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Journal articles on the topic 'Epidemiology – Mathematical models'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Lopatin, A. A., E. V. Kuklev, V. A. Safronov, A. S. Razdorsky, L. V. Samoilova, and V. P. Toporkov. "Verification of Mathematical Models of Plague." Problems of Particularly Dangerous Infections, no. 3(113) (June 20, 2012): 26–28. http://dx.doi.org/10.21055/0370-1069-2012-3-26-28.

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Mathematic modeling and prognostication of infectious diseases epidemic process is a promising trend of epidemiologic investigations. The complex of mathematic models (SEIRF type) of plague epidemic process was developed for this purpose by the Russian Research Anti-Plague Institute “Microbe” and laboratory of epidemiologic cybernetics of N.F.Gamaleya Institute for Epidemiology and Microbiology. The data on the plague outbreak in 1945 in the rural settlement Avan’ (Aral region of Kzyl-Orda district of Kazakh SSR) were used to test working efficiency of this complex. The data analysis permitted to obtain the starting and boundary conditions for epidemic process modeling. In the process of modeling the mathematical models of epidemic process of plague with various ways of infection transmission for each epidemic focus in regard with historical data were used. The data were processed by the analytical platform Deductor 5.1. Identified was strong positive correlation between estimated and historical data – r = +0,71. The results received testify that mathematic models are effective and give high degree of confidence. They can be used to receive quantitative characteristics of prognosis for plague epidemic process development with different transmission routes considering that anti-epidemic measures have been taken.

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2

Henson, Shandelle M., Fred Brauer, and Carlos Castillo-Chavez. "Mathematical Models in Population Biology and Epidemiology." American Mathematical Monthly 110, no. 3 (March 2003): 254. http://dx.doi.org/10.2307/3647954.

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3

Rosner, Bernard A., Graham A. Colditz, Penny M. Webb, and Susan E. Hankinson. "Mathematical Models of Ovarian Cancer Incidence." Epidemiology 16, no. 4 (July 2005): 508–15. http://dx.doi.org/10.1097/01.ede.0000164557.81694.63.

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4

BLOWER, SALLY, and GRAHAM MEDLEY. "Epidemiology, HIV and drugs: mathematical models and data." Addiction 87, no. 3 (March 1992): 371–79. http://dx.doi.org/10.1111/j.1360-0443.1992.tb01938.x.

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5

King, P. "Mathematical models in population biology and epidemiology [Book Reviews]." IEEE Engineering in Medicine and Biology Magazine 20, no. 4 (July 2001): 101. http://dx.doi.org/10.1109/memb.2001.940057.

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6

Naz, R., I. Naeem, and F. M. Mahomed. "A Partial Lagrangian Approach to Mathematical Models of Epidemiology." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/602915.

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This paper analyzes the first integrals and exact solutions of mathematical models of epidemiology via the partial Lagrangian approach by replacing the three first-order nonlinear ordinary differential equations by an equivalent system containing one second-order equation and a first-order equation. The partial Lagrangian approach is then utilized for the second-order ODE to construct the first integrals of the underlying system. We investigate the SIR and HIV models. We obtain two first integrals for the SIR model with and without demographic growth. For the HIV model without demography, five first integrals are established and two first integrals are deduced for the HIV model with demography. Then we utilize the derived first integrals to construct exact solutions to the models under investigation. The dynamic properties of these models are studied too. Numerical solutions are derived for SIR models by finite difference method and are compared with exact solutions.

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7

Rosenberg, Noah A. "Population models, mathematical epidemiology, and the COVID-19 pandemic." Theoretical Population Biology 137 (February 2021): 1. http://dx.doi.org/10.1016/j.tpb.2021.01.001.

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8

Chu, Kenneth C. "A nonmathematical view of mathematical models for cancer." Journal of Chronic Diseases 40 (January 1987): 163S—170S. http://dx.doi.org/10.1016/s0021-9681(87)80019-x.

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9

&NA;. "Biologically Based Mathematical Models of Lung Cancer Risk." Epidemiology 4, no. 3 (May 1993): 193–94. http://dx.doi.org/10.1097/00001648-199305000-00002.

