Journal articles: 'Basic reproduction ratio'

1

Adler, Frederick R. "The effects of averaging on the basic reproduction ratio." Mathematical Biosciences 111, no. 1 (September 1992): 89–98. http://dx.doi.org/10.1016/0025-5564(92)90080-g.

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Turner, Joanne, Roger G. Bowers, and Matthew Baylis. "Two-Host, Two-Vector Basic Reproduction Ratio (R0) for Bluetongue." PLoS ONE 8, no. 1 (January 8, 2013): e53128. http://dx.doi.org/10.1371/journal.pone.0053128.

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Massad, Eduardo, Francisco Antonio Bezerra Coutinho, Hyan Mo Yang, Heráclito Barbosa De Carvalho, Fábio Mesquita, and Marcelo Nascimento Burattini. "The basic reproduction ratio of HIV among intravenous drug users." Mathematical Biosciences 123, no. 2 (October 1994): 227–47. http://dx.doi.org/10.1016/0025-5564(94)90013-2.

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Li, Yunfei, Rui Xu, Zhe Li, and Shuxue Mao. "Global Dynamics of a Delayed HIV-1 Infection Model with CTL Immune Response." Discrete Dynamics in Nature and Society 2011 (2011): 1–13. http://dx.doi.org/10.1155/2011/673843.

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A delayed HIV-1 infection model with CTL immune response is investigated. By using suitable Lyapunov functionals, it is proved that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio for viral infection is less than or equal to unity; if the basic reproduction ratio for CTL immune response is less than or equal to unity and the basic reproduction ratio for viral infection is greater than unity, the CTL-inactivated infection equilibrium is globally asymptotically stable; if the basic reproduction ratio for CTL immune response is greater than unity, the CTL-activated infection equilibrium is globally asymptotically stable.

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Diekmann, O., K. Dietz, and J. A. P. Heesterbeek. "The basic reproduction ratio for sexually transmitted diseases: I. theoretical considerations." Mathematical Biosciences 107, no. 2 (December 1991): 325–39. http://dx.doi.org/10.1016/0025-5564(91)90012-8.

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Auger, Pierre, Ali Moussaoui, and Gauthier Sallet. "Basic Reproduction Ratio for a Fishery Model in a Patchy Environment." Acta Biotheoretica 60, no. 1-2 (March 15, 2012): 167–88. http://dx.doi.org/10.1007/s10441-012-9155-3.

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Wang, Haibin, and Rui Xu. "Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response." Discrete Dynamics in Nature and Society 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/169427.

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An HIV-1 infection model with latently infected cells and delayed immune response is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria is established and the existence of Hopf bifurcations at the CTL-activated infection equilibrium is also studied. By means of suitable Lyapunov functionals and LaSalle’s invariance principle, it is proved that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio for viral infectionR0≤1; if the basic reproduction ratio for viral infectionR0>1and the basic reproduction ratio for CTL immune responseR1≤1, the CTL-inactivated infection equilibrium is globally asymptotically stable. If the basic reproduction ratio for CTL immune responseR1>1, the global stability of the CTL-activated infection equilibrium is also derived when the time delayτ=0. Numerical simulations are carried out to illustrate the main results.

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Charles, S., S. Morand, J. L. Chassé, and P. Auger. "Host Patch Selection Induced by Parasitism: Basic Reproduction Ratio R0 and Optimal Virulence." Theoretical Population Biology 62, no. 2 (September 2002): 97–109. http://dx.doi.org/10.1006/tpbi.2002.1598.

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Хлынин, Э., E. Khlynin, А. Борисов, A. Borisov, В. Фатуев, and V. Fatuev. "Definition of Rational Structure of Financing of Process of Innovative Reproduction of the Basic Means of the Enterprise." Scientific Research and Development. Economics 6, no. 6 (January 23, 2019): 54–58. http://dx.doi.org/10.12737/article_5c1b6b094b3a02.03375703.

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The mechanism of formation of rational structure of financing of process of innovative reproduction of the basic means of the enterprise is developed, allowing to define the most expedient ratio between own and extra sources of financing of process of innovative reproduction of means of work which provides realization of effective financial activity of the enterprise. For this purpose, it is offered to form two clusters financial assets of the enterprise, one of which includes own sources of financing of process of innovative reproduction of the basic means, and another — extra sources of financing. The hypothesis of existence of the most preferable ratio between the sizes of the first and the second clusters is put forward and proved. For confirmation of the put forward hypothesis the nonlinear economic-mathematical model of criterion of formation of rational structure of financing of process of innovative reproduction of the basic means of the enterprise is developed. As the important parameters nonlinear economic-mathematical model of criterion it is offered to take into account not only size of own and extra financial assets, but also their cost.

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Tian, Xiaohong, and Rui Xu. "Global Stability of a Virus Infection Model with Time Delay and Absorption." Discrete Dynamics in Nature and Society 2011 (2011): 1–20. http://dx.doi.org/10.1155/2011/152415.

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In this paper, a virus infection model with time delay and absorption is studied. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the model is established. By using comparison arguments, it is shown that the infection free equilibrium is globally asymptotically stable when the basic reproduction ratio is less than unity. When the basic reproduction ratio is greater than unity, sufficient conditions are derived for the global stability of the virus-infected equilibrium. Numerical simulations are carried out to illustrate the theoretical results.

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Tian, Xiaohong, and Rui Xu. "Asymptotic Properties of a Hepatitis B Virus Infection Model with Time Delay." Discrete Dynamics in Nature and Society 2010 (2010): 1–21. http://dx.doi.org/10.1155/2010/182340.

