Analysis of tinea capitis epidemic fractional order model with optimal control theory

Abstract

Tinea Capitis is a common worldwide fungal infectious disease. This paper investigates the transmission dynamics of tinea captis infection using Caputo fractional derivative approach. The qualitative analysis part of the proposed fractional order model investigates: the model solutions existence and uniqueness by using the well-known Picard–Lindelöf criteria, the basic reproduction number using the next generation matrix approach, the model equilibrium points and their stabilities. The study re-formulates the fractional order optimal control problem with the three time-dependent controlling variables such as prevention measure, acute infection treatment measure and chronic infection treatment measure and also investigates the necessary optimality conditions and the existence of optimal control strategies by applying Pontryagin's Maximum Principle. Finally, the paper examines the effectiveness of the combinations of the three controlling strategies through numerical simulations and the results indicate that the simultaneous implementation of the three time-dependent controlling strategies significantly minimizes the number of tinea capitis infected individuals in the community.