F. Sabrekov, and Vladimir M. Goncharov. "Delay differential equations as a tool for mathematical modelling of population dynamic." Environmental Dynamics and Global Climate Change 9, no. 2 (November 27, 2018): 40–63. http://dx.doi.org/10.17816/edgcc10483.

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The manuscript constitutes a lecture from a course “Mathematical modelling of biological processes”, adapted to the format of the journal paper. This course of lectures is held by one of authors in Ugra State University. Delay differential equations are widely used in different ecological and biological problems. It has to do with the fact that delay differential equations are able to take into account that different biological processes depend not only on the state of the system at the moment but on the state of the system in previous moments too. The most popular case of using delay differential equations in biology is modelling in population ecology (including the modelling of several interacting populations dynamic, for example, in predator-prey system). Also delay differential equations are considered in demography, immunology, epidemiology, molecular biology (to provide mathematical description of regulatory mechanisms in a cell functioning and division), physiology as well as for modelling certain important production processes (for example, in agriculture). In the beginning of the paper as introduction some basic concepts of differential difference equation theory (delay differential equations are specific type of differential difference equations) is considered and their classification is presented. Then it is discussed in more detail how such an important equations of population dynamic as Maltus equation and logistic (Verhulst-Pearl) equation are transformed into corresponsive delay differential equations – Goudriaan-Roermund and Hutchinson. Then several discussion questions on using of a delay differential equations in biological models are considered. It is noted that in a certain cases using of a delay differential equations lead to an incorrect behavior from the point of view of common sense. Namely solution of Goudriaan-Roermund equation with harvesting, stopped when all species were harvested, shows that spontaneous generation takes place in the system. This incorrect interpretation has to do with the fact that delay differential equations are used to simplify considered models (that are usually are systems of ordinary differential equations). Using of integro-differential equations could be more appropriate because in these equations background could be taken into account in a more natural way. It is shown that Hutchinson equation can be obtained by simplification of Volterra integral equation with a help of Diraq delta function. Finally, a few questions of analytical and numerical solution of delay differential equations are discussed.

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Callan, Torrington, and Stephen Woodcock. "Stochastic modelling of chlamydial infections." ANZIAM Journal 61 (July 6, 2020): C89—C103. http://dx.doi.org/10.21914/anziamj.v61i0.15159.

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Chlamydia trachomatis is a bacterial pathogen that can cause serious reproductive harm. We describe a class of stochastic branching processes and their application in modelling the growth of an infection by Chlamydia. Using simulations we show that the model can reproduce biological phenomena of interest, and we show the variability in outcomes of infections under the same parameter conditions. We further speculate how this model might be used to explain long-term adverse reproductive sequelae. References Y. M. AbdelRahman and R. J. Belland. The chlamydial developmental cycle. FEMS Microbio. Rev., 29(5):949–959, 2005. doi:10.1016/j.femsre.2005.03.002. T. E. Harris. Branching processes. Ann. Math. Stat., 19(4):474–494, 12 1948. doi:10.1214/aoms/1177730146. C. Jacob. Branching processes: Their role in epidemiology. Int. J. Env. Res. Public Health, 7(3):1186–1204, 2019. doi:10.3390/ijerph7031204. N. Low, M. Egger, J. A. C. Sterne, R. M. Harbord, F. Ibrahim, B. Lindblom, and B. Herrmann. Incidence of severe reproductive tract complications associated with diagnosed genital chlamydial infection: The Uppsala women's cohort study. Sexually Trans. Infect., 82(3):212–218, 2006. doi:10.1136/sti.2005.017186. D. Mallet, M. Bagher-Oskouei, A. Farr, D. Simpson, and K. Sutton. A mathematical model of chlamydial infection incorporating movement of chlamydial particles. Bull. Math. Bio., 75:2257–2270, 10 2013. doi:10.1007/s11538-013-9891-9. H. K. Maxion, W. Liu, M.-H. Chang, and K. A. Kelly. The infecting dose of chlamydia muridarum modulates the innate immune response and ascending infection. Infect. Immun., 72(11):6330–6340, 2004. doi:10.1128/IAI.72.11.6330-6340.2004. S. Menon, P. Timms, J. A. Allan, K. Alexander, L. Rombauts, P. Horner, M. Keltz, J. Hocking, and W. M. Huston. Human and pathogen factors associated with chlamydia trachomatis-related infertility in women. Clinic. Microbio. Rev., 28(4):969–985, 2015. doi:10.1128/CMR.00035-15. D. P. Wilson. Mathematical modelling of chlamydia. In J. Crawford and A. J. Roberts, editors, Proc. of 11th Computational Techniques and Applications Conference CTAC-2003, ANZIAM J., volume 45, pages C201–C214, 2004. doi:10.21914/anziamj.v45i0.883. D. P. Wilson and D. L. S. McElwain. A model of neutralization of chlamydia trachomatis based on antibody and host cell aggregation on the elementary body surface. J. Theor. Bio., 226(3):321–330, 2004. doi:10.1016/j.jtbi.2003.09.010. D. P. Wilson, P. Timms, and D. L. S. McElwain. A mathematical model for the investigation of the Th1 immune response to chlamydia trachomatis. Math. Biosci., 182(1):27–44, 2003. doi:10.1016/S0025-5564(02)00180-3.

