On the global attractivity for a reaction-diffusion malaria model with incubation period in the vector population. (English) Zbl 1489.92188
Summary: 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 [Y. Lou and X.-Q. Zhao, ibid. 62, No. 4, 543–568 (2011; Zbl 1232.92057)] by using the fluctuation method, but with a sufficient condition that the disease will become stable requires a sufficiently large basic reproduction number \(\mathfrak{R}_0\). 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 \(\mathfrak{R}_0\) is exactly greater than one, which remarkably improves the known results in [loc. cit.].
Keywords:
malaria; reaction-diffusion model; global attractivity; Lyapunov functional; nonlocal delayCitations:
Zbl 1232.92057References:
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