TITLE:
Fuzzy Global Stability Analysis of the Dynamics of Malaria with Fuzzy Transmission and Recovery Rates
AUTHORS:
Yves Tinda Mangongo, Joseph-Désiré Kyemba Bukweli, Justin Dupar Busili Kampempe
KEYWORDS:
Malaria, Fuzzy Analysis, Fuzzy Basic Reproduction Number, Fuzzy Variable, Credibility Measure, Fuzzy Equilibrium, Fuzzy Global Stability
JOURNAL NAME:
American Journal of Operations Research,
Vol.11 No.6,
October
26,
2021
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 equilibriumis 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.