DYNAMICS OF A MULTI-PATCH MODEL OF MALARIA TRANSMISSION WITH EULERIAN APPROACH

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Résumé

This work deals with an SEIRS-SEI compartmental multi-patch epidemic model of malaria transmission in which, only human hosts can travel among \(n\) patches. The model is formulated as a system of \(7 n\) ordinary differential equations, whose terms take into account epidemiological parameters relating to human hosts and mosquitoes in different patches. To capture the effects of host mobility matrices, > \(\mathbb{P}^{\bullet}\) on malaria dispersal, we compute the global basic reproduction number, \(\mathcal{R}_{0}\left(n, \mathbb{P}^{\bullet}\right)\) and show that it is the key parameter predicting malaria dynamics over all patches. Thus, our study shows that while the model exhibits a unique strongly endemic equilibrium for \(\mathcal{R}_{0}\left(n, \mathbb{P}^{\bullet}\right)>1\), the malaria-free equilibrium (MFE) is globally asymptotically stable if \(\mathcal{R}_{0}\left(n, \mathbb{P}^{\bullet}\right)

Mots-clés

malaria transmission, human mobility, global stability, endemic equilibrium, Eulerian approach