# American Institute of Mathematical Sciences

2008, 5(4): 729-741. doi: 10.3934/mbe.2008.5.729

## Modeling evolution and persistence of neurological viral diseases in wild populations

 1 Fred Hutchinson Cancer Research Center, 1100 Fairview Ave N., LE-400, P.O. Box 19024, Seattle, WA 98109-1024, United States 2 Departments of Ecology and Evolutionary Biology and Mathematics, University of Michigan, North University Avenue, Ann Arbor, MI 48109-1048, United States

Received  January 2008 Revised  April 2008 Published  October 2008

Viral infections are one of the leading source of mortality worldwide. The great majority of them circulate and persist in wild reservoirs and periodically spill over into humans or domestic animals. In the wild reservoirs, the progression of disease is frequently quite different from that in spillover hosts. We propose a mathematical treatment of the dynamics of viral infections in wild mammals using models with alternative outcomes. We develop and analyze compartmental epizootic models assuming permanent or temporary immunity of the individuals surviving infections and apply them to rabies in bats. We identify parameter relations that support the existing patterns in the viral ecology and estimate those parameters that are unattainable through direct measurement. We also investigate how the duration of the acquired immunity affects the disease and population dynamics.
Citation: Dobromir T. Dimitrov, Aaron A. King. Modeling evolution and persistence of neurological viral diseases in wild populations. Mathematical Biosciences & Engineering, 2008, 5 (4) : 729-741. doi: 10.3934/mbe.2008.5.729
 [1] Wendi Wang. Epidemic models with nonlinear infection forces. Mathematical Biosciences & Engineering, 2006, 3 (1) : 267-279. doi: 10.3934/mbe.2006.3.267 [2] Carlota Rebelo, Alessandro Margheri, Nicolas Bacaër. Persistence in some periodic epidemic models with infection age or constant periods of infection. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 1155-1170. doi: 10.3934/dcdsb.2014.19.1155 [3] Sukhitha W. Vidurupola, Linda J. S. Allen. Basic stochastic models for viral infection within a host. Mathematical Biosciences & Engineering, 2012, 9 (4) : 915-935. doi: 10.3934/mbe.2012.9.915 [4] Yilei Tang, Dongmei Xiao, Weinian Zhang, Di Zhu. Dynamics of epidemic models with asymptomatic infection and seasonal succession. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1407-1424. doi: 10.3934/mbe.2017073 [5] Liming Cai, Maia Martcheva, Xue-Zhi Li. Epidemic models with age of infection, indirect transmission and incomplete treatment. Discrete & Continuous Dynamical Systems - B, 2013, 18 (9) : 2239-2265. doi: 10.3934/dcdsb.2013.18.2239 [6] Chandrani Banerjee, Linda J. S. Allen, Jorge Salazar-Bravo. Models for an arenavirus infection in a rodent population: consequences of horizontal, vertical and sexual transmission. Mathematical Biosciences & Engineering, 2008, 5 (4) : 617-645. doi: 10.3934/mbe.2008.5.617 [7] H. Thomas Banks, Shuhua Hu, Michele Joyner, Anna Broido, Brandi Canter, Kaitlyn Gayvert, Kathryn Link. A comparison of computational efficiencies of stochastic algorithms in terms of two infection models. Mathematical Biosciences & Engineering, 2012, 9 (3) : 487-526. doi: 10.3934/mbe.2012.9.487 [8] Curtis L. Wesley, Linda J. S. Allen, Michel Langlais. Models for the spread and persistence of hantavirus infection in rodents with direct and indirect transmission. Mathematical Biosciences & Engineering, 2010, 7 (1) : 195-211. doi: 10.3934/mbe.2010.7.195 [9] Christine K. Yang, Fred Brauer. Calculation of $R_0$ for age-of-infection models. Mathematical Biosciences & Engineering, 2008, 5 (3) : 585-599. doi: 10.3934/mbe.2008.5.585 [10] Erika Asano, Louis J. Gross, Suzanne Lenhart, Leslie A. Real. Optimal control of vaccine distribution in a rabies metapopulation model. Mathematical Biosciences & Engineering, 2008, 5 (2) : 219-238. doi: 10.3934/mbe.2008.5.219 [11] Khalaf M. Alanazi, Zdzislaw Jackiewicz, Horst R. Thieme. Spreading speeds of rabies with territorial and diffusing rabid foxes. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 0-0. doi: 10.3934/dcdsb.2019222 [12] Jeng-Huei Chen. An analysis of functional curability on HIV infection models with Michaelis-Menten-type immune response and its generalization. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2089-2120. doi: 10.3934/dcdsb.2017086 [13] Jinliang Wang, Xiu Dong. Analysis of an HIV infection model incorporating latency age and infection age. Mathematical Biosciences & Engineering, 2018, 15 (3) : 569-594. doi: 10.3934/mbe.2018026 [14] Miguel Atencia, Esther García-Garaluz, Gonzalo Joya. The ratio of hidden HIV infection in Cuba. Mathematical Biosciences & Engineering, 2013, 10 (4) : 959-977. doi: 10.3934/mbe.2013.10.959 [15] Don A. Jones, Hal L. Smith, Horst R. Thieme. Spread of viral infection of immobilized bacteria. Networks & Heterogeneous Media, 2013, 8 (1) : 327-342. doi: 10.3934/nhm.2013.8.327 [16] Nicola Bellomo, Youshan Tao. Stabilization in a chemotaxis model for virus infection. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 105-117. doi: 10.3934/dcdss.2020006 [17] Samantha Erwin, Stanca M. Ciupe. Germinal center dynamics during acute and chronic infection. Mathematical Biosciences & Engineering, 2017, 14 (3) : 655-671. doi: 10.3934/mbe.2017037 [18] Xuejuan Lu, Shaokai Wang, Shengqiang Liu, Jia Li. An SEI infection model incorporating media impact. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1317-1335. doi: 10.3934/mbe.2017068 [19] Yuming Chen, Junyuan Yang, Fengqin Zhang. The global stability of an SIRS model with infection age. Mathematical Biosciences & Engineering, 2014, 11 (3) : 449-469. doi: 10.3934/mbe.2014.11.449 [20] Kokum R. De Silva, Shigetoshi Eda, Suzanne Lenhart. Modeling environmental transmission of MAP infection in dairy cows. Mathematical Biosciences & Engineering, 2017, 14 (4) : 1001-1017. doi: 10.3934/mbe.2017052

2018 Impact Factor: 1.313