A Study of Mathematical Epidemiology Model of Dengue Spread with Fractional Properties

Mosquitoes in tropical regions of the world disseminate the severe and common disease dengue, which is brought on by four viruses, namely, Den 1–Den 4. A bite from a female adult Aedes mosquito can spread the disease from one person to another. Nonlocal differential operators with nonlocal and non-singular kernels can be used to represent the dynamics of spread because they transition from the exponential decay law to the power law as the waiting time distribution. The memory effect is evident because spread dynamics don’t actually follow the Markovian process. In this study, we used the recently developed fractional differential operators known as the Caputo-Fabrizio derivative to convert the classical model to a fractional kind systems in mathematics that account for crossover and memory effects. A recently developed numerical approach was used to solve the difficult unique system, and multiple numerical simulations were carried out to examine the crossover effect caused by the Mittag-Leffler law.