Mathematical fractional model for the dynamics and control of Diphtheria transmission

Abstract

Diphtheria is an acute bacterial infection primarily affecting the upper respiratory tract, caused by Corynebacterium diphtheriae. This study uses a fractional-order mathematical model to assess the effects of therapy and vaccination on diphtheria transmission dynamics. Initially, the model employs integer-order nonlinear differential equations with minimal vaccination and treatment. To better understand disease dynamics, it is then adapted with fractional-order derivatives and power laws. The research includes a stability analysis of the endemic equilibrium using the Lyapunov function approach and establishes conditions for the existence and uniqueness of solutions in the fractional-order model. To explore factors influencing disease spread, a sensitivity analysis of the basic reproduction number was conducted. Numerical simulations using the fractional Adams–Bashforth–Moulton method offer insights into how model parameters and fractional-order values impact diphtheria dynamics and control. Additional simulations with surface and contour plots revealed that higher contact rates and lower vaccine efficiency would increase diphtheria prevalence. Conversely, improving treatment and immunization programs is expected to reduce the incidence of diphtheria in the general population.