Mathematical Analysis for the Influence of Seasonality on Chikungunya Virus Dynamics

In this article, we discuss a mathematical system modelling Chikungunya virus dynamics in a seasonal environment with general incidence rates. We establish the existence, uniqueness, positivity and boundedness of a periodic orbit. We show that the global dynamics is determined using the basic reproduction number denoted by R0 and calculated using the spectral radius of a linear integral operator. We show the global stability of the disease free periodic solution if R0<1 and we show also the persistence of the disease if R0>1 where the trajectories converge to a periodic orbit. Finally, we display some numerical examples confirming the theoretical findings.