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A hepatitis B virus infection model with time delay is discussed. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the model is studied. By using comparison arguments, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable. If the basic reproduction ratio is greater than unity, by means of an iteration technique, sufficient conditions are derived for the global asymptotic stability of the virus-infected equilibrium. Numerical simulations are carried out to illustrate the theoretical results.

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12

KLINKENBERG, D., J. DE BREE, H. LAEVENS, and M. C. M. DE JONG. "Within- and between-pen transmission of Classical Swine Fever Virus: a new method to estimate the basic reproduction ratio from transmission experiments." Epidemiology and Infection 128, no. 2 (April 2002): 293–99. http://dx.doi.org/10.1017/s0950268801006537.

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We present a method to estimate basic reproduction ratio R0 from transmission experiments. By using previously published data of experiments with Classical Swine Fever Virus more extensively, we obtained smaller confidence intervals than the martingale method used in the original papers. Moreover, our method allows simultaneous estimation of a reproduction ratio within pens R0w and a modified reproduction ratio between pens R′0b. Resulting estimates of R0w and R′0b for weaner pigs were 100 (95% CI 54·4–186) and 7·77 (4·68–12·9), respectively. For slaughter pigs they were 15·5 (6·20–38·7) and 3·39 (1·54–7·45), respectively. We believe, because of the smaller confidence intervals we were able to obtain, that the method presented here is better suited for use in future experiments.

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13

pada Das, Krishna, Prodip Roy, Subhabrata Ghosh, and Somnath Maiti. "External Source of Infection and Nutritional Efficiency Control Chaos in a Predator–Prey Model with Disease in the Predator." Biophysical Reviews and Letters 12, no. 02 (June 2017): 87–115. http://dx.doi.org/10.1142/s1793048017500059.

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This paper deals with an eco-epidemiological approach with disease circulating through the predator species. Disease circulation in the predator species can be possible by contact as well as by external sources. Here, we try to discuss the role of external source of infection along with nutritional value on system dynamics. To establish our findings, we have worked out the local and global stability analysis of the equilibrium points with Hopf bifurcation analysis associated with interior equilibrium point. The ecological consequence by ecological basic reproduction number as well as the disease basic reproduction number or basic reproductive ratio are obtained and we have analyzed the community structure of the particular system with the help of ecological and disease basic reproduction numbers. Further we pay attention to the chaotic dynamics which is produced by disease circulating in predator species by contact. Our numerical simulations reveal that eco-epidemiological system without external source of infection induced chaotic dynamics for increasing force of infection due to contact, whereas in the presence of external source of infection, it exhibits stable solution. It is also observed that nutritional value can prevent chaotic dynamics. We conclude that chaotic dynamics can be controlled by the external source of infection as well as nutritional value. We apply basic tools of nonlinear dynamics such as Poincare section and maximum Lyapunov exponent to investigate chaotic behavior of the system.

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Gao, Shu-Jing, Yu-Ying He, Yu-Jiang Liu, Guo-Jing Yang, and Xiao-Nong Zhou. "Field transmission intensity of Schistosoma japonicum measured by basic reproduction ratio from modified Barbour’s model." Parasites & Vectors 6, no. 1 (2013): 141. http://dx.doi.org/10.1186/1756-3305-6-141.

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15

Dietz, K., J. A. P. Heesterbeek, and D. W. Tudor. "The basic reproduction ratio for sexually transmitted diseases part 2. Effects of variable HIV infectivity." Mathematical Biosciences 117, no. 1-2 (September 1993): 35–47. http://dx.doi.org/10.1016/0025-5564(93)90016-4.

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16

XU, RUI. "GLOBAL DYNAMICS OF A DELAYED HIV-1 INFECTION MODEL WITH ABSORPTION AND SATURATION INFECTION." International Journal of Biomathematics 05, no. 03 (May 2012): 1260012. http://dx.doi.org/10.1142/s1793524512600121.

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In this paper, an HIV-1 infection model with absorption, saturation infection and an intracellular delay accounting for the time between viral entry into a target cell and the production of new virus particles is investigated. By analyzing the characteristic equations, the local stability of an infection-free equilibrium and a chronic-infection equilibrium of the model is established. By using suitable Lyapunov functionals and LaSalle's invariance principle, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable; and if the basic reproduction ratio is greater than unity, sufficient condition is derived for the global stability of the chronic-infection equilibrium.

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17

WALLINGA, J., D. LÉVY-BRUHL, N. J. GAY, and C. H. WACHMANN. "Estimation of measles reproduction ratios and prospects for elimination of measles by vaccination in some Western European countries." Epidemiology and Infection 127, no. 2 (October 2001): 281–95. http://dx.doi.org/10.1017/s095026880100601x.

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The objective of this study is to estimate the measles reproduction ratio for eight Western European vaccination programmes. Because many plausible age-structured transmission patterns result in a similar description of the observations, it is not possible to estimate a unique value of the reproduction ratio. A method is developed to estimate bounds and confidence intervals for plausible values of the reproduction ratios using maximum likelihood methods. Lower and upper bounds for plausible values of the basic reproduction ratio are estimated to be 7·17 (95% CI 7·14–7·20) and 45·41 (95% CI 9·77–49·57), corresponding to lower and upper bounds on critical vaccine coverage of 86·6% and 98·1%. Of the eight evaluated vaccination programmes, four have vaccine coverage below the lower bound and allow measles to persist, and four have vaccine coverage at the upper bound and may eventually eliminate measles.