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10

Tom, Eric, and Kevin A. Schulman. "Mathematical Models in Decision Analysis." Infection Control and Hospital Epidemiology 18, no. 1 (January 1997): 65–73. http://dx.doi.org/10.2307/30141966.

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11

Tom, Eric, and Kevin A. Schulman. "Mathematical Models in Decision Analysis." Infection Control and Hospital Epidemiology 18, no. 1 (January 1997): 65–73. http://dx.doi.org/10.1086/647503.

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12

Kraemer, Helena Chmura. "The Usefulness of Mathematical Models in Assessing Medical Tests." Epidemiology 21, no. 1 (January 2010): 139–41. http://dx.doi.org/10.1097/ede.0b013e3181c42d60.

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13

Garnett, G. P. "An introduction to mathematical models in sexually transmitted disease epidemiology." Sexually Transmitted Infections 78, no. 1 (February 1, 2002): 7–12. http://dx.doi.org/10.1136/sti.78.1.7.

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14

Martsenyuk, Vasiliy P., Igor E. Andrushchak, and Alexandra M. Kuchvara. "On Conditions of Asymptotic Stability in SIR-Models of Mathematical Epidemiology." Journal of Automation and Information Sciences 43, no. 12 (2011): 59–68. http://dx.doi.org/10.1615/jautomatinfscien.v43.i12.70.

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15

Cohen, Ted, Christopher Dye, Caroline Colijn, Brian Williams, and Megan Murray. "Mathematical models of the epidemiology and control of drug-resistant TB." Expert Review of Respiratory Medicine 3, no. 1 (February 2009): 67–79. http://dx.doi.org/10.1586/17476348.3.1.67.

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16

Dukic, Vanja, and David M. Bortz. "Uncertainty quantification using probabilistic numerics: application to models in mathematical epidemiology." Inverse Problems in Science and Engineering 26, no. 2 (April 6, 2017): 223–32. http://dx.doi.org/10.1080/17415977.2017.1312364.

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17

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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18

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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19

BOULT, C. "Forecasting the number of future disabled elderly using Markovian and mathematical models." Journal of Clinical Epidemiology 44, no. 9 (1991): 973–80. http://dx.doi.org/10.1016/0895-4356(91)90068-k.

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20

Zhang, X. S., and J. Holt. "Mathematical Models of Cross Protection in the Epidemiology of Plant-Virus Diseases." Phytopathology® 91, no. 10 (October 2001): 924–34. http://dx.doi.org/10.1094/phyto.2001.91.10.924.

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Mathematical models of plant-virus disease epidemics were developed where cross protection occurs between viruses or virus strains. Such cross protection can occur both naturally and through artificial intervention. Examples of diseases with continuous and discontinuous crop-host availability were considered: citrus tristeza and barley yellow dwarf, respectively. Analyses showed that, in a single host population without artificial intervention, the two categories of host plants, infected with a protecting virus alone and infected with a challenging virus, could not coexist in the long term. For disease systems with continuous host availability, the virus (strain) with the higher basic reproductive number (R0) always excluded the other eventually; whereas, for discontinuous systems, R0 is undefined and the virus (strain) with the larger natural transmission rate was the one that persisted in the model formulation. With a proportion of hosts artificially inoculated with a protecting mild virus, the disease caused by a virulent virus could be depressed or eliminated, depending on the proportion. Artificial inoculation may be constant or adjusted in response to changes in disease incidence. The importance of maintaining a constant level of managed cross protection even when the disease incidence dropped was illustrated. Investigations of both pathosystem types showed the same qualitative result: that managed cross protection need not be 100% to eliminate the virulent virus (strain). In the process of replacement of one virus (strain) by another over time, the strongest competition occurred when the incidence of both viruses or virus strains was similar. Discontinuous crop-host availability provided a greater opportunity for viruses or virus strains to replace each other than did the more stable continuous cropping system. The process by which one Barley yellow dwarf virus replaced another in New York State was illustrated.

