Analysis of a malaria epidemic model with age structure and spatial diffusion. (English) Zbl 1464.35383
Summary: This paper aims to provide the complete analysis on the threshold dynamics of an age-space structured malaria epidemic model. We formulate the model in a spatially bounded domain by assuming that: (i) the density of susceptible humans at space \(x\) stabilizes at \(H(x)\); (ii) the force of infection between human population and mosquitoes is given by the mass action incidence. By appealing to the theory of fixed point problem and Picard sequences and iteration, the well-posedness of the model is shown by verifying that the solution exists globally and the model admits a global attractor. In the spatially homogeneous case, we establish the explicit formula for the basic reproduction number, which governs the malaria extinction and persistence. The local and global stability of equilibria is achieved by studying the distribution of characteristic roots of characteristic equation and constructing the suitable Lyapunov functions, respectively.
MSC:
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 35K57 | Reaction-diffusion equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 92D30 | Epidemiology |
| 92D25 | Population dynamics (general) |
| 35B35 | Stability in context of PDEs |
| 35B41 | Attractors |
| 35P25 | Scattering theory for PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
Keywords:
age-space structured; spatial heterogeneity; basic reproduction number; malaria model; global stabilityReferences:
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