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A metapopulation model for the population dynamics of anopheles mosquito. (English) Zbl 1411.92280
Summary: A more robust assessment of malaria control will come from a better understanding of the distribution and connectivity of breeding and blood feeding sites. Spatial heterogeneity of mosquito resources, such as hosts and breeding sites, affects mosquito dispersal behavior. This paper analyzes and simulates the spreading of anopheles mosquito on a complex metapopulation, that is, networks of populations connected by migratory flows whose configurations are described in terms of connectivity distribution of nodes (patches) and the conditional probabilities of connections between nodes. We examine the impacts of vector dispersal on the persistence and extinction of a mosquito population in both homogeneous and heterogeneous landscapes. For uncorrelated networks in a homogeneous landscape, we derive an explicit formula of the basic offspring number \(\mathcal{R}_0^{(m)}\). Using the theory of monotone operators, we obtain sufficient conditions for the global asymptotic stability of equilibria. Precisely, the value 1 of the basic offspring number is a forward bifurcation for the dynamics of anopheles mosquito, with the trivial (mosquito-free) equilibrium point being globally asymptotically stable (GAS) when \(\mathcal{R}_0^{(m)} \leq 1\), and one stable nontrivial (mosquito-persistent) equilibrium point being born with well determined basins of attraction when \(\mathcal{R}_0^{(m)} > 1\). Theoretical results are numerically supported and the impact of the migration of mosquitoes are discussed through global sensitivity analysis and numerical simulations.

MSC:
92D30 Epidemiology
92D25 Population dynamics (general)
92-08 Computational methods for problems pertaining to biology
34D20 Stability of solutions to ordinary differential equations
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