Threshold Dynamics, Stability and Sensitivity Analysis of a Multi-hosts West Nile Virus Model Incorporating Lateral Transmission in Hosts and Vertical Transmission in the Vector Population

Source abstract

West Nile virus is a mosquito-borne flavivirus that cycles between Culex mosquitoes and birds, with humans as incidental, dead-end hosts. Existing compartmental models of the virus focused mainly on the cross-transmission route and therefore ignore the lateral routes that operate within the avian and human populations and the transovarial route that occurs within the vector. This paper formulates and analyzes a twenty-two compartment deterministic model with constant control that divides the avian hosts into corvid and non-corvid classes, resolves the immature vector stages, carries an environmentally persistent viral compartment, and admits predatory and non-predatory bird-to-bird transmission, transfusion and transplant transmission in humans, and vertical transmission in mosquitoes. Positivity and boundedness of solutions are established, and a biologically feasible invariant region is identified. Two disease-free equilibria are obtained, and the non-trivial one is shown to exist only when a demographic vector reproduction ratio exceeds unity. The basic reproduction number is derived by the next-generation matrix method and is shown to decompose into four sub-reproduction numbers associated with the mosquito-bird cycle, the bird-to-bird and environmental pathway, vertical transmission and human spill over, the human component being structurally decoupled from the enzootic cycle. The disease-free equilibrium is proved to be locally asymptotically stable by the Routh-Hurwitz criterion and globally asymptotically stable by the Castillo-Chavez framework, while a logarithmic Lyapunov function together with LaSalle's invariance principle establishes global asymptotic stability of the endemic equilibrium. Sensitivity analysis identifies vector survival, biting, and transmission intensity and environmental viral persistence as the dominant drivers of transmission, and numerical simulations confirm the analytical findings.