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.

Fig. 1

Illustration of the PRCC results of significance test for ${\mathcal{R}}_0$

Fig. 2

Graphical view analysis of the solution pathways of the recommended model (5) of LF with the input parameter $ħ$

Fig. 3

Graphical view analysis of the time series of the suggested model (5) of LF with the input factor $ħ$

Fig. 4

Illustration of the progression route of the model (5) of LF with various values of input factor ${\varrho }_{\mathrm{h}}$

Fig. 5

Illustration of the progression route of the model (5) of LF infection with various values of input factor ${\varrho }_{\mathrm{h}}$

Fig. 6

Graphical representation of the solutin pathways of the fractional system (5) of LF with different values of $\beta$