Dynamical behavior of an epidemic model with fuzzy transmission and fuzzy treatment control

In this paper, we have considered an SIS epidemic model with arbitrary disease transmission function and arbitrary treatment control function. We have analyzed the model considering the disease transmission function as an increasing and decreasing function separately. To introduce heterogeneity in the system we have taken both the disease transmission function and treatment function as fuzzy numbers. Fuzzy expected value of the infected individual is defined and determined. Then fuzzy basic reproduction number is computed. At last, a threshold value is determined in both the cases where the system undergoes a transcritical and backward bifurcation.

Automated summary

In this study, an SIS epidemic model with arbitrary disease transmission function and treatment control function was considered. The model was analyzed by treating the disease transmission function as both an increasing and decreasing function. To introduce heterogeneity, fuzzy numbers were used for both the disease transmission and treatment functions. The fuzzy expected value of the infected individual was defined and computed, leading to the determination of a fuzzy basic reproduction number. A threshold value was then determined for both cases of the system undergoing a transcritical and backward bifurcation.