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21

Coen, Pietro G. "How mathematical models have helped to improve understanding the epidemiology of infection." Early Human Development 83, no. 3 (March 2007): 141–48. http://dx.doi.org/10.1016/j.earlhumdev.2007.01.005.

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22

Jungck, John R., Holly Gaff, and Anton E. Weisstein. "Mathematical Manipulative Models: In Defense of “Beanbag Biology”." CBE—Life Sciences Education 9, no. 3 (September 2010): 201–11. http://dx.doi.org/10.1187/cbe.10-03-0040.

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Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process—1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets—we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project ( http://bioquest.org/esteem ) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount ). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.

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23

Barnes, Sean L., Parastu Kasaie, Deverick J. Anderson, and Michael Rubin. "Research Methods in Healthcare Epidemiology and Antimicrobial Stewardship—Mathematical Modeling." Infection Control & Hospital Epidemiology 37, no. 11 (August 8, 2016): 1265–71. http://dx.doi.org/10.1017/ice.2016.160.

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Mathematical modeling is a valuable methodology used to study healthcare epidemiology and antimicrobial stewardship, particularly when more traditional study approaches are infeasible, unethical, costly, or time consuming. We focus on 2 of the most common types of mathematical modeling, namely compartmental modeling and agent-based modeling, which provide important advantages—such as shorter developmental timelines and opportunities for extensive experimentation—over observational and experimental approaches. We summarize these advantages and disadvantages via specific examples and highlight recent advances in the methodology. A checklist is provided to serve as a guideline in the development of mathematical models in healthcare epidemiology and antimicrobial stewardship.Infect Control Hosp Epidemiol2016;1–7

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24

Perasso, Antoine. "An Introduction to The Basic Reproduction Number in Mathematical Epidemiology." ESAIM: Proceedings and Surveys 62 (2018): 123–38. http://dx.doi.org/10.1051/proc/201862123.

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This article introduces the notion of basic reproduction number R0 in mathematical epi-demiology. After an historic reminder describing the steps leading to the statement of its mathematical deﬁnition, we explain the next-generation matrix method allowing its calculation in the case of epidemic models described by ordinary diﬀerential equations (ODEs). The article then focuses, through four ODEs examples and an infection load structured PDE model, on the usefulness of the R0 to address biological as well mathematical issues.

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25

Becker, Nikolaus, and Werner Rittgen. "Some Mathematical Properties of Cumulative Damage Models Regarding Their Application in Cancer Epidemiology." Biometrical Journal 32, no. 1 (1990): 1–15. http://dx.doi.org/10.1002/bimj.4710320102.

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26

Anđelić, Nikola, Sandi Baressi Šegota, Ivan Lorencin, Vedran Mrzljak, and Zlatan Car. "Estimation of COVID-19 epidemic curves using genetic programming algorithm." Health Informatics Journal 27, no. 1 (January 2021): 146045822097672. http://dx.doi.org/10.1177/1460458220976728.

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This paper investigates the possibility of the implementation of Genetic Programming (GP) algorithm on a publicly available COVID-19 data set, in order to obtain mathematical models which could be used for estimation of confirmed, deceased, and recovered cases and the estimation of epidemiology curve for specific countries, with a high number of cases, such as China, Italy, Spain, and USA and as well as on the global scale. The conducted investigation shows that the best mathematical models produced for estimating confirmed and deceased cases achieved R2 scores of 0.999, while the models developed for estimation of recovered cases achieved the R2 score of 0.998. The equations generated for confirmed, deceased, and recovered cases were combined in order to estimate the epidemiology curve of specific countries and on the global scale. The estimated epidemiology curve for each country obtained from these equations is almost identical to the real data contained within the data set.

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27

Rao, Darcy White, Margo M. Wheatley, Steven M. Goodreau, and Eva A. Enns. "Partnership dynamics in mathematical models and implications for representation of sexually transmitted infections: a review." Annals of Epidemiology 59 (July 2021): 72–80. http://dx.doi.org/10.1016/j.annepidem.2021.04.012.

