Modeling and Simulation of Typhoid Fever Using a Fractional-Order Approach with the Generalized Adams–Bashforth–Moulton Method

We consider the epidemiological characteristics of Typhoid fever infection in this paper in the equation of a fractional-order mathematical model in Caputo derivative. The interventions that are employed in the model to control the disease include treatment and vaccination to investigate the impact of the controls on the dynamics of the disease. The existence and uniqueness of solutions under the frame of the fractional order and the stability of the endemic equilibrium point are defined and tested by the theory of Lyapunov functions. The model is numerically determined by using the fractional Adams-Bashforth-Moulton algorithm to point out the modification of the model parameters and the fractional orders of the model parameters into the influence of each of the above parameters on the disease progression. It has been demonstrated by the use of simulation that increased treatment and vaccination of the disease reduces the prevalence of Typhoid fever, and indicates the high degree of flexibility and realism of the fractional-order models compared to the classical integer order equations. The significance of fractional modeling in the description of the interactions between the effects of memory and nonlocal interaction between the biological systems is identified in the paper, and this improves the comprehension and management of infectious diseases. The model however presupposes that the population is homogeneous mixed and hypothetical values of the parameters therefore inhibits empirical validation. In order to render the model more predictive and applicable in practice in the development of effective control strategies on Typhoid fever, future investigations should be able to incorporate the spatial heterogeneity, stochastic effects.