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18

Puglisi, Lisa B., Giovanni S. P. Malloy, Tyler D. Harvey, Margaret L. Brandeau, and Emily A. Wang. "Estimation of COVID-19 basic reproduction ratio in a large urban jail in the United States." Annals of Epidemiology 53 (January 2021): 103–5. http://dx.doi.org/10.1016/j.annepidem.2020.09.002.

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19

Koeijer, Aline de, Hans Heesterbeek, Bram Schreuder, John Wilesmith, Herman van Roermund, Radulf Oberth�r, and Mart de Jong. "Quantifying BSE control by calculating the basic reproduction ratio R 0 for the infection among cattle." Journal of Mathematical Biology 48, no. 1 (January 1, 2004): 1–22. http://dx.doi.org/10.1007/s00285-003-0206-x.

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20

Yang, Hyun M. "Malaria transmission model for different levels of acquired immunity and temperature-dependent parameters (vector)." Revista de Saúde Pública 34, no. 3 (June 2000): 223–31. http://dx.doi.org/10.1590/s0034-89102000000300003.

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OBJECTIVE: Describe the overall transmission of malaria through a compartmental model, considering the human host and mosquito vector. METHODS: A mathematical model was developed based on the following parameters: human host immunity, assuming the existence of acquired immunity and immunological memory, which boosts the protective response upon reinfection; mosquito vector, taking into account that the average period of development from egg to adult mosquito and the extrinsic incubation period of parasites (transformation of infected but non-infectious mosquitoes into infectious mosquitoes) are dependent on the ambient temperature. RESULTS: The steady state equilibrium values obtained with the model allowed the calculation of the basic reproduction ratio in terms of the model's parameters. CONCLUSIONS: The model allowed the calculation of the basic reproduction ratio, one of the most important epidemiological variables.

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21

Traoré, Bakary, Boureima Sangaré, and Sado Traoré. "A Mathematical Model of Malaria Transmission with Structured Vector Population and Seasonality." Journal of Applied Mathematics 2017 (2017): 1–15. http://dx.doi.org/10.1155/2017/6754097.

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In this paper, we formulate a mathematical model of nonautonomous ordinary differential equations describing the dynamics of malaria transmission with age structure for the vector population. The biting rate of mosquitoes is considered as a positive periodic function which depends on climatic factors. The basic reproduction ratio of the model is obtained and we show that it is the threshold parameter between the extinction and the persistence of the disease. Thus, by applying the theorem of comparison and the theory of uniform persistence, we prove that if the basic reproduction ratio is less than 1, then the disease-free equilibrium is globally asymptotically stable and if it is greater than 1, then there exists at least one positive periodic solution. Finally, numerical simulations are carried out to illustrate our analytical results.

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22

HAGE, J. J., Y. H. SCHUKKEN, H. SCHOLS, M. A. MARIS-VELDHUIS, F. A. M. RIJSEWIJK, and C. H. L. KLAASSEN. "Transmission of bovine herpesvirus 1 within and between herds on an island with a BHV1 control programme." Epidemiology and Infection 130, no. 3 (June 2003): 541–52. http://dx.doi.org/10.1017/s0950268803008379.

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Transmission of bovine herpesvirus 1 (BHV1) within and between herds was studied on the island of Ameland, The Netherlands. There were 50 herds with 3300 head of cattle on the island. Herds were divided into three groups: (1) only containing seronegative cattle, (2) containing seronegative cattle and vaccinated seropositive cattle, and (3) containing only vaccinated cattle. All 23 herds in groups 1 and 2 were monitored. Three major outbreaks of BHV1 infections were observed due to the introduction of infectious cattle. Another major outbreak was most likely induced by reactivation of latent BHV1 in seropositive cattle. The basic reproduction ratio within these herds was estimated at least 4. Only one of these outbreaks led to three secondary outbreaks in susceptible herds in which all cattle were seronegative. These outbreaks were most likely due to respectively, direct animal contact, human transmission, and aerogenic transmission. The basic reproduction ratio between herds in this study was estimated to be 0·6.

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23

LEITE, MARIA BEATRIZ FERREIRA, RODNEY CARLOS BASSANEZI, and HYUN MO YANG. "The basic reproduction ratio for a model of directly transmitted infections considering the virus charge and the immunological response." IMA Journal of Mathematical Control and Information 17, no. 1 (2000): 15–31. http://dx.doi.org/10.1093/imamci/17.1.15.

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Leite, M. "The basic reproduction ratio for a model of directly transmitted infections considering the virus charge and the immunological response." Mathematical Medicine and Biology 17, no. 1 (March 1, 2000): 15–31. http://dx.doi.org/10.1093/imammb/17.1.15.

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25

Schwermer, Heinzpeter, Aline De Koeijer, Franz Brülisauer, and Dagmar Heim. "Comparison of the Historic Recycling Risk for BSE in Three European Countries by Calculating the Basic Reproduction Ratio R0." Risk Analysis 27, no. 5 (December 7, 2007): 1169–78. http://dx.doi.org/10.1111/j.1539-6924.2007.00952.x.

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26

Kretzschmar, Mirjam, Johannes C. Jager, Dick P. Reinking, Gertjan Van Zessen, and Henk Brouwers. "The basic reproduction ratio R0 for a sexually transmitted disease in pair formation model with two types of pairs." Mathematical Biosciences 124, no. 2 (December 1994): 181–205. http://dx.doi.org/10.1016/0025-5564(94)90042-6.

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27

Kadnikova, Irina, Natalya Aminina, and Yevgeniy Yakush. "Compound feed for industrial rearing of juveniles trepang Apostishopus japonicus (Selenka)." Fisheries 2021, no. 2 (April 9, 2021): 68–71. http://dx.doi.org/10.37663/0131-6184-2021-2-68-71.