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Zhang, Hong, Wilson Osafo Apeanti, Liqiong Ma, Dianchen Lu, Xizhong Zheng, and Paul Georgescu. "Impact of social influence in English proficiency and performance in English examinations of mathematics students from a Sino-US undergraduate education program." Nonlinear Analysis: Modelling and Control 25, no. 6 (November 1, 2020): 938–57. http://dx.doi.org/10.15388/namc.2020.25.20556.

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This study examines the influence of certain academic and demographic variables upon the academic performance of Chinese students enrolled in a cooperative Bachelor’s degree program in Pure and Applied Mathematics. The program is English taught and jointly organised by Jiangsu University, China and Arcadia University, USA. Data from a sample of 166 students is processed using inferential and path analysis, as well as mathematical modelling. As evidenced by the inferential and path analysis, no steady improvement in the English proficiency of students has been observed, while the latter has been found to be influenced by gender and to strongly influence academic performance in Mathematics courses. The effects of negative social influences are assessed via a qualitative analysis of the mathematical model. Threshold quantities similar to the basic reproduction number of mathematical epidemiology have been found to be stability triggers. Possible interventional measures are discussed based on these findings.

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Hurford, Amy, Daniel Cownden, and Troy Day. "Next-generation tools for evolutionary invasion analyses." Journal of The Royal Society Interface 7, no. 45 (December 2, 2009): 561–71. http://dx.doi.org/10.1098/rsif.2009.0448.

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Evolutionary invasion analysis is a powerful technique for modelling in evolutionary biology. The general approach is to derive an expression for the growth rate of a mutant allele encoding some novel phenotype, and then to use this expression to predict long-term evolutionary outcomes. Mathematically, such ‘invasion fitness’ expressions are most often derived using standard linear stability analyses from dynamical systems theory. Interestingly, there is a mathematically equivalent approach to such stability analyses that is often employed in mathematical epidemiology, and that is based on so-called ‘next-generation’ matrices. Although this next-generation matrix approach has sometimes also been used in evolutionary invasion analyses, it is not yet common in this area despite the fact that it can sometimes greatly simplify calculations. The aim of this article is to bring the approach to a wider evolutionary audience in two ways. First, we review the next-generation matrix approach and provide a novel, and easily intuited, interpretation of how this approach relates to more standard techniques. Second, we illustrate next-generation methods in evolutionary invasion analysis through a series of informative examples. Although focusing primarily on evolutionary invasion analysis, we provide several insights that apply to biological modelling in general.

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Gubbins, Simon, Suzanne Touzeau, and Thomas J. Hagenaars. "The role of mathematical modelling in understanding the epidemiology and control of sheep transmissible spongiform encephalopathies: a review." Veterinary Research 41, no. 4 (February 23, 2010): 42. http://dx.doi.org/10.1051/vetres/2010014.

