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Modelling the Effects of Vertical Transmission in Mosquito and the Use of Imperfect Vaccine on Chikungunya Virus Transmission Dynamics

DOI: 10.4236/am.2019.104019, PP. 245-267

Keywords: Chikungunya Virus, Stability, Equilibrium, Vaccination, Endemic

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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< 1 ). 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.

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