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Application of enzymatic hydrolysis of macrophytes in the technology of feed for juvenile sea cucumber was justified. A basic recipe for compound feed based on fermented marine vegetable raw materials has been developed. Biological tests in the department for the reproduction of sea cucumber on the basis of the Pacific branch of the FSBSI VNIRO (TINRO) (Primorsky region, Popova island) confirmed the effectiveness of the use of fermented algae in the composition of feed. The average daily weight gains of sea cucumber individual increases, and the feed ratio decreases in comparison with feeds based on natural marine plants.

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LAEGREID, W. W., and J. E. KEEN. "Estimation of the basic reproduction ratio (R0) for Shiga toxin-producing Escherichia coli O157:H7 (STEC O157) in beef calves." Epidemiology and Infection 132, no. 2 (February 26, 2004): 291–95. http://dx.doi.org/10.1017/s0950268803001705.

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To understand the dynamics of transmission of Shiga toxin-producing Escherichia coli O157:H7 (STEC O157) in beef calves, serum samples were obtained from calves in a beef cow-calf herd approximately every 6 weeks from birth until weaning for three consecutive years. The presence of specific anti-O157 antibodies in these serum samples was detected using a blocking ELISA assay incorporating an anti-O157 monoclonal antibody. Using seroconversion data, the basic reproduction ratio (R0) was estimated for each of the three years as well as in aggregate using both deterministic and Martingale methods. R0 for STEC O157 infection in range beef calves by deterministic methods varied from 2·9–5·6, with an average of 4·3 (95% CI 2·8–5·9). Martingale estimates of R0 ranged from 3·5–7·4, or 5·3 (95% CI 3·9–6·6), for data from all three years. Given the above estimate of R0, it is predicted that 65–86% of a herd of calves must be effectively vaccinated, or must be rendered non-susceptible through other means, to eliminate STEC O157 infection from a herd.

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Kennedy, Karen J., Nathan S. Boyd, Vilis O. Nams, and A. Randall Olson. "The Impacts of Fertilizer and Hexazinone on Sheep Sorrel (Rumex acetosella) Growth Patterns in Lowbush Blueberry Fields." Weed Science 59, no. 3 (September 2011): 335–40. http://dx.doi.org/10.1614/ws-d-10-00088.1.

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Sheep sorrel is an invasive, creeping perennial weed of lowbush blueberry fields that decreases yields and hinders harvest. Much of the basic phenology of sheep sorrel in blueberry fields is unknown and not documented in peer-reviewed journals. Three levels of fertilizer (0, 20, and 40 kg N ha−1) and two levels of hexazinone (0 and 1.92 kg ai ha−1) were applied to three vegetative-year blueberry fields to determine their effects on root and shoot growth, biomass allocation, and seed production of sheep sorrel plants. Hexazinone efficacy varied widely between sites, but suppressed shoot biomass, achene number and weight, and reproductive biomass, as well as the reproductive : shoot biomass ratio. Fertilizer tended to increase achene number and increased sheep sorrel shoot biomass in the absence of hexazinone, but had no effect on achene weight, root biomass, or reproductive biomass. When fertilizer was applied, sheep sorrel allocated resources to sexual reproduction at the expense of vegetative growth.

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Okosun, Kazeem Oare, M. Mukamuri, and Daniel Oluwole Makinde. "Global stability analysis and control of leptospirosis." Open Mathematics 14, no. 1 (January 1, 2016): 567–85. http://dx.doi.org/10.1515/math-2016-0053.

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AbstractThe aim of this paper is to investigate the effectiveness and cost-effectiveness of leptospirosis control measures, preventive vaccination and treatment of infective humans that may curtail the disease transmission. For this, a mathematical model for the transmission dynamics of the disease that includes preventive, vaccination, treatment of infective vectors and humans control measures are considered. Firstly, the constant control parameters’ case is analyzed, also calculate the basic reproduction number and investigate the existence and stability of equilibria. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved when the basic reproduction number is less than unity. The model is found to exhibit the existence of multiple endemic equilibria. Furthermore, to assess the relative impact of each of the constant control parameters measures the sensitivity index of the basic reproductive number to the model’s parameters are calculated. In the time-dependent constant control case, Pontryagin’s Maximum Principle is used to derive necessary conditions for the optimal control of the disease. The cost-effectiveness analysis is carried out by first of all using ANOVA to check on the mean costs. Then followed by Incremental Cost-Effectiveness Ratio (ICER) for all the possible combinations of the disease control measures. Our results revealed that the most cost-effective strategy for the control of leptospirosis is the combination of the vaccination and treatment of infective livestocks. Though the combinations of all control measures is also effective, however, this strategy is not cost-effective and so too costly. Therefore, more efforts from policy makers on vaccination and treatment of infectives livestocks regime would go a long way to combat the disease epidemic.

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Jiang, Xin, Ran Zhang, and Zhikun She. "Dynamics of a diffusive predator–prey system with ratio-dependent functional response and time delay." International Journal of Biomathematics 13, no. 06 (July 27, 2020): 2050036. http://dx.doi.org/10.1142/s1793524520500369.

