TITLE:
Modelling the Effects of Vertical Transmission in Mosquito and the Use of Imperfect Vaccine on Chikungunya Virus Transmission Dynamics
AUTHORS:
Martins O. Onuorah, Emmanuel I. Obi, Bala G. Babangida
KEYWORDS:
Chikungunya Virus, Stability, Equilibrium, Vaccination, Endemic
JOURNAL NAME:
Applied Mathematics,
Vol.10 No.4,
April
29,
2019
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,Rc(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 (ΛM) 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 Rc. 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.