Global Stability Analysis of a Caputo Fractional‐Order SEIR Model With a Linear Incidence Rate

ABSTRACT

To deal with real‐world problems across a variety of fields in basic and management sciences, mathematical modelling is decisive as such models rely on statistical findings to authenticate the conclusions of dynamic analyses. In this study, a fractional‐order model is investigated that incorporates a compartment for individuals who have been treated. We identified several properties of the model's solutions and examined the analytical results concerning the model's dynamics, which are influenced by the reproduction number, . Our analysis indicates that when is less than one, the disease‐free equilibrium () is globally, asymptotically stable (), suggesting that the disease will eventually diminish and disappear. On the other hand, if exceeds one, the becomes unstable, leading to the emergence of an endemic equilibrium () that is globally stable under specific conditions. Additionally, we utilized the Euler modification method for fractional‐order differential systems to conduct numerical simulations and assess the impact of treatment. Most of the computational work was done using MATLAB to demonstrate and confirm the accuracy of our analytical results and it was observed that as the treatment rate increases, the decreases. That is, the disease will eventually diminish and disappear as the treatment rate increases.