Dynamical analysis of Malaria transmission with temporary immunity and fuzzy parameters through mathematical modeling

Resumen

Malaria is one of the most prevalent mosquito-borne diseases across the globe, which is contracted through an Anopheles mosquito bite and continues to pose a major threat to human health in tropical and subtropical regions of the world. The vaccine for malaria has not been developed yet to provide full immunity from the infection of the disease. The best defense against this disease's spread is to control the interaction between individuals and mosquitoes. Also, the spread of malaria can be reduced by administering effective treatment and monitoring the duration of immunity in the recovered individual. In view of this, to examine the dynamics of malaria transmission, we incorporated fuzzy theory to account for the uncertainty in disease dynamics caused by fluctuations in viral loads. Thus, the novel fuzzy SIRSI compartmental epidemic model for malaria disease transmission has been proposed, including the rate of disease transmission, rate of acquired temporary immunity, and rate of disease-induced mortality as functions of the viral load. The positivity and boundedness of the epidemic model have been established. A mathematical analysis of the epidemic model has been conducted, where equilibrium points, basic reproduction number as a function of viral load, and fuzzy basic reproduction number have been obtained, and stability analysis for equilibrium points has been performed. An expression for the bifurcation value of the viral load, where the basic reproduction number becomes one, has been derived. Also, fuzzy global stability has been carried out by using the approach of graph theory. Numerical simulations have been performed to verify the analytical findings of the epidemic model. Latin hypercube sampling and partial rank correlation coefficients have been used to perform global sensitivity analysis for the basic reproduction number. These findings highlight the necessity for public health officials and policymakers to implement prevention strategies to effectively control the spread of malaria disease in human society.