The Impact of Mobility between Rural Areas and Forests on the Spread of Zika

TL;DR

This paper develops a mathematical model to analyze how human movement between rural areas and forests influences the spread of Zika virus, incorporating various transmission routes and providing insights into disease dynamics.

Contribution

It introduces a comprehensive mathematical model that includes human mobility and multiple transmission pathways, offering new insights into Zika spread mechanisms.

Findings

Human movement significantly affects Zika transmission dynamics.

The basic reproduction number is sensitive to movement-related parameters.

Numerical simulations confirm the theoretical impact of mobility on disease spread.

Abstract

A mathematical model of Zika virus transmission incorporating human movement between rural areas and nearby forests is presented to investigate the role of human movement in the spread of Zika virus infections in human and mosquito populations. Proportions of both susceptible and infected humans living in rural areas are assumed to move to nearby forest areas. Direct, indirect and vertical transmission routes are incorporated for all populations. Mathematical analysis of the proposed model has been presented. The analysis starts with normalizing the proposed model. Positivity and boundedness of solutions to the normalized model have been then addressed. The basic reproduction number has been calculated using the next generation matrix method and its relation to the three routes of disease transmission has been presented. The sensitivity analysis of the basic reproduction number to all model parameters has been investigated. The analysis also includes existence and stability of disease free and endemic equilibrium points. Bifurcation analysis has been also carried out. Finally, numerical solutions to the normalized model have been obtained to confirm the theoretical results and to demonstrate the impact of human movement in the disease transmission in human and mosquito populations.