MODELING AND ANALYSIS OF LOW-LEVEL TRANSMISSION ZIKV DYNAMICS VIA A POISSON POINT PROCESS ON SEXUAL TRANSMISSION ROUTE

Abstract

In this project, we modeled the low-level ZIKV transmission that was reported in Thailand [? ]. The secondary sexual transmission route is modeled by a Poisson point process, which leads to an increasing and saturating contact rate. This nonlinear contact rate further induces backward and Hopf bifurcations. Oscillations bifurcating from the Hopf bifurcation demonstrate the low-level persistent ZIKV transmission with sharp outbreaks, which further show varying amplitudes and frequency by considering stochastic variations on the sexual transmission rate. Global stability analysis of the diseasefree equilibrium drives the disease elimination criteria for models considering vector transmission route only and considering both vector and sexual transmission routes. Bifurcation analyses prove the existence of forward and backward bifurcations, saddle-node bifurcation, and Bogdanov-Takens analytically, and further suggest the occurrence of cusp, Hopf, and general Hopf bifurcations numerically. One and two-dimensional bifurcation diagrams demonstrate the analytical results under the influence of both vector and sexual transmission rates. Sensitivity analysis suggests that an increase in mosquito death rate has the largest effect on the basic reproduction number, and an increase in human recovery rate has the most influence on decreasing human host prevalence.