Numerical and Dynamical Analysis of an Infectious Disease Epidemic Model Through Fractional Derivative

Abstract

Nipah virus infection is a dreadful disease for human lives. In this work, an integer order model of Nipah virus transmission is converted into a fractional order model by using Caputo fractional differential operator for a more realistic approach to the disease transmission phenomena. On that account, the projected fractional model is dealt with analytically and numerically. The continuous system has two states of dynamic disease equilibrium i.e. disease-free state and endemic state. Moreover, the underlying system has a unique solution. The positivity and the boundedness of the fractional system are thoroughly investigated. The basic reproduction number R0 is worked out mathematically. The contribution of basic reproductive number R0 in stability analysis and disease dynamics is explored. The nonstandard numerical scheme is developed for finding the approximate solutions of the fractional system. The salient features of the state variables are examined to measure the efficacy of the numerical method. The article is closed by enlisting some productive and novel outcomes of the study.

Keywords Fractional epidemic model, GL non-standard finite difference schemes, LaSalle Principal, Nipah virus (NVD)