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28

Ellis, Alexandra G., Rowan Iskandar, Christopher H. Schmid, John B. Wong, and Thomas A. Trikalinos. "Active learning for efficiently training emulators of computationally expensive mathematical models." Statistics in Medicine 39, no. 25 (August 11, 2020): 3521–48. http://dx.doi.org/10.1002/sim.8679.

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29

Mauro, F., G. Arcangeli, L. DʼAngelo, C. Marino, and M. Benassi. "Mathematical Models of Cell Survival After Ionizing Radiation." Health Physics 57 (July 1989): 355–61. http://dx.doi.org/10.1097/00004032-198907001-00050.

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30

Ledford, A. W., and T. J. Cole. "Mathematical models of growth in stature throughout childhood." Annals of Human Biology 25, no. 2 (January 1998): 101–15. http://dx.doi.org/10.1080/03014469800005482.

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31

Hashem, H. H. G., and H. M. H. Alsehail. "QUALITATIVE ASPECTS OF THE FRACTIONAL AIR-BORNE DISEASES MODEL WITH MITTAGE-LEFFLER KERNEL." Advances in Mathematics: Scientific Journal 10, no. 5 (May 4, 2021): 2335–49. http://dx.doi.org/10.37418/amsj.10.5.4.

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Mathematical models are used to describe transmission and propagation of diseases which have gained momentum over the last hundred years. Formulated mathematical models are currently applied to understand the epidemiology of various diseases including viral diseases viz Influenza, SARS, measles, etc. In this paper, we shall introduce the fractional air-borne diseases model with Mittage-Leffler kernel and prove some qualitative properties of the fractional the air-borne diseases model with Mittage-Leffler kernel and Ulam-Hyers stability.

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32

Akpa, Onoja Matthew, and Benjamin Agboola Oyejola. "Modeling the Transmission Dynamics of HIV/AIDS epidemics: an introduction and a review." Journal of Infection in Developing Countries 4, no. 10 (June 17, 2010): 597–608. http://dx.doi.org/10.3855/jidc.542.

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Introduction: One of the greatest causes of morbidity and mortality in the Sub-Saharan Africa, particularly among young adults, is HIV/AIDS. Many mathematical models have been suggested for describing the epidemiology as well as the epidemiological consequences of the epidemic. A review of some these models would aid researchers in applying them to better understand and control the incidence and distribution of the disease in their countries. Methodology: This study reviews some of the models proposed by various authors for describing the epidemiology as well as the epidemiological consequences of the HIV/AIDS epidemic and how some of them could be modified to suit the situations in other countries. We also discuss the limitations and the place of such models in the fight against the HIV epidemic. Results: A clear explanation of the premises and assumptions on which the models were based was reached by reviewing the models across different scenarios. Conclusion: Mathematical models have been very useful in HIV research, particularly for empirical studies on people living with HIV/AIDS (PLWHA). These models make predictions that generate questions of social and ethical interest.

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33

Pertsev, N. V., B. Yu Pichugin, and A. N. Pichugina. "Application of M-Matrices for the Study of Mathematical Models of Living Systems." Mathematical Biology and Bioinformatics 13, no. 1 (June 28, 2018): 208–37. http://dx.doi.org/10.17537/2018.13.208.

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Some results are presented of application of M-matrices to the study the stability problem of the equilibriums of differential equations used in models of living systems. The models studied are described by differential equations with several delays, including distributed delay, and by high-dimensional systems of differential equations. To study the stability of the equilibriums the linearization method is used. Emerging systems of linear differential equations have a specific structure of the right-hand parts, which allows to effectively use the properties of M-matrices. As examples, the results of studies of models arising in immunology, epidemiology and ecology are presented.

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34

Allard, Robert. "A Family of Mathematical Models to Describe the Risk of Infection by a Sexually Transmitted Agent." Epidemiology 1, no. 1 (January 1990): 30–33. http://dx.doi.org/10.1097/00001648-199001000-00007.

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35

Jeger, M. J., L. V. Madden, and F. van den Bosch. "Plant Virus Epidemiology: Applications and Prospects for Mathematical Modeling and Analysis to Improve Understanding and Disease Control." Plant Disease 102, no. 5 (May 2018): 837–54. http://dx.doi.org/10.1094/pdis-04-17-0612-fe.

