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A reaction-diffusion model of dengue transmission

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  • This paper is devoted to the mathematical analysis of a reaction-diffusion model of dengue transmission. In the case of a bounded spatial habitat, we obtain the local stability as well as the global stability of either disease-free or endemic steady state in terms of the basic reproduction number $\mathcal{R}_0$. In the case of an unbounded spatial habitat, we establish the existence of the traveling wave solutions connecting the two constant steady states when $\mathcal{R}_0>1$, and the nonexistence of the traveling wave solutions that connect the disease-free steady state itself when $\mathcal{R}_0<1$. Numerical simulations are performed to illustrate the main analytic results.
    Mathematics Subject Classification: Primary: 34D20, 35C07; Secondary: 35Q92, 92D30.


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