# American Institute of Mathematical Sciences

2016, 13(2): 401-424. doi: 10.3934/mbe.2015009

## A mathematical model for the spread of west nile virus in migratory and resident birds

 1 Department of Mathematics, Tulane University, New Orleans, LA 70118, United States, United States, United States

Received  January 2015 Revised  November 2015 Published  December 2015

We develop a mathematical model for transmission of West Nile virus (WNV) that incorporates resident and migratory host avian populations and a mosquito vector population. We provide a detailed analysis of the model's basic reproductive number and demonstrate how the exposed infected, but not infectious, state for the bird population can be approximated by a reduced model. We use the model to investigate the interplay of WNV in both resident and migratory bird hosts. The resident host parameters correspond to the American Crow (Corvus brachyrhynchos), a competent host with a high death rate due to disease, and migratory host parameters to the American Robin (Turdus migratorius), a competent host with low WNV death rates. We find that yearly seasonal outbreaks depend primarily on the number of susceptible migrant birds entering the local population each season. We observe that the early growth rates of seasonal outbreaks is more influenced by the the migratory population than the resident bird population. This implies that although the death of highly competent resident birds, such as American Crows, are good indicators for the presence of the virus, these species have less impact on the basic reproductive number than the competent migratory birds with low death rates, such as the American Robins. The disease forecasts are most sensitive to the assumptions about the feeding preferences of North American mosquito vectors and the effect of the virus on the hosts. Increased research on the these factors would allow for better estimates of these important model parameters, which would improve the quality of future WNV forecasts.
Citation: Louis D. Bergsman, James M. Hyman, Carrie A. Manore. A mathematical model for the spread of west nile virus in migratory and resident birds. Mathematical Biosciences & Engineering, 2016, 13 (2) : 401-424. doi: 10.3934/mbe.2015009
##### References:

show all references

##### References:
 [1] Rongsong Liu, Jiangping Shuai, Jianhong Wu, Huaiping Zhu. Modeling spatial spread of west nile virus and impact of directional dispersal of birds. Mathematical Biosciences & Engineering, 2006, 3 (1) : 145-160. doi: 10.3934/mbe.2006.3.145 [2] Abdelrazig K. Tarboush, Jing Ge, Zhigui Lin. Coexistence of a cross-diffusive West Nile virus model in a heterogenous environment. Mathematical Biosciences & Engineering, 2018, 15 (6) : 1479-1494. doi: 10.3934/mbe.2018068 [3] Jing Chen, Jicai Huang, John C. Beier, Robert Stephen Cantrell, Chris Cosner, Douglas O. Fuller, Guoyan Zhang, Shigui Ruan. Modeling and control of local outbreaks of West Nile virus in the United States. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2423-2449. doi: 10.3934/dcdsb.2016054 [4] Chuncheng Wang, Rongsong Liu, Junping Shi, Carlos Martinez del Rio. Traveling waves of a mutualistic model of mistletoes and birds. Discrete & Continuous Dynamical Systems - A, 2015, 35 (4) : 1743-1765. doi: 10.3934/dcds.2015.35.1743 [5] Hui Cao, Yicang Zhou. The basic reproduction number of discrete SIR and SEIS models with periodic parameters. Discrete & Continuous Dynamical Systems - B, 2013, 18 (1) : 37-56. doi: 10.3934/dcdsb.2013.18.37 [6] Huimin Liang, Peixuan Weng, Yanling Tian. Bility and traveling wavefronts for a convolution model of mistletoes and birds with nonlocal diffusion. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2207-2231. doi: 10.3934/dcdsb.2017093 [7] Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger. On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China. Mathematical Biosciences & Engineering, 2007, 4 (4) : 595-607. doi: 10.3934/mbe.2007.4.595 [8] Huimin Liang, Peixuan Weng, Yanling Tian. Threshold asymptotic behaviors for a delayed nonlocal reaction-diffusion model of mistletoes and birds in a 2D strip. Communications on Pure & Applied Analysis, 2016, 15 (4) : 1471-1495. doi: 10.3934/cpaa.2016.15.1471 [9] Gerardo Chowell, R. Fuentes, A. Olea, X. Aguilera, H. Nesse, J. M. Hyman. The basic reproduction number $R_0$ and effectiveness of reactive interventions during dengue epidemics: The 2002 dengue outbreak in Easter Island, Chile. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1455-1474. doi: 10.3934/mbe.2013.10.1455 [10] Cameron J. Browne, Sergei S. Pilyugin. Global analysis of age-structured within-host virus model. Discrete & Continuous Dynamical Systems - B, 2013, 18 (8) : 1999-2017. doi: 10.3934/dcdsb.2013.18.1999 [11] Andrei Korobeinikov, Conor Dempsey. A continuous phenotype space model of RNA virus evolution within a host. Mathematical Biosciences & Engineering, 2014, 11 (4) : 919-927. doi: 10.3934/mbe.2014.11.919 [12] Jane M. Heffernan, Yijun Lou, Jianhong Wu. Range expansion of Ixodes scapularis ticks and of Borrelia burgdorferi by migratory birds. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3147-3167. doi: 10.3934/dcdsb.2014.19.3147 [13] Naveen K. Vaidya, Feng-Bin Wang, Xingfu Zou. Avian influenza dynamics in wild birds with bird mobility and spatial heterogeneous environment. Discrete & Continuous Dynamical Systems - B, 2012, 17 (8) : 2829-2848. doi: 10.3934/dcdsb.2012.17.2829 [14] Xinli Hu. Threshold dynamics for a Tuberculosis model with seasonality. Mathematical Biosciences & Engineering, 2012, 9 (1) : 111-122. doi: 10.3934/mbe.2012.9.111 [15] 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 [16] Adam Sullivan, Folashade Agusto, Sharon Bewick, Chunlei Su, Suzanne Lenhart, Xiaopeng Zhao. A mathematical model for within-host Toxoplasma gondii invasion dynamics. Mathematical Biosciences & Engineering, 2012, 9 (3) : 647-662. doi: 10.3934/mbe.2012.9.647 [17] Stephen Pankavich, Christian Parkinson. Mathematical analysis of an in-host model of viral dynamics with spatial heterogeneity. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1237-1257. doi: 10.3934/dcdsb.2016.21.1237 [18] Cameron J. Browne, Sergei S. Pilyugin. Minimizing $\mathcal R_0$ for in-host virus model with periodic combination antiviral therapy. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3315-3330. doi: 10.3934/dcdsb.2016099 [19] Scott W. Hansen. Controllability of a basic cochlea model. Evolution Equations & Control Theory, 2016, 5 (4) : 475-487. doi: 10.3934/eect.2016015 [20] Kjartan G. Magnússon, Sven Th. Sigurdsson, Petro Babak, Stefán F. Gudmundsson, Eva Hlín Dereksdóttir. A continuous density Kolmogorov type model for a migrating fish stock. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 695-704. doi: 10.3934/dcdsb.2004.4.695

2018 Impact Factor: 1.313