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In this paper, we investigate the qualitative behaviors of a predator–prey system with ratio-dependent function. The system accommodates the diffusion effect to model the migration of individuals and the time delay induced by reproduction. We start with some basic properties of the system. Then the sufficient condition independent of time delay and diffusion effect for global asymptotical stability of the boundary equilibrium is obtained by using the comparison principle. Afterwards, based on the LaSalle’s invariance principle and Lyapunov functional, we investigate the global attractiveness of the positive equilibrium, arriving at its global asymptotical stability. Further, Hopf bifurcation induced by time delay around the positive equilibrium is explored. Finally, numerical examples are listed to verify the corresponding analytical results.

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Degallier, Nicolas, Charly Favier, Jean-Philippe Boulanger, and Christophe Menkes. "Imported and autochthonous cases in the dynamics of dengue epidemics in Brazil." Revista de Saúde Pública 43, no. 1 (February 2009): 1–7. http://dx.doi.org/10.1590/s0034-89102009000100001.

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OBJECTIVE: To estimate the basic reproduction number (R0) of dengue fever including both imported and autochthonous cases. METHODS: The study was conducted based on epidemiological data of the 2003 dengue epidemic in Brasília, Brazil. The basic reproduction number is estimated from the epidemic curve, fitting linearly the increase of initial cases. Aiming at simulating an epidemic with both autochthonous and imported cases, a "susceptible-infectious-resistant" compartmental model was designed, in which the imported cases were considered as an external forcing. The ratio between R0 of imported versus autochthonous cases was used as an estimator of real R0. RESULTS: The comparison of both reproduction numbers (only autochthonous versus all cases) showed that considering all cases as autochthonous yielded a R0 above one, although the real R0 was below one. The same results were seen when the method was applied on simulated epidemics with fixed R0. This method was also compared to some previous proposed methods by other authors and showed that the latter underestimated R0 values. CONCLUSIONS: It was shown that the inclusion of both imported and autochthonous cases is crucial for the modeling of the epidemic dynamics, and thus provides critical information for decision makers in charge of prevention and control of this disease.

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TRAORÉ, BAKARY, OUSMANE KOUTOU, and BOUREIMA SANGARÉ. "GLOBAL DYNAMICS OF A SEASONAL MATHEMATICAL MODEL OF SCHISTOSOMIASIS TRANSMISSION WITH GENERAL INCIDENCE FUNCTION." Journal of Biological Systems 27, no. 01 (March 2019): 19–49. http://dx.doi.org/10.1142/s0218339019500025.

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In this paper, we investigate a nonautonomous and an autonomous model of schistosomiasis transmission with a general incidence function. Firstly, we formulate the nonautonomous model by taking into account the effect of climate change on the transmission. Through rigorous analysis via theories and methods of dynamical systems, we show that the nonautonomous model has a globally asymptotically stable disease-free periodic equilibrium when the associated basic reproduction ratio [Formula: see text] is less than unity. Otherwise, the system admits at least one positive periodic solutions if [Formula: see text] is greater than unity. Secondly, using the average of periodic functions, we further derive the autonomous model associated with the nonautonomous model. Therefore, we show that the disease-free equilibrium of the autonomous model is locally and globally asymptotically stable when the associated reproduction ratio [Formula: see text] is less than unity. When [Formula: see text] is greater than unity, the existence and global asymptotic stability of the endemic equilibrium is established under certain conditions. Finally, using linear and nonlinear specific incidence function, we perform some numerical simulations to illustrate our theoretical results.

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Gulenkin, V. M., F. I. Korennoy, A. K. Karaulov, and S. A. Dudnikov. "Cartographical analysis of African swine fever outbreaks in the territory of the Russian Federation and computer modeling of the basic reproduction ratio." Preventive Veterinary Medicine 102, no. 3 (December 2011): 167–74. http://dx.doi.org/10.1016/j.prevetmed.2011.07.004.

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35

Andreasen, G. K. "Double Mode Pulsating Stars and Opacity Changes." International Astronomical Union Colloquium 111 (1989): 248. http://dx.doi.org/10.1017/s0252921100011568.

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AbstractThe basic physical properties of double mode Cepheids and double mode δ Scuti stars are still highly controversial. Based on results of very recent opacity calculations a detailed consistent, possible solution of the problem of the nature of double mode variable stars has been developed. Extensive studies have been performed to establish the rules governing the morphology of the period ratio diagrams. An ideal reproduction of the period ratio data for both stellar types are obtained assuming an increase of the Cox-Steward opacity by a factor of about 2.5 in the temperature range from 1.5 X 105K to 8.0 X 105K. Consequences for the mass calibration of Petersen diagrams are evaluated.

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Nåsell, Ingemar. "The quasi-stationary distribution of the closed endemic sis model." Advances in Applied Probability 28, no. 3 (September 1996): 895–932. http://dx.doi.org/10.2307/1428186.

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The quasi-stationary distribution of the closed stochastic SIS model changes drastically as the basic reproduction ratio R0 passes the deterministic threshold value 1. Approximations are derived that describe these changes. The quasi-stationary distribution is approximated by a geometric distribution (discrete!) for R0 distinctly below 1 and by a normal distribution (continuous!) for R0 distinctly above 1. Uniformity of the approximation with respect to R0 allows one to study the transition between these two extreme distributions. We also study the time to extinction and the invasion and persistence thresholds of the model.

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Gashaw, Kassahun Workalemahu, Semu Mitiku Kassa, and Rachid Ouifki. "Climate-dependent malaria disease transmission model and its analysis." International Journal of Biomathematics 12, no. 08 (November 2019): 1950087. http://dx.doi.org/10.1142/s1793524519500876.