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In recent years, mathematical modeling has increasingly been used to complement experimental and observational studies of biological phenomena across different levels of organization. In this article, we consider the contribution of mathematical models developed using a wide range of techniques and uses to the study of plant virus disease epidemics. Our emphasis is on the extent to which models have contributed to answering biological questions and indeed raised questions related to the epidemiology and ecology of plant viruses and the diseases caused. In some cases, models have led to direct applications in disease control, but arguably their impact is better judged through their influence in guiding research direction and improving understanding across the characteristic spatiotemporal scales of plant virus epidemics. We restrict this article to plant virus diseases for reasons of length and to maintain focus even though we recognize that modeling has played a major and perhaps greater part in the epidemiology of other plant pathogen taxa, including vector-borne bacteria and phytoplasmas.

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36

JOHNSON, L. F., R. E. DORRINGTON, and D. BRADSHAW. "The role of immunity in the epidemiology of gonorrhoea, chlamydial infection and trichomoniasis: insights from a mathematical model." Epidemiology and Infection 139, no. 12 (February 7, 2011): 1875–83. http://dx.doi.org/10.1017/s0950268811000045.

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SUMMARYMost mathematical models of sexually transmitted infections (STIs) assume that infected individuals become susceptible to re-infection immediately after recovery. This paper assesses whether extending the standard model to allow for temporary immunity after recovery improves the correspondence between observed and modelled levels of STI prevalence in South Africa, for gonorrhoea, chlamydial infection and trichomoniasis. Five different models of immunity and symptom resolution were defined, and each model fitted to South African STI prevalence data. The models were compared in terms of Bayes factors, which show that in the case of gonorrhoea and chlamydial infection, models that allow for immunity provide a significantly better fit to STI prevalence data than models that do not allow for immunity. For all three STIs, estimates of the impact of changes in STI treatment and sexual behaviour are significantly lower in models that allow for immunity. Mathematical models that do not allow for immunity could therefore overestimate the effectiveness of STI interventions.

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37

Frank, S. A. "Commentary: Mathematical models of cancer progression and epidemiology in the age of high throughput genomics." International Journal of Epidemiology 33, no. 6 (December 1, 2004): 1179–81. http://dx.doi.org/10.1093/ije/dyh222.

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38

DEL REY, A. MARTIN, and G. RODRIGUEZ SÁNCHEZ. "A DISCRETE MATHEMATICAL MODEL TO SIMULATE MALWARE SPREADING." International Journal of Modern Physics C 23, no. 10 (October 2012): 1250064. http://dx.doi.org/10.1142/s0129183112500647.

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With the advent and worldwide development of Internet, the study and control of malware spreading has become very important. In this sense, some mathematical models to simulate malware propagation have been proposed in the scientific literature, and usually they are based on differential equations exploiting the similarities with mathematical epidemiology. The great majority of these models study the behavior of a particular type of malware called computer worms; indeed, to the best of our knowledge, no model has been proposed to simulate the spreading of a computer virus (the traditional type of malware which differs from computer worms in several aspects). In this sense, the purpose of this work is to introduce a new mathematical model not based on continuous mathematics tools but on discrete ones, to analyze and study the epidemic behavior of computer virus. Specifically, cellular automata are used in order to design such model.

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39

Tasnim, Farah, and Md Kamrujjaman. "Dynamics of Spruce budworms and single species competition models with bifurcation analysis." Biometrics & Biostatistics International Journal 9, no. 6 (December 30, 2020): 217–22. http://dx.doi.org/10.15406/bbij.2020.09.00323.

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Choristoneura Fumiferana is perilous defoliators of forest lands in North America and many countries in Europe. In this study, we consider mathematical models in ecology, epidemiology and bifurcation studies; the spruce budworm model and the population model with harvesting. The study is designed based on bifurcation analysis. In particular, the results support population thresholds necessary for survival in certain cases. In a series of numerical examples, the outcomes are presented graphically to compare with bifurcation results.

