Fractional modeling of Hansen's disease (Leprosy) transmission dynamics

Hamadjam Abboubakar (1) , Raissa Kom (1) , Rubin Fandio (2) , H P Ekobena Fouda (2)

1 UN - Université de Ngaoundéré/University of Ngaoundéré [Cameroun]
2 UY1 - Université de Yaoundé I

In this work, we study a mathematical model for the Hansen's disease (leprosy) transmission dynamics with both integer and fractional derivatives in the Caputo sense. After the model formulation, we compute the leprosy reproduction number R 0 and prove the existence of two steady states named the Leprosy-free equilibrium and the leprosy-endemic equilibrium which exists and is unique if and only if R 0 > 1. Using the general theory of Lyapunov, we prove the global asymptotic stability of both steady states, for both models. The existence and uniqueness of the solutions of the fractional model are proved using fixed point theory. We finally perform numerical simulations to validate our analytical results, as well as to evaluate the impact of varying the fractional-order parameter on the disease dynamics.

Mots clés: Hansen's disease (Leprosy); Fractional derivative; Caputo derivative; Asymptotic stability; Fixed point theory

Domaines: Systèmes dynamiques [math.DS]

Hamadjam Abboubakar, Raissa Kom, Rubin Fandio, H P Ekobena Fouda. Fractional modeling of Hansen's disease (Leprosy) transmission dynamics. Colloque Africain sur la Recherche en Informatique et en Mathématiques Appliquées (CARI), Oct 2022, Tunis, Tunisia. ⟨hal-03702649⟩