VL; HIV; Co-infection; MEnhancing reservoir control in the co-dynamics of HIV-VL: from mathematical modeling perspectiveathematical model; Stability analysis; Numerical simulation 1 Introduction Visceral leishmaniasis (VL)

Abstract

HIV patients are vulnerable to developing active visceral leishmaniasis (VL). To understand this complication, we studied a mathematical model for HIV and visceral leishmaniasis coinfection. In this approach, we reckoned two distinct equilibria: the disease-free and the endemic equilibria. The local and global stability of the disease-free equilibrium were thoroughly investigated. To further support the qualitative findings, we performed simulations to quantify the changes of the dynamical behavior of the full model for variation of relevant parameters. Increasing the rate of VL recovery (φ1), the recovery rate for VL–HIV Co-infection (φ2), removing reservoirs (c1), minimizing the contact rate (βh) are important in controlling the transmission of individual and co-infection disease of VL and HIV. In conclusion, possible measures should be implemented to reduce the number of infected individuals. Therefore, we recommend that policy makers and stakeholders incorporate these measures during planing and implementation phases to control the transmission of VL–HIV co-infection. Keywords: VL; HIV; Co-infection; Mathematical model; Stability analysis; Numerical simulation 1 Introduction Visceral leishmaniasis (VL) also known as ‘Kala-azar’ is a vector borne, zoonotic disease caused by Leishmania donovani species [1, 2]. There are more than 20 species of leishmania that can cause human infection. The infection is transmitted following a successful bite and inoculation by the infected phlebotomine female sand flies [3, 4]. TheWorld Health Organization(WHO) considