Spreading speed for a time-periodic vector-borne disease system on a growing domain

This paper is concerned with the study of the asymptotic speed of spread for a timeperiodic vector-borne disease system posed on the whole space for the host population and on a time varying domain for the vector population.We firstly examine the spreading properties of a time-periodic Fisher-KPP equation posed on a growing domain by constructing appropriate sub- and super-solutions. Then, using the basic reproduction number of the corresponding kinetic system, we describe the long time behavior of the system. In particular when this basic reproduction number is larger than one, we prove that the epidemic is endemic and we derive some estimates for the spreading speed of the invasion of the disease. Finally, numerical simulations are carried out to illustrate our theoretical results.