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Barnabas, Ruanne V., Päivi Laukkanen, Pentti Koskela, Osmo Kontula, Matti Lehtinen, and Geoff P. Garnett. "Epidemiology of HPV 16 and Cervical Cancer in Finland and the Potential Impact of Vaccination: Mathematical Modelling Analyses." PLoS Medicine 3, no. 5 (April 4, 2006): e138. http://dx.doi.org/10.1371/journal.pmed.0030138.

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Ortega-Quijano, Daniel, and Noe Ortega-Quijano. "Impact of age-selective vs non-selective physical-distancing measures against coronavirus disease 2019: a mathematical modelling study." International Journal of Epidemiology 50, no. 4 (March 12, 2021): 1114–23. http://dx.doi.org/10.1093/ije/dyab043.

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Abstract Background There is a real possibility of successive COVID-19-epidemic waves with devastating consequences. In this context, it has become mandatory to design age-selective measures aimed at achieving an optimal balance between protecting public health and maintaining a viable economic activity. Methods We programmed a Susceptible, Exposed, Infected, Removed (SEIR) model in order to introduce epidemiologically relevant age classes into the outbreak-dynamics analysis. The model was fitted to the official death toll and calculated age distribution of deaths in Wuhan using a constrained linear least-squares algorithm. Subsequently, we used synthetic location-specific and age-structured contact matrices to quantify the effect of age-selective interventions both on mortality and on economic activity in Wuhan. For this purpose, we simulated four different scenarios ranging from an absence of measures to age-selective interventions with stronger physical-distancing measures for older individuals. Results An age-selective strategy could reduce the death toll by >30% compared with the non-selective measures applied during Wuhan’s lockdown for the same workforce. Moreover, an alternative age-selective strategy could allow a 5-fold increase in the population working on site without a detrimental impact on the death toll compared with the Wuhan scenario. Conclusion Our results suggest that age-selective-distancing measures focused on the older population could have achieved a better balance between COVID-19 mortality and economic activity during the first COVID-19 outbreak in Wuhan. However, the implications of this need to be interpreted along with considerations of the practical feasibility and potential wider benefits and drawbacks of such a strategy.

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GAO, Z., H. F. GIDDING, J. G. WOOD, and C. R. MacINTYRE. "Modelling the impact of one-dose vs. two-dose vaccination regimens on the epidemiology of varicella zoster virus in Australia." Epidemiology and Infection 138, no. 4 (September 28, 2009): 457–68. http://dx.doi.org/10.1017/s0950268809990860.

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SUMMARYWe examined the impact of one-dose vs. two-dose vaccination strategies on the epidemiology of varicella zoster virus (VZV) in Australia, using a mathematical model. Strategies were assessed in terms of varicella (natural and breakthrough) and zoster incidence, morbidity, average age of infection and vaccine effectiveness (VE). Our modelling results suggest that compared to a one-dose vaccination strategy (Australia's current vaccination schedule), a two-dose strategy is expected to not only produce less natural varicella cases (5% vs. 13% of pre-vaccination state, respectively) but also considerably fewer breakthrough varicella cases (only 11·4% of one-dose strategy). Therefore a two-dose infant vaccination programme would be a better long-term strategy for Australia.

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Liao, Jian-Qin, Xiao-Bing Hu, Ming Wang, and Mark S. Leeson. "Epidemic Modelling by Ripple-Spreading Network and Genetic Algorithm." Mathematical Problems in Engineering 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/506240.

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Mathematical analysis and modelling is central to infectious disease epidemiology. This paper, inspired by the natural ripple-spreading phenomenon, proposes a novel ripple-spreading network model for the study of infectious disease transmission. The new epidemic model naturally has good potential for capturing many spatial and temporal features observed in the outbreak of plagues. In particular, using a stochastic ripple-spreading process simulates the effect of random contacts and movements of individuals on the probability of infection well, which is usually a challenging issue in epidemic modeling. Some ripple-spreading related parameters such as threshold and amplifying factor of nodes are ideal to describe the importance of individuals’ physical fitness and immunity. The new model is rich in parameters to incorporate many real factors such as public health service and policies, and it is highly flexible to modifications. A genetic algorithm is used to tune the parameters of the model by referring to historic data of an epidemic. The well-tuned model can then be used for analyzing and forecasting purposes. The effectiveness of the proposed method is illustrated by simulation results.

