Mathematical Design of a Discrete Delay-Based Epidemiological Model for Assessing Yellow Fever Spread and Its Stability in Heterogeneous Populations
TL;DR
A mathematical model incorporating discrete time delays to examine the transmission dynamics of yellow fever indicates that the mosquito infection susceptibility rate is crucial in determining the expansion of the infected mosquito population, where elevated rates correspond to a greater fraction of infected mosquitoes.
Abstract
We developed a mathematical model incorporating discrete time delays to examine the transmission dynamics of yellow fever. We determined the stability of this delayed system by identifying both the disease-free and endemic equilibrium points. We further assessed stability by calculating the basic reproduction number using the next-generation matrix approach. Numerical simulations revealed that time delays significantly influence the stability of the endemic equilibrium. The yellow fever-free equilibrium was found to be locally asymptotically stable. As a result, introducing a small number of infected individuals into a fully susceptible population typically fails to sustain reproduction, preventing the disease from spreading. Additionally, a higher effective biting rate destabilizes the endemic equilibrium, leading us to infer that more infectious bites on susceptible humans would amplify the size of the infected human population. The findings also indicate that the mosquito infection susceptibility rate is crucial in determining the expansion of the infected mosquito population, where elevated rates correspond to a greater fraction of infected mosquitoes.