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Malaria infection continues to be a major problem in many parts of the world including Africa. Environmental variables are known to significantly affect the population dynamics and abundance of insects, major catalysts of vector-borne diseases, but the exact extent and consequences of this sensitivity are not yet well established. To assess the impact of the variability in temperature and rainfall on the transmission dynamics of malaria in a population, we propose a model consisting of a system of non-autonomous deterministic equations that incorporate the effect of both temperature and rainfall to the dispersion and mortality rate of adult mosquitoes. The model has been validated using epidemiological data collected from the western region of Ethiopia by considering the trends for the cases of malaria and the climate variation in the region. Further, a mathematical analysis is performed to assess the impact of temperature and rainfall change on the transmission dynamics of the model. The periodic variation of seasonal variables as well as the non-periodic variation due to the long-term climate variation have been incorporated and analyzed. In both periodic and non-periodic cases, it has been shown that the disease-free solution of the model is globally asymptotically stable when the basic reproduction ratio is less than unity in the periodic system and when the threshold function is less than unity in the non-periodic system. The disease is uniformly persistent when the basic reproduction ratio is greater than unity in the periodic system and when the threshold function is greater than unity in the non-periodic system.

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Nåsell, Ingemar. "The quasi-stationary distribution of the closed endemic sis model." Advances in Applied Probability 28, no. 03 (September 1996): 895–932. http://dx.doi.org/10.1017/s0001867800046541.

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The quasi-stationary distribution of the closed stochastic SIS model changes drastically as the basic reproduction ratio R 0 passes the deterministic threshold value 1. Approximations are derived that describe these changes. The quasi-stationary distribution is approximated by a geometric distribution (discrete!) for R 0 distinctly below 1 and by a normal distribution (continuous!) for R 0 distinctly above 1. Uniformity of the approximation with respect to R 0 allows one to study the transition between these two extreme distributions. We also study the time to extinction and the invasion and persistence thresholds of the model.

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Burattini, Marcelo N., Francisco A. B. Coutinho, Luis F. Lopez, and Eduardo Massad. "Modelling the Dynamics of Leishmaniasis Considering Human, Animal Host and Vector Populations." Journal of Biological Systems 06, no. 04 (December 1998): 337–56. http://dx.doi.org/10.1142/s0218339098000224.

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Some of the vector-borne infections with public health importance involve an animal reservoir. This work describes, through a compartimental model, the dynamics of leishmaniasis considering the interactions between the three populations involved, namely the sandfly, the domestic dog (as the principal intermediate host), and the human population. An expression for the Basic Reproduction Ratio (R0), which takes into account the time delay representing the extrinsic incubation period of the parasite in the vector, is presented. Numerical simulation, equilibrium and stability analysis provided insights into the transmission dynamics of the infection that can help in the design of control strategies.

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Amanati, Farida, and Muhammad Wakhid Musthofa. "Model Matematika Penyebaran Penyakit Demam Chikungunya Dengan Dua Jenis Nyamuk Ades (Aedes aegepty dan Aedes albopictus)." Jurnal Fourier 6, no. 2 (October 25, 2017): 45. http://dx.doi.org/10.14421/fourier.2017.62.45-54.

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Demam Chikungunya adalah penyakit yang disebabkan oleh nyamuk Aedes Aegepty dan Aedes Albopictus. Pengobatan untuk demam Chikungunya hanya dengan pengobatan secara simptomatik yaitu hanya mengurangi gejalanya saja seperti penurun panas, gejala nyeri sendi. Dalam tulisan ini mempelajari tentang model matematika penyebaran virus Chikungunya dengan dua jenis Nyamuk Aedes pembawa virus Chikungunya berdasarkan asumsi–asumsi yang telah dibuat. Dalam model ini dihasilkan titik ekulibrium bebas penyakit dan endenik, basic reproduction ratio, dan analisis kestabilan model di sekitar titik ekuilibrium. Kestabilan titik ekuilibrium dijelaskan secaraanalisis dengan menggunakan kriteria Routh-Hurwitz. Simulasi diberikan sebagai bentuk pendekatan model terhadap nilai–nilai parameter yang diberikan.

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Lambura, Aristide G., Gasper G. Mwanga, Livingstone Luboobi, and Dmitry Kuznetsov. "Mathematical Model for Optimal Control of Soil-Transmitted Helminth Infection." Computational and Mathematical Methods in Medicine 2020 (August 1, 2020): 1–15. http://dx.doi.org/10.1155/2020/6721919.

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In this paper, we study the dynamics of soil-transmitted helminth infection. We formulate and analyse a deterministic compartmental model using nonlinear differential equations. The basic reproduction number is obtained and both disease-free and endemic equilibrium points are shown to be asymptotically stable under given threshold conditions. The model may exhibit backward bifurcation for some parameter values, and the sensitivity indices of the basic reproduction number with respect to the parameters are determined. We extend the model to include control measures for eradication of the infection from the community. Pontryagian’s maximum principle is used to formulate the optimal control problem using three control strategies, namely, health education through provision of educational materials, educational messages to improve the awareness of the susceptible population, and treatment by mass drug administration that target the entire population(preschool- and school-aged children) and sanitation through provision of clean water and personal hygiene. Numerical simulations were done using MATLAB and graphical results are displayed. The cost effectiveness of the control measures were done using incremental cost-effective ratio, and results reveal that the combination of health education and sanitation is the best strategy to combat the helminth infection. Therefore, in order to completely eradicate soil-transmitted helminths, we advise investment efforts on health education and sanitation controls.

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Azrita, Azrita, Hafrijal Syandri, and Netti Aryani. "Reproductive characteristics of the giant gurami sago strain (Osphronemus goramy Lacepède, 1801): basic knowledge for a future hatchery development strategy." F1000Research 10 (September 15, 2021): 922. http://dx.doi.org/10.12688/f1000research.53760.1.

