Exploration of the Impact of Complex Host Dynamics on a West-Nile Virus Epidemic

Abstract

In this project, we use mathematical modeling and optimal control to study the impli- cations of variable host competency and host demographics on a West Nile virus epidemic with the primary objective being to determine how horizontal transmission in birds and variable bird competency impacts the model reproduction number and endemic steady- sates(s). The model uses ordinary differential equations to describe the transmission of the virus between birds and mosquitoes, vertical transmission in mosquitoes, horizontal transmission in birds, the mosquito life cycle, and bird demographics. Previous work, which focused on mosquito dynamics, demonstrated the choice of objective functional can significantly impact the optimal control and its impact on the mosquito population. However, due to the simplistic treatment of the bird demographics, these conclusions were limited to the late summer and early fall. Moreover, previous work did not consider the impact of variable host competency on the epidemic and its control. Here, we for- mulate and parameterize a model including bird recruitment and two bird types which are thought to be important for West Nile virus maintenance and transmission: Corvides (e.g. crows and jays) and Passerides (e.g. sparrows, wrens and buntings). We investigate how the incorporation of multiple bird types impacts the model reproduction number us- ing the next-generation-matrix method and investigate the existence of endemic steady states.