Mathematical study of the dynamics of lymphatic filariasis infection via fractional-calculus

Abstract

The infection of lymphatic filariasis (LF) is the primary cause of poverty and disability in individuals living with the disease. Many organizations globally are working toward mitigating the disease’s impact and enhancing the quality of life of the affected patients. It is paramount to inspect the transmission pattern of this infection to provide effective interventions for its prevention and control. Here, we formulate an epidemic model for the progression process of LF with acute and chronic infection in the fractional framework. The basic concept of the novel Atangana-Baleanu operator is presented for the analysis of suggested system. We determine the basic reproduction number of the system via the approach of next-generation matrix and investigate the equilibria of the system for stability analysis. We have shown the impact of input factors on the outcomes of reproduction parameter with the help of partial rank correlation coefficient approach and visualize the most critical factors. To conceptualize the time series analysis of the suggested dynamics, we propose utilizing a numerical approach. The solution pathways of the system are illustrated to demonstrate how different settings affect the system. We demonstrate the dynamics of the infection numerically to educate the policy makers and health authorities about the mechanisms necessary for management and control.

Qualitative and quantitative analysis of vector-borne infection through fractional framework

“…These models depart from traditional integer-order models by incorporating fractional calculus operators, which offer a more nuanced representation of epidemic processes characterized by complex and non-local interactions [31,29]. The effectiveness of fractional order models in the context of epidemic dynamics stems from their ability to capture the intricate and non-local interactions inherent in infectious disease transmission [11,4]. To further improve our comprehension of the dynamics of yellow fever transmission, we choose to use fractional derivatives to construct the dynamics of the infection.…”