A statistical estimation of fractional order cryptosporidiosis epidemic model

Abstract

Abstract In this study, a statistical estimation is done for an epidemic model of cryptosporidiosis by changing it into a fractional order system. The disease-free equilibrium point, and the endemic equilibrium point are the two equilibrium points and Jacobian matrix theory is used to determine stability. The basic reproductive number $${R}_{0}$$ is calculated and examined for its role in disease dynamics and stability analysis. The numerical technique named Grunwald Letnikov non-standard finite difference (GL-NSFD) scheme is designed for solving the fractional epidemic model. To investigate the characteristics and properties of numerical design, a test problem is considered for the simulation. For the underlying system, a non-classical numerical approach is suggested. The state variables cannot be negative because they describe the number of people. The suggested numerical scheme must have the properties of positivity and boundedness. The positivity and boundedness of the fractional order cryptosporidiosis epidemic model are investigated with the help of Laplace and inverse Laplace transformation. Finally, the conclusions of the study are elaborated.

Keywords

• Statistical estimation
• Fractional epidemic model
• GL non-standard finite difference schemes
• Positivity
• Boundedness
• Simulations