A dynamically consistent approximation for an epidemic model with fuzzy parameters. (30th December 2022) - Dayan, Fazal; Ahmed, Nauman; Rafiq, Muhammad; Iqbal, Muhammad Sajid; Khan, Ilyas; Raza, Ali; Ahmad, Muhammad Ozair
Abstract: In this article, a susceptible, infectious, and recovered (SIR) model with fuzzy parameters is discussed. These concepts are uncertain due to the different degrees of susceptibility, infectivity, and recovery among the individuals in the population. Differences may appear when the populations considered have different ages, habits, customs, and different levels of resistance, etc. More realistic models are needed which consider these different degrees of susceptibility, infectivity, and recovery of the individuals to overcome the above uncertainties. The existence and uniqueness of the model are studied. Forward Euler and NSFD methods were employed to solve the model in classical and fuzzy senses. The developed fuzzy NSFD method preserves positivity and convergence which are the main features of a dynamic system. To the best of our knowledge, the numerical analysis of the studied SIR model using the forward Euler, fuzzy Euler, NSFD, and FNSFD schemes has not been specifically studied in the literature. Highlights: A SIR epidemic model with fuzzy parameters is proposed. Existence analysis of fuzzy epidemic model is given. Fuzzy reproduction number is computed in this paper. A structure preserving numerical method is used for the solution of fuzzy epidemic model. Comparison of the proposed method with other methods is also presented.