Modelling the dynamics of Chikungunya in human and mosquito populations

Abstract

In this paper, we developed and qualitatively analyzed a model for the transmission
dynamics of chikungunya virus in a human a nd mosquito populations. The chikungunya
virus is transmitted by Aedes mosquitoes usually Aedes albopictus mosquito and it is of big
threat to global public health. Rigorous analysis of the model shows that the model has a
locally asymptotically stable disease free equilibrium whenever a certain epidemiological
threshold quantity, called the basic reproduction number is less than unity (hence, the
diseases would not persist in the community). The model has a unique endemic
equilibrium when the reproduction number exceeds unity. Furthermore, the model exhibits
the phenomenon of backward bifurcation, where the stable disease free equilibrium
coexists with a stable endemic equilibrium.

Keywords: Chikungunya virus; vertical transmission; stability; backward bifurcation.