Abstract

In this paper, a deterministic mathematical model for Chikungunya virus

(Chikv) transmission and control is developed and analyzed to underscore

the effect of vaccinating a proportion of the susceptible human, and vertical

transmission in mosquito population. The disease free, and endemic equilibrium

states were obtained and the conditions for the local and global stability

or otherwise were given. Sensitivity analysis of the effective reproductive

number, c R (the number of secondary infections resulting from the introduction

of a single infected individual into a population where a proportion is

fairly protected) shows that the recruitment rate of susceptible mosquito

( M Λ ) and the proportion of infectious new births from infected mosquito

( β ) are the most sensitive parameters. Bifurcation analysis of the model using

center manifold theory reveals that the model undergoes backward bifurcation

(coexistence of disease free and endemic equilibrium when C 1 R < ).

Numerical simulation of the model shows that vaccination of susceptible

human population with imperfect vaccine will have a positive impact and that

vertical transmission in mosquito population has a negligible effect. To the

best of our knowledge, our model is the first to incorporate vaccinated human

compartment and vertical transmission in (Chikv) model.