Fractional order malaria epidemic model: Qualitative and computational study to determine the dynamics for sensitivity prevalence

Abstract

In this study, we created a nonlinear mathematical model with eight compartments to understand the dynamics of malaria transmission in North Cyprus region using the Caputo fractional operator. Because of their memory and genetic features, fractional-order models are regarded to be more adaptable than integer-order models. To explore the malaria compartmental model, we use the stability theory of fractional-order differential equations with the Caputo operator. A full explanation of the proposed model’s qualitative and quantitative analysis is offered, as well as a brief overview of its essential aspects and a theoretical evaluation. The Lipschitz criterion and well-known fixed point theorems are used to prove the existence and uniqueness of solutions. In addition to establishing equilibrium points, sensitivity analysis of reproductive number parameters is carried out. The proposed system has been validated in terms of Ulam–Hyers–Rassias. To deal with chaotic circumstances a linear feedback control strategy directs system dynamics near equilibrium points. To verify the existence of bifurcation, we apply bifurcation principles. The study uses numerical methodology based on Newton polynomial interpolation method to graphically model the solutions. The study analyzes system behavior by investigating parameter alterations at various fractional orders while retaining model stability. The long-term memory effect, represented by the Caputo fractional order derivative, has no influence on steady point stability, but solutions get closer to equilibrium faster at higher fractional-orders.