Investigating the effects of some controls measures on the dynamics of diphtheria infection using fractional order model

In this study, we presented a computationally intensive alternative and a suitable time-fractional order model to further comprehend the transmission dynamics of Diphtheria and study the overall effects of some control measures on its transmission. Public awareness (U1), immediate treatment after being diagnosed (U2) and the combination of both controls (U3) are the three measures considered and all parameters and conditions that guarantee feasible of the proposed SEIR model: uniqueness and existence of solutions, the reproduction number, boundedness and positivity of solutions, global and local stability analysis of the disease-free equilibrium state was thoroughly analyzed and established, the Adam’s Bashforth predictor-corrector method was utilized for the numerical solution, More interestingly, analysis of the optimal control from simulations emphasized gradual elimination of the infection in the population and finally flattens the transmission curve and so health practitioner and concerned authorities are better educated about possible control measures and the overall combine effects of such measures.