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BEGUN, M., A. T. NEWALL, G. B. MARKS, and J. G. WOOD. "Revisiting Styblo's law: could mathematical models aid in estimating incidence from prevalence data?" Epidemiology and Infection 143, no. 7 (September 19, 2014): 1556–65. http://dx.doi.org/10.1017/s0950268814002428.

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SUMMARYEstimation of the true incidence of tuberculosis (TB) is challenging. The approach proposed by Styblo in 1985 is known to be inaccurate in the modern era where there is widespread availability of treatment for TB. This study re-examines the relationship of incidence to prevalence and other disease indicators that can be derived from surveys. We adapt a simple, previously published model that describes the epidemiology of TB in the presence of treatment to investigate a revised ratio-based approach to estimating incidence. We show that, following changes to treatment programmes for TB, the ratio of incidence to prevalence reaches an equilibrium value rapidly; long before other model indicators have stabilized. We also show that this ratio relies on few parameters but is strongly dependent on, and requires knowledge of, the efficacy and timeliness of treatment.

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ZHANG, HAO, ZHI-HONG JIANG, HUI WANG, FEI XIE, and CHAO CHEN. "ROLE OF EDGES IN COMPLEX NETWORK EPIDEMIOLOGY." International Journal of Modern Physics C 23, no. 09 (September 2012): 1250059. http://dx.doi.org/10.1142/s0129183112500593.

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In complex network epidemiology, diseases spread along contacting edges between individuals and different edges may play different roles in epidemic outbreaks. Quantifying the efficiency of edges is an important step towards arresting epidemics. In this paper, we study the efficiency of edges in general susceptible-infected-recovered models, and introduce the transmission capability to measure the efficiency of edges. Results show that deleting edges with the highest transmission capability will greatly decrease epidemics on scale-free networks. Basing on the message passing approach, we get exact mathematical solution on configuration model networks with edge deletion in the large size limit.

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42

Louca, Stilianos, Angela McLaughlin, Ailene MacPherson, Jeffrey B. Joy, and Matthew W. Pennell. "Fundamental Identifiability Limits in Molecular Epidemiology." Molecular Biology and Evolution 38, no. 9 (May 19, 2021): 4010–24. http://dx.doi.org/10.1093/molbev/msab149.

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Abstract Viral phylogenies provide crucial information on the spread of infectious diseases, and many studies fit mathematical models to phylogenetic data to estimate epidemiological parameters such as the effective reproduction ratio (Re) over time. Such phylodynamic inferences often complement or even substitute for conventional surveillance data, particularly when sampling is poor or delayed. It remains generally unknown, however, how robust phylodynamic epidemiological inferences are, especially when there is uncertainty regarding pathogen prevalence and sampling intensity. Here, we use recently developed mathematical techniques to fully characterize the information that can possibly be extracted from serially collected viral phylogenetic data, in the context of the commonly used birth-death-sampling model. We show that for any candidate epidemiological scenario, there exists a myriad of alternative, markedly different, and yet plausible “congruent” scenarios that cannot be distinguished using phylogenetic data alone, no matter how large the data set. In the absence of strong constraints or rate priors across the entire study period, neither maximum-likelihood fitting nor Bayesian inference can reliably reconstruct the true epidemiological dynamics from phylogenetic data alone; rather, estimators can only converge to the “congruence class” of the true dynamics. We propose concrete and feasible strategies for making more robust epidemiological inferences from viral phylogenetic data.

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43

Mishra, S., D. N. Fisman, and M. C. Boily. "The ABC of terms used in mathematical models of infectious diseases." Journal of Epidemiology & Community Health 65, no. 1 (October 21, 2010): 87–94. http://dx.doi.org/10.1136/jech.2009.097113.

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44

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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45

Faraone, Stephen V., John C. Simpson, and Walter A. Brown. "Mathematical models of complex dose-response relationships: Implications for experimental design in psychopharmacologic research." Statistics in Medicine 11, no. 5 (1992): 685–702. http://dx.doi.org/10.1002/sim.4780110512.

