Spatiotemporal analysis of Zika virus transmission dynamics incorporating human mobility and seasonal variations using modified homotopy perturbation method

Abstract

This study employed a mathematical model to evaluate how seasonal variations, vector dispersal, and mobility of people affect the spread of the Zika virus. The model's positive solutions, invariant zones, and solution existence and uniqueness were validated through proved theorems. The equilibria points were identified, and the basic reproduction number was calculated. The model was semi-analytically solved using a modified homotopy perturbation approach, and an applied convergence test proved that the solution converges. The simulation results indicated that under optimal breeding conditions, the density of healthy mosquitoes peaked in the fourth month. Two months later, increased mosquito dispersal and human carriers facilitated by favorable weather led to a rise in mosquito infectiousness, peaking between the fourth and eighth months due to significant seasonal effects, resulting in high Zika transmission. To effectively control mosquito populations and reduce Zika transmission, it is recommended that public health interventions focus on the critical periods spanning the third to eighth months.