On the global attractivity for a reaction-diffusion malaria model with incubation period in the vector population.

Abstract

This paper establishes the global attractivity of a positive constant equilibrium of a nonlocal and time-delayed diffusive malaria model in a homogeneous case. The same problem was achieved in a recent paper (Lou and Zhao in J Math Biol 62:543-568, 2011) by using the fluctuation method, but with a sufficient condition that the disease will become stable requires a sufficiently large basic reproduction number [Formula: see text]. The present study is devoted to remove the sufficient condition by utilizing an appropriate Lyapunov functional and shows that the disease will become stable when [Formula: see text] is exactly greater than one, which remarkably improves the known results in Lou and Zhao (2011).