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Brown, David W., and Robert F. Anda. "Risk Factors for Disease Risk Factors and Attributable Risk Calculations: Are There Mathematical Limits?" Open Epidemiology Journal 3, no. 1 (January 7, 2010): 1–2. http://dx.doi.org/10.2174/1874297101003010001.

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The Adverse Childhood Experiences (ACE) Study, a collaborative effort between Kaiser Permanente (San Diego, CA) and the Centers for Disease Control and Prevention (Atlanta, GA), was designed to examine the long-term relationship between adverse childhood experiences (ACEs) and a variety of health behaviors and outcomes in adulthood [1]. ACEs include childhood emotional, physical, or sexual abuse and household dysfunction during childhood. The ACE Study, based on chronic disease prevention and control models, proposes that ACEs influence social, emotional, and cognitive impairments which in turn increase the probability of adopting health risk behaviors that have been documented to influence the subsequent development of disease, disability, social problems, and ultimately premature death. We use the ACE pyramid to depict this concept (see www.cdc.gov/nccdphp/ace/pyramid.htm).

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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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Лузянина, Т., and T. Luzyanina. "Численный бифуркационный анализ математических моделей с запаздыванием по времени с использованием пакета программ DDE-BIFTOOL." Mathematical Biology and Bioinformatics 12, no. 2 (December 13, 2017): 496–520. http://dx.doi.org/10.17537/2017.12.496.

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Mathematical modeling with delay differential equations (DDEs) is widely used for analysis and making predictions in various areas of the life sciences, e.g., population dynamics, epidemiology, immunology, physiology, neural networks. The time delays in these models take into account a dependence of the present state of the modeled system on its past history. The delay can be related to the duration of certain hidden processes like the stages of the life cycle, the time between infection of a cell and the production of new viruses, the duration of the infectious period, the immune period and so on. Due to an infinite-dimensional nature of DDEs, analytical studies of the corresponding mathematical models can only give limited results. Therefore, a numerical analysis is the major way to achieve both a qualitative and quantitative understanding of the model dynamics. A bifurcation analysis of a dynamical system is used to understand how solutions and their stability change as the parameters in the system vary. The package DDE-BIFTOOL is the first general-purpose package for bifurcation analysis of DDEs. This package can be used to compute and analyze the local stability of steady-state (equilibria) and periodic solutions of a given system as well as to study the dependence of these solutions on system parameters via continuation. Further one can compute and continue several local and global bifurcations: fold and Hopf bifurcations of steady states; folds, period doublings and torus bifurcations of periodic orbits; and connecting orbits between equilibria. In this paper we describe the structure of DDE-BIFTOOL, numerical methods implemented in the package and we illustrate the use of the package using a certain DDE system.

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Dye, C. "Leishmaniasis epidemiology: the theory catches up." Parasitology 104, S1 (June 1992): S7—S18. http://dx.doi.org/10.1017/s0031182000075211.

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SUMMARYUntil recently, almost all studies of leishmaniasis epidemiology were qualitative and descriptive. But now that the natural history of manyLeishmaniaparasites is quite well known, there is growing interest in quantitative analysis. In this paper I use mathematical models in conjunction with field data to try to answer a wider range of questions than has previously been possible with descriptive techniques, and to sharpen some of the outstanding questions for laboratory workers. This is done with reference to the persistence and resilience of canine leishmaniasis, the maintenance of virulence poly morphisms inLeishmaniapopulations, and the possible existence of cycles of human kala-azar. I conclude by posing a set of problems under three headings: diagnosis of infection (as distinct from disease), natural immunity toLeishmaniainfection in the vertebrate host, and genetic variation in the parasite population. Some solutions from the laboratory can be found in the companion paper by Black (1992).

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Melsew, Yayehirad A., Adeshina I. Adekunle, Allen C. Cheng, Emma S. McBryde, Romain Ragonnet, and James M. Trauer. "Heterogeneous infectiousness in mathematical models of tuberculosis: A systematic review." Epidemics 30 (March 2020): 100374. http://dx.doi.org/10.1016/j.epidem.2019.100374.

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