A Malaria Status Model: The Perspective of Mittag-Leffler Function with Stochastic Component

Abstract

Malaria continues to affect many individuals irrespective of the status or class particularly in Sub-Saharan Africa. In this work, an existing malaria status classical model is studied in fractionalized perspective. The positivity and boundedness of the malaria model is studied. The existence and uniqueness of solutions based on fractional derivative and stochastic perspective is established. The numerical simulation results depict that the infectious classes of humans and vector increase as the fractional order derivative increases. Susceptible classes humans and vector reduce as the fractional order derivative increases. This phenomenon is peculiar with epidemiological models. The implications of the results are that in managing the dynamics of the status model, the fractional order derivative as well as its associated operator is important. It is observed that fractional order derivative based on Mittag-Leffler function provides a better prediction because of its crossover property, its non-local and non-singular property.