Optimal control and cost-effectiveness analysis of a fractional order drug-resistant malaria transmission model with recovered carriers

Malaria is still a life threatening parasitic disease due to the change in environmental and socio-economic conditions. This paper introduces a novel mathematical model to study the impact of drug-resistant strain, recovered-carrier, and relapse on malaria dynamics by implementing Caputo-Fabrizio fractional order derivative (CFFOD). We begin by presenting theoretical results that are derived for our model. We also derive the expression for the control reproduction number and investigate the equilibria of the proposed model. Theoretical analysis guarantees the presence of a unique solution to the suggested model. We use a combination of Runge-Kutta fourth order method and three-step Adams-Bashforth scheme to obtain numerical solution. Additionally, to control the spread of malaria and also to understand the epidemiological characteristics and public health indicators of malaria, three control variables are introduced in this model. Finally, a rigorous cost-effectiveness analysis is performed to determine the most economical control variable. The possibility of backward bifurcation is suggested by numerical simulation, which reveal the coexistence of a stable disease free equilibrium (DFE) and a stable endemic equilibrium point (EEP). According to the simulation, it is also observed that due to the existence of recovered carriers in the population the disease tends to linger. The study further reveals that an increase in the drug-resistant strain increase the disease-related complexity. A thorough sensitivity analysis is also carried out to identify the most sensitive parameters that control the basic reproduction number. According to our findings, vaccination control is the most cost-effective strategy to reduce disease burden.