Analysis of fractional-order dynamics of dengue infection with non-linear incidence functions

Abstract

The infection of dengue is a devastating mosquito-borne infection around the globe that affects human health, social and economic sectors in low-income areas. Therefore, policymakers and health experts are trying to point out better policies to reduce these losses and provide better information for the development of vaccination and medication. Here, we formulated a compartmental model for the transmission phenomena of dengue fever with nonlinear forces of infection through fractional derivative. We established several results related to the solution of our dengue model by using the basic properties of fractional calculus. We determined the basic reproduction number of our fractional-order system, symbolized by $R_0$ . We established the local asymptotic stability of the infection-free equilibrium of our dengue system for $R_0<1$ , and proved that the infection-free equilibrium is globally asymptotically stable without vaccination. The threshold dynamics $R_0$ is tested through partial rank correlation coefficient method to notice the importance of parameters in the transmission of dengue infection. In addition, we have shown the impact of memory on the basic reproduction number numerically with the variation of different parameters. We conclude that the biting rate, recruitment rate of mosquitoes and index of memory are the most sensitive factors, which can effectively lower the level of dengue fever. The dynamical behavior of the proposed fractional system is presented through a numerical scheme to explore the overall transmission process. We predict that the fractional-order model can explore more accurately and preciously the intricate dengue disease transmission model rather than the integer-order derivative.