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VIET, A. F., C. FOURICHON, and H. SEEGERS. "Review and critical discussion of assumptions and modelling options to study the spread of the bovine viral diarrhoea virus (BVDV) within a cattle herd." Epidemiology and Infection 135, no. 5 (November 17, 2006): 706–21. http://dx.doi.org/10.1017/s095026880600745x.

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SUMMARYRelevance of epidemiological models depends on assumptions on the population structure and dynamics, on the biology of the host–parasite interaction, and on mathematical modelling. In this paper we reviewed published models of the bovine viral diarrhoea virus (BVDV) spread within a herd. Modelling options and assumptions on herd dynamics and BVDV transmission were discussed. A cattle herd is a population with a controlled size. Animals are separated into subgroups according to their age or their physiological status inducing heterogeneity of horizontal transmission. Complexity of models results from: (1) horizontal and vertical virus transmission, (2) birth of persistently infected animals, (3) excretion by transiently and persistently infected animals. Areas where there was a lack of knowledge were identified. Assumptions on the force of infection used to model the horizontal virus transmission were presented and discussed. We proposed possible ways of improving models (e.g. force of infection, validation) and essential model features for further BVDV models.

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Mastroeni, Pietro, and Omar Rossi. "Immunology, epidemiology and mathematical modelling towards a better understanding of invasive non-typhoidal Salmonella disease and rational vaccination approaches." Expert Review of Vaccines 15, no. 12 (May 27, 2016): 1545–55. http://dx.doi.org/10.1080/14760584.2016.1189330.

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Schmidt, Vanessa, Angelyn Lao, Katja Rateitschak, Olaf Wolkenhauer, and Thomas E. Willnow. "P2-451: Mathematical Modelling of APP Processing as influenced by SORLA." Alzheimer's & Dementia 6 (July 2010): e8-e8. http://dx.doi.org/10.1016/j.jalz.2010.08.025.

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Ciapponi, Agustín, Sacha Alexis Virgilio, Mabel Berrueta, Natalie Claire Soto, Álvaro Ciganda, Moisés Freddy Rojas Illanes, Briseida Rubio Martinez, et al. "Epidemiology of inflammatory bowel disease in Mexico and Colombia: Analysis of health databases, mathematical modelling and a case-series study." PLOS ONE 15, no. 1 (January 27, 2020): e0228256. http://dx.doi.org/10.1371/journal.pone.0228256.

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VOLKOVA, V. V., Z. LU, C. LANZAS, and Y. T. GROHN. "Evaluating targets for control of plasmid-mediated antimicrobial resistance in enteric commensals of beef cattle: a modelling approach." Epidemiology and Infection 141, no. 11 (January 23, 2013): 2294–312. http://dx.doi.org/10.1017/s0950268812002993.

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SUMMARYEnteric commensal bacteria of food animals may serve as a reservoir of genes encoding antimicrobial resistance (AMR). The genes are often plasmidic. Different aspects of bacterial ecology can be targeted by interventions to control plasmid-mediated AMR. The field efficacy of interventions remains unclear. We developed a deterministic mathematical model of commensalEscherichia coliin its animate and non-animate habitats within a beef feedlot's pen, with someE. colihaving plasmid-mediated resistance to the cephalosporin ceftiofur. We evaluated relative potential efficacy of within- or outside-host biological interventions delivered throughout rearing depending on the targeted parameter of bacterial ecology. Most instrumental in reducing the fraction of resistant entericE. coliat steer slaughter age were interventions acting on the entericE. coliand capable of either ‘plasmid curing’E. coli, or lowering maximumE. colinumbers or the rate of plasmid transfer in this habitat. Also efficient was to increase the regular replacement of entericE. coli. Lowering replication rate of resistantE. colialone was not an efficient intervention target.

