A fractional modeling approach of Buruli ulcer in Possum mammals

Abstract

Buruli ulcer is an increasingly common tropical disease that has been even ignored in advanced nations like Australia and Japan. Some mammals, including possums, have shown symptoms of the disease. Fractional derivatives are applied for a better understanding of biological processes and their crossover behavior. Infectious disease can be controlled by predicting the future spread while using Mathematical Models. Recently, various mathematical models based on classical integer-order and non-integer-order models have been proposed to predict the dynamics of infectious disease outbreaks. As a consequence, it is investigated the dynamics of the possum model using non-integer order derivatives in order to gain a better understanding and deeper insight into several biological models. The model’s important properties, such as the positivity of the model solution, equilibrium points, and the invariant property of the proposed model have also been discussed. The next-generation approach is used to compute the basic reproductive number . Both the stability i.e. the local and global are obtained when is less or greater than 1. The global stability of the fractional Possum model is achieved using the Lyapunov function in a fractional environment. Furthermore, The existence and uniqueness of the fractional order models are demonstrated. Numerical simulations of the model are done, along with their graphical representations, to examine the effects of arbitrary order derivatives and depict the implications of our theoretical results. It can be seen from the graphical findings that the fractional model provides more clarity and a better understanding.