Analysis, state estimation and control of a malaria transmission model with semi-immune compartment for humans
Résumé
The aim of this paper is to study a mathematical model describing the dynamics of malaria transmission. The model tracks that humans gain a temporary immunity but they can still transmit the disease to susceptible mosquitoes with a probability less than that of infected humans. Furthermore, we take in consideration both return from the semi-immune class as a probability of loss of immunity and the return from the infected directly to the susceptible class. We investigate the existence of both trivial and non trivial equilibria and their stability. We show how to estimate the size of different human populations using the host incidence which is, in general, the only available information. To this end, we construct some observers or "software sensors" that allow to dynamically estimate the non-measured state variables. We also provide some strategies to control the disease using Lyapunov control functions.
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