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Bellomo, Nicola, Richard Bingham, Mark A. J. Chaplain, Giovanni Dosi, Guido Forni, Damian A. Knopoff, John Lowengrub, Reidun Twarock, and Maria Enrica Virgillito. "A multiscale model of virus pandemic: Heterogeneous interactive entities in a globally connected world." Mathematical Models and Methods in Applied Sciences 30, no. 08 (July 2020): 1591–651. http://dx.doi.org/10.1142/s0218202520500323.

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This paper is devoted to the multidisciplinary modelling of a pandemic initiated by an aggressive virus, specifically the so-called SARS–CoV–[Formula: see text] Severe Acute Respiratory Syndrome, corona virus n.[Formula: see text]. The study is developed within a multiscale framework accounting for the interaction of different spatial scales, from the small scale of the virus itself and cells, to the large scale of individuals and further up to the collective behaviour of populations. An interdisciplinary vision is developed thanks to the contributions of epidemiologists, immunologists and economists as well as those of mathematical modellers. The first part of the contents is devoted to understanding the complex features of the system and to the design of a modelling rationale. The modelling approach is treated in the second part of the paper by showing both how the virus propagates into infected individuals, successfully and not successfully recovered, and also the spatial patterns, which are subsequently studied by kinetic and lattice models. The third part reports the contribution of research in the fields of virology, epidemiology, immune competition, and economy focussed also on social behaviours. Finally, a critical analysis is proposed looking ahead to research perspectives.

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Mariën, Joachim, Benny Borremans, Fodé Kourouma, Jatta Baforday, Toni Rieger, Stephan Günther, N’Faly Magassouba, Herwig Leirs, and Elisabeth Fichet-Calvet. "Evaluation of rodent control to fight Lassa fever based on field data and mathematical modelling." Emerging Microbes & Infections 8, no. 1 (January 1, 2019): 640–49. http://dx.doi.org/10.1080/22221751.2019.1605846.

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Razali, K., J. Amin, GJ Dore, MG Law, and HCV Projections Working Group. "Modelling and calibration of the hepatitis C epidemic in Australia." Statistical Methods in Medical Research 18, no. 3 (November 26, 2008): 253–70. http://dx.doi.org/10.1177/0962280208094689.

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Hepatitis C virus (HCV) infection in Australia is predominantly transmitted through injecting drug use. A reduction in the heroin supply in Australia in late 2000 and early 2001 may have impacted the number of injecting drug users (IDUs) and the number of new hepatitis C infections. This paper updates estimates of HCV incidence between 1960 and 2005 and models long-term sequelae from infection. Outcomes among those with HCV were also recently assessed in a linkage study assessing cancer and causes of death following HCV diagnosis in New South Wales. Linkage study outcomes have been used here to calibrate modelled outcomes. Mathematical models were used to estimate HCV incidence among IDUs, migrants to Australia from high HCV-prevalence countries, and other HCV exposure groups. Recent trends in numbers of IDUs were based on indicators of injecting drug use. A natural history of HCV model was applied to estimate the prevalence of HCV in the population. Model predicted endpoints that were calibrated against the NSW linkage data over the period 1995—2002 were: (i) incident hepatocellular carcinoma (HCC); (ii) opioid overdose deaths; (iii) liver-related deaths; and (iv) all-cause mortality. Modelled estimates and the linkage data show reasonably good calibration for HCC cases and all-cause mortality. The estimated HCC incidence was increased from 70 cases in 1995 to 100 cases in 2002. All-cause mortality estimated at 1000 in 1995 increased to 1600 in 2002. Comparison of annual opioid deaths shows some agreement. However, the models underestimate the rate of increase observed between 1995 and 1999 and do not entirely capture the rapid decrease in overdose deaths from 2000 onwards. The linkage data showed a peak of overdose deaths at 430 in 1999 compared to 320 estimated by the models. Comparison of observed liver deaths with the modelled numbers showed poor agreement. A good agreement would require an increase in liver deaths from the assumed 2 to 5% per annum following cirrhosis in the models. Mathematical models suggest that HCV incidence decreased from a peak of 14,000 infections in 1999 to 9700 infections in 2005, largely attributable to a reduction in injecting drug use. The poor agreement between projected and linked liver deaths could reflect differing coding of causes of deaths, underestimates of the numbers of people with cirrhosis following HCV, or underestimates of rates of liver death following cirrhosis. The reasonably good agreement between most of the modelled estimates with observed linkage data provides some support for the assumptions used in the models.

