On a Spatial Mosquito-Borne Disease Model with Density-Dependent Dispersal
Kai Wang, Peng Wu, Qian Ding, Jianshe Yu
Source abstract
Abstract. Chemotaxis of mosquito movement has been widely confirmed, but it has rarely been incorporated into infectious disease modeling. This paper proposes a novel mosquito-borne disease model driven by density-suppressed motility and spatial heterogeneity. Via overcoming the difficulties caused by dispersal mechanism and heterogeneity, we establish the global existence and ultimate boundedness of solutions for the model following a priori estimates and the parabolic regularity theory. We define the basic reproduction ratio [Formula: see text] and derive its upper bound [Formula: see text] and lower bound [Formula: see text], and obtain the threshold dynamics of model. Specifically, we prove that the system is uniformly persistent as [Formula: see text] and the disease will disappear as [Formula: see text] by invoking the comparison principle to the corresponding integral system. In the case of spatial homogeneity, the global asymptotic stability of endemic equilibrium is achieved with the aid of a suitable Lyapunov functional and the eigenvalue theory. Numerically, we apply the model to dengue transmission and demonstrate that the chemotaxis of infected mosquitoes may exacerbate the disease in some regions which highlights the impacts of mosquito taxis on the spread of dengue.
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