Dynamics Of Mosquito-borne Diseases With Growth Zone

Different from previous studies on epidemic disease transmission on fixed region,this paper intends to study the spatio-temporal dynamics of two reaction diffusion epidemic disease models(dengue fever and Zika)in growing regions.The model is based on the following assumptions:(i)the spatial region increases monotonously and tends to be saturated with time in all directions;(ii)mosquito population satisfies spatial Logistic growth;(iii)the spread of the disease does not affect the growth of the human population(i.e.human population is a constant);(iv)consider vector bias.In terms of mathematical analysis,we use Lagrange transform to transform the model in the growing region to the fixed region.By the upper and lower solutions,comparison principle,asymptotic autonomous semiflows and the technique of Lyapunov function,we investigate the stabilities of equilibria in terms of the basic reproduction number that(i)if R0ρ>1,the solutions starting from the upper and lower solutions of the model approach to the set formulated by the maximal and minimal solutions of its related elliptic problem;(ii)the disease-free equilibrium is globally asymptotically stable when R0ρ>1.Comparing our problem on different settings that growing domain,fixed domain,and without spatial structure,we find from the expression of the basic reproduction numbers that the growth domain alters disease transmission pattern in the sense that the disease can spread in the growing domain,while vanish in the fixed domain could increase the transmission risk,that is,habitat expansion catalyzes disease transmission.Our results also demonstrate that when studying the disease transmission,the spatial model decreases the transmission risk compared with the system without spatial structure.