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RÜEGG, S. R., D. HEINZMANN, A. D. BARBOUR, and P. R. TORGERSON. "Estimation of the transmission dynamics of Theileria equi and Babesia caballi in horses." Parasitology 135, no. 5 (February 27, 2008): 555–65. http://dx.doi.org/10.1017/s0031182008004204.

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SUMMARYFor the evaluation of the epidemiology of Theileria equi and Babesia caballi in a herd of 510 horses in SW Mongolia, several mathematical models of the transmission dynamics were constructed. Because the field data contain information on the presence of the parasite (determined by PCR) and the presence of antibodies (determined by IFAT), the models cater for maternal protection with antibodies, susceptible animals, infected animals and animals which have eliminated the parasite and also allow for age-dependent infection in susceptible animals. Maximum likelihood estimation procedures were used to estimate the model parameters and a Monte Carlo approach was applied to select the best fitting model. Overall, the results are in line with previous experimental work, and add evidence that the epidemiology of T. equi differs from that of Babesia spp. The presented modelling approach provides a useful tool for the investigation of some vector-borne diseases and the applied model selection procedure avoids asymptotical assumptions that may not be adequate for the analysis of epidemiological field data.

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MONTI, G. E., K. FRANKENA, and M. C. M. De JONG. "Transmission of bovine leukaemia virus within dairy herds by simulation modelling." Epidemiology and Infection 135, no. 5 (November 1, 2006): 722–32. http://dx.doi.org/10.1017/s0950268806007357.

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SUMMARYIn Argentina, bovine leukaemia virus (BLV) infection is common in dairy herds. The country currently has a National Voluntary Control Programme but relatively few farms have enrolled. However, there is increased interest from authorities and farmers to implement regional compulsory programmes but there is scarce quantitative information of the transmission of BLV in cattle herds. This information is a prerequisite to develop effective BLV control strategies. Mathematical modelling offers ways of integrating population-level knowledge and epidemiological data to predict the outcomes of intervention scenarios. The purpose of the current paper is to gain understanding about the dynamics of the transmission of BLV in dairy herds from Argentina by simulation and to compare various BLV transmission models and select the one that is most appropriate. The hypothetical herd is conceptually described in terms of BLV status as a population of individuals that are protected by maternal antibodies (M), that are susceptible (S), that are in the latent period (E) or that are infectious (I). BLV is spread by horizontal and vertical transmission. We used an age-structured population model and within-herd transmission was simulated by Monte Carlo techniques. The next-generation approach has been used for the systematic computation of the basic reproduction ratio (R0). Parameter values for disease transmission were derived from previously published data; rates of entry, exit or transition between age groups were calculated based on our previous study, observational data, expert opinions and literature. With these parameter values the probability of a minor outbreak was estimated to be 10%, the probability of extinction was estimated as <0·001% and the expected time to extinction as more than 80 years. The probability of a minor outbreak and changes in prevalence were different when the index case was an adult cow compared to introduction by a heifer. Prediction of prevalences from MSI models fit the data satisfactorily. R0 was estimated as 9·5. The sensitivity analysis on R0 showed that all measures directed to reduce the transmission rate are potentially effective given operational control measures. An important prediction of these models is that, even in a relatively small, closed dairy herd, the time-scale for a BLV outbreak may be as long as several years and within-herd control of BLV requires intensive efforts.

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Journal articles on the topic 'Mathematical modelling - Epidemiology'

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