Global dynamics of a reaction–advection–diffusion model for Chikungunya disease with seasonality

Chikungunya fever is a mosquito-borne viral disease caused by the ChIkungunya Virus (CHIKV). To examine the combined impacts of seasonality, spatial heterogeneity, and advection-diffusion processes on CHIKV transmission, we propose a delayed reaction–advection–diffusion model that incorporates both human and mosquito populations with time-varying parameters. We obtain the mosquito reproduction number [Formula: see text] and the basic reproduction number [Formula: see text] of the system, and develop threshold-type results that describe its global dynamics based on [Formula: see text] and [Formula: see text]. We also show the influence of advection factors on [Formula: see text]. Numerical simulations, motivated by the 2016 Chikungunya outbreak in Delhi, illustrate how advection and diffusion affect mosquito population size and disease spread.