Abstract
In this paper, fuzzy techniques have been used to track the problem of malaria transmission dynamics. The fuzzy equilibrium of the proposed model was discussed for different amounts of parasites in the body. We proved that when the amounts of parasites are less than the minimum amounts required for disease transmission (), we reach the model disease-free equilibrium. Using Choquet integral, the fuzzy basic reproduction number through the expected value of fuzzy variable was introduced for the fuzzy Susceptible, Exposed, Infected, Recovered, susceptible-Susceptible, Exposed and Infected (SEIRS-SEI) malaria model. The fuzzy global stabilities were introduced and discussed. The disease-free equilibrium is globally asymptotically stable if or if the basic reproduction number is less than one (). When and , there exists a co-existing endemic equilibrium which is globally asymptotically stable in the interior of feasible set . Finally, the numerical simulation has been done for showing the effectiveness of our analytical results.
Highlights
Malaria, a mosquito-borne disease, is one of the oldest diseases studied in mathematical approaches
All the data used have been taken in the literature and the ones for fuzzy variables are assumed according for the amount of parasites required for malaria transmission in a particular group of individuals
We have proposed and studied the SEIRS-SEI model for malaria transmission dynamics in fuzzy environment
Summary
A mosquito-borne disease, is one of the oldest diseases studied in mathematical approaches. Most of these models used a deterministic approach with constant parameters They assumed that the contact transmission and recovery rates are constant. C. de Barros et al in 2003 studied an SI epidemiological model with a fuzzy transmission parameter In this model, they consider different degrees of infectivity of contact rate. Bhuju et al used a fuzzy approach to track the problem of Dengue transmission dynamics in Nepal using the SEIR-SEI scheme In their work, they assumed that the transmission and the recovery rates. Following this way, in this paper, we present a SEIRS-SEI model for transmission of malaria dynamics in fuzzy environment.
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