Fractional modeling and optimal control analysis of rabies virus under the convex incidence rate

Abstract

In this article, deterministic and fractional properties of the epidemic model for rabies considered with convex incidence rate are discussed. The dynamics are studied without control and some basic properties and results are studied. For disease-free equilibrium, the local and global stabilities conditions are given. For the given model, the basic reproductive number is derived using the next generation matrix method. We further consider the dynamics with some suitable strategies for optimal control. In the host population, for minimizing the infection, we have used four control variables. The effect of pre- and post-presentation prophylaxis on the two compartments is discussed. The results obtained are verified numerically using MATLAB. The mathematical and epidemiological meaningfulness is demonstrated by the obtained results. We have further shown that the implementation of additional control measures on the infected class of dogs and humans can minimize the spread of rabies infection in both populations. The study is performed using an operator of Caputo with a convex incidence rate. Using the fixed point approach, we further discuss the existence and uniqueness of the integral of the fractional model for rabies. Along with Ulam–Hyers stability analysis, for the given model, all basic properties are studied. Simulations are conducted using Adam’s Bashforth numerical approach to determine how parameters change influences the system’s dynamical behavior.

Keywords

• Rabies virus
• Fractional modeling
• Stability analysis
• Optimal control
• Adam’s Bashforth method