Malaria and cholera co-dynamic model analysis furnished with fractional-order differential equations

Abstract

This paper presents malaria and cholera co-dynamics under Caputo-Fabrizio derivative of order $\alpha\in(0,1)$ varied with some notable parameters in the fractional system. The fractional order system comprises ten compartments divided into human and vector classes. The human population is exposed to obnoxious diseases such as malaria and cholera which can lead to an untimely death if proper care is not taken. As a result, we present the qualitative analysis of the fractional order system where the existence and uniqueness of the solution using the well-known Banach and Schauder fixed point theorems. The numerical solution of the system is achieved through the famous iterative Atangana-Baleanu fractional order Adams-Bashforth scheme. The numerical algorithm obtained from the scheme is used for graphic simulation for different fractional orders $\alpha\in (0,1)$. The figures produced using various fractional orders show total convergence and stability as time increases. It is also evident that stability and convergence are achieved as the fractional orders tend to 1. The actual behavior of the fractional co-dynamical system of the diseases is established also in the numerical simulation.

Study of fractional order SIR model with M-H type treatment rate and its stability analysis

“…Indeed, high vaccination rates have resulted in dramatic reductions or even elimination of a variety of infectious illnesses, such as smallpox [18], SARS-CoV-2 infection [19,20]. In the modeling of infectious illnesses [21][22][23][24][25][26][27], the incidence rate is crucial in determining the behavior at phenomena. In 1927, Kermack and Mckendrick [1] proposed the transmission rate as βSI.…”