Vector-borne diseases models with residence times – a Lagrangian perspective. (English) Zbl 1348.92144
Summary: A multi-patch and multi-group modeling framework describing the dynamics of a class of diseases driven by the interactions between vectors and hosts structured by groups is formulated. Hosts’ dispersal is modeled in terms of patch-residence times with the nonlinear dynamics taking into account the effective patch-host size. The residence times basic reproduction number \(\mathcal{R}_0\) is computed and shown to depend on the relative environmental risk of infection. The model is robust, that is, the disease free equilibrium is globally asymptotically stable (GAS) if \(\mathcal{R}_0 \leq 1\) and a unique interior endemic equilibrium is shown to exist that is GAS whenever \(\mathcal{R}_0 > 1\) whenever the configuration of host-vector interactions is irreducible. The effects of patchiness and groupness, a measure of host-vector heterogeneous structure, on the basic reproduction number \(\mathcal{R}_0,\) are explored. Numerical simulations are carried out to highlight the effects of residence times on disease prevalence.
MSC:
| 92D30 | Epidemiology |
| 34D23 | Global stability of solutions to ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 34C12 | Monotone systems involving ordinary differential equations |
Keywords:
vector-borne diseases; human dispersal; basic reproduction number; global stability; nonlinear dynamical systemsReferences:
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