Investigating the Role of Mobility between Rural Areas and Forests on the Spread of Zika

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. A mathematical analysis of the proposed model is presented. The analysis starts with normalizing the proposed model. The positivity and boundedness of solutions to the normalized model are then addressed. The basic reproduction number is 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 is investigated. The analysis also includes the existence and stability of disease-free and endemic equilibrium points. Bifurcation analysis is also carried out. Finally, numerical solutions to the normalized model are obtained to confirm the theoretical results and demonstrate human movement's role in disease transmission in human and mosquito populations.