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Background: The giant gourami sago strain (Osphronemus goramy Lacepède) has been approved in 2018 as a candidate for freshwater aquaculture in Indonesia. However, information on the species’ reproduction is minimal. This study analyzed the reproductive characteristics of the gourami sago strain broodfish to provide basic knowledge for a future hatchery development strategy. Methods: A total of 10 female and 10 male mature gourami sago strain broodfish were measured for body weight and length, and were evaluated for their reproductive characteristics. Breeding fish were spawned naturally in a 2×1×0.6 m concrete pond with a male-female sex ratio of 1:1. Egg weight and diameter were measured in 25 eggs per female using, respectively, ACIS AD- 600i scales with 0.01 g accuracy, and a microscope (Labo model L-711) using Canon Digital Camera Software 3 . Semen was collected using plastic syringes in 3 mL aliquots, then placed in an insulated ice-cooled container, and analyzed within two hours of collection. Results: Average weights of female and male broodfish before spawning were 2180±159.78 g and 3060±134.99 g, respectively. The relative fecundity and egg diameter were 1029±36 eggs kg-1 and 2.42±0.05 mm, respectively. The hatching rate and embryo survival to an eyed-egg stage were respectively 76.40±2.27% and 94.76±0.42%. Sperm characteristics showed that volume was 0.60±0.12 ml kg-1 and percentage of motile sperm was 70.04±2.27%. Female broodfish weight after spawning was strongly correlated with the weight before spawned (r2 = 0.999) and absolute fecundity was also strongly correlated with female broodfish weight before spawning (r2= 0.921). Sperm concentration was moderately correlated with sperm motility (r2 = 0.556) and duration of sperm motility (r2 = 0.502). Conclusions: The gourami sago strain broodfish has suitable reproductive characteristics for the development of hatcheries. Successful natural spawning should be followed by larval weaning and feeding technology to increase growth and survival.

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Daley, Daryl J., and Randall J. Swift. "The size of a major epidemic of a vector-borne disease." Journal of Applied Probability 48, A (August 2011): 235–47. http://dx.doi.org/10.1017/s0021900200099253.

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Based on a simple model due to Dietz, it is shown that the size of a major epidemic of a vector-borne disease with basic reproduction ratio R 0>1 is dominated by the size of a standard SIR (susceptible–infected–removed) epidemic with direct host-to-host transmission of disease and the same R 0. Further bounds and numerical illustrations are provided, broadly spanning situations where the size of the epidemic is short of infecting almost all those susceptible. The total size is moderately sensitive to changes in the population parameters that contribute to R 0, so that the fluctuating behaviour in ‘annual’ epidemics is not surprising.

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Daley, Daryl J., and Randall J. Swift. "The size of a major epidemic of a vector-borne disease." Journal of Applied Probability 48, A (August 2011): 235–47. http://dx.doi.org/10.1239/jap/1318940468.

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Based on a simple model due to Dietz, it is shown that the size of a major epidemic of a vector-borne disease with basic reproduction ratio R0>1 is dominated by the size of a standard SIR (susceptible–infected–removed) epidemic with direct host-to-host transmission of disease and the same R0. Further bounds and numerical illustrations are provided, broadly spanning situations where the size of the epidemic is short of infecting almost all those susceptible. The total size is moderately sensitive to changes in the population parameters that contribute to R0, so that the fluctuating behaviour in ‘annual’ epidemics is not surprising.

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Trihandaru, Suryasatriya, Hanna Arini Parhusip, Bambang Susanto, and Yohanes Sardjono. "Simple Forward Finite Difference for Computing Reproduction Number of COVID-19 in Indonesia During the New Normal." JTAM (Jurnal Teori dan Aplikasi Matematika) 5, no. 1 (April 17, 2021): 88. http://dx.doi.org/10.31764/jtam.v5i1.3468.

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The research purpose shown in this article is describing the time dependent reproduction number of coronavirus called by COVID-19 in the new normal period for 3 types areas, i.e. small, medium and global areas by considering the number of people in these areas. It is known that in early June 2020, Indonesia has claimed to open activities during the pandemic with the new normal system. Though the number of COVID-19 cases is still increasing in almost infected areas, normal activities are coming back with healty care protocols where public areas are opened as usual with certain restrictions. In order to have observations of spreading impact of COVID-19, the basic reproduction number (Ro) i.e. the reproduction number (Ro) is the ratio between 2 parameters of SIR model where SIR stands for Susceptible individuals, Infected individuals, and Recovered individuals respectively. The reproduction numbers are computed as discrete values depending on time. The used research method is finite difference scheme for computing rate of change parameters in SIR models based on the COVID-19 cases in Indonesia (global area), Jakarta (medium area) and Salatiga (small area) by considering the number of people in these areas respectively. The simple forward finite difference is employed to the SIR model to have time dependent of parameters. The second approach is using the governing linear system to obtain the values of parameter daily. These parameters are computed for each day such that the values of Ro are obtained as function of time. The research result shows that 3 types areas give the same profiles of parameters that the rate of changes of reproduction numbers are decreasing with respect to time. This concludes that the reproduction numbers are most likely decreasing.

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C.*, Vasanth Pandiyan, and S. Ravichandran. "Treatment of textile milldye sludge by vermicomposting using Perionyx excavatus species." International Journal of Bioassays 5, no. 11 (October 31, 2016): 4999. http://dx.doi.org/10.21746/ijbio.2016.11.002.

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The accumulation of solid waste sludge from Textile dye sludge causes a great problem in its safe disposal. Perionyx excavatus were cultured under laboratory condition with 60-80%moisture in mud pot container following with the mixing ratio of TMS (Textile Mill Sludge) + SD(Sawdust) designated as X (1:1) respectively add inoculums (EM) Effective microorganisms and (CD) Cow dung were also used in the above ratio. Once in 15days upto 90days number of hatchling, worm growth rate and the weight of earthworms were determined and analysed statistically. On the basic of the efficiency of four treatments with control condition, (EM) separately, (CD) separately and (EM+SD) combined together were analysed to support the reproduction and growth of Perionyx excavatus has been done. The growth rate, weight gain, and hatchling production observed in the mixed ratio of TMS+SD (1:1) ratio with the above treatments were determined and better combination of mixed ratio with appropriated inoculums was determined. The mixed of TMS+SD+(EM+CD) gave high growth rate, weight gain and hatchling production of selected vermiculture Perionyx excavatus. Hence TMS in combination SD in (1:1ratio) can be used for vermiculture.

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Sutimin, Siti Khabibah, Dita Anies Munawwaroh, and R. Heri Soelistyo U. "Analysis of HIV Transmission of Commercial Sex Wokers and Their Clients with Condom Use Treatment." E3S Web of Conferences 125 (2019): 05003. http://dx.doi.org/10.1051/e3sconf/201912505003.

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A model of the HIV/AIDS epidemic among sex workers and their clients is discussed to study the effects of condom use in the prevention of HIV transmission. The model is addressed to determine the existence of equilibrium states, and then analyze the global stability of disease free and endemic equilibrium states. The global stability of equilibria depends on the vales of the basic reproduction ratio derived from the next generation matrix of the model. The endemic equilibrium state is globally stable when the ratio exceeds unity. The simulation results are presented to discuss the effect of condom use treatment in preventing the spread of HIV/AIDS among sex workers and their clients. The results show that the effectiveness level in using condoms in sexual intercourse corresponds to the decreasing level of the spread of HIV/AIDS. We use Maple and Matlab software to simulate the impact of condom use.

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Emvudu, Yves, Ramsès Demasse, and Dany Djeudeu. "Optimal Control of the Lost to Follow Up in a Tuberculosis Model." Computational and Mathematical Methods in Medicine 2011 (2011): 1–12. http://dx.doi.org/10.1155/2011/398476.

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This paper deals with the problem of optimal control for the transmission dynamics of tuberculosis (TB). A TB model that considers the existence of a new class (mainly in the African context) is considered: the lost to follow up individuals. Based on the model formulated and studied in the work of Plaire Tchinda Mouofo, (2009), the TB control is formulated and solved as an optimal control theory problem using the Pontryagin's maximum principle (Pontryagin et al., 1992). This control strategy indicates how the control of the lost to follow up class can considerably influence the basic reproduction ratio so as to reduce the number of lost to follow up. Numerical results show the performance of the optimization strategy.

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Liu, Guiyun, Jieyong Chen, Zhongwei Liang, Zhimin Peng, and Junqiang Li. "Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs." Mathematics 9, no. 9 (April 22, 2021): 929. http://dx.doi.org/10.3390/math9090929.

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With the rapid development of science and technology, the application of wireless sensor networks (WSNs) is more and more widely. It has been widely concerned by scholars. Viruses are one of the main threats to WSNs. In this paper, based on the principle of epidemic dynamics, we build a SEIR propagation model with the mutated virus in WSNs, where E nodes are infectious and cannot be repaired to S nodes or R nodes. Subsequently, the basic reproduction number R0, the local stability and global stability of the system are analyzed. The cost function and Hamiltonian function are constructed by taking the repair ratio of infected nodes and the repair ratio of mutated infected nodes as optimization control variables. Based on the Pontryagin maximum principle, an optimal control strategy is designed to effectively control the spread of the virus and minimize the total cost. The simulation results show that the model has a guiding significance to curb the spread of mutated virus in WSNs.

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Álvarez-Dagnino, Ernesto, Apolinar Santamaría-Miranda, Manuel García-Ulloa, and Andrés Martín Góngora-Gómez. "Reproduction of Megapitaria squalida (Bivalvia: Veneridae) in the Southeast Gulf of California, Mexico." Revista de Biología Tropical 65, no. 3 (April 20, 2017): 881. http://dx.doi.org/10.15517/rbt.v65i3.26371.

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Bivalves reproductive cycle varies according to the particular environmental conditions where they are found, and these reproductive details represent basic information for their capture, management and conservation strategies. With this objective, the reproductive cycle of the clam Megapitaria squalida, inhabiting the Southeast of the Gulf of California (Altata Bay, Sinaloa, Mexico), was studied using histology and changes in the number and size of oocytes, from June 2013 to June 2014. Histological analysis of the gonads showed spawning activity throughout the year, with two peaks. The first was registered in October and it was accompanied by the highest decrease of weight; the second was in February with the highest percentage of spawning population; besides, a resting period was observed in December. The sex-ratio (female:male) of the clam population was 1.08:1 (χ2 = 5.72, d.f. = 1, P < 0.05). Mean oocyte size and number were different (P < 0.05) among all sampling months and fluctuated from 34.6 ± 5.8 µm in June 2014, to 41.9 ± 6.8 µm in February 2014, and from 443.8 ± 424.5 in February 2014, to 1 214.4 ± 267.6 counted in April, respectively. With these results we suggest a protection season from October to November, when the most intense release of gametes occur in this population.

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Journal articles on the topic 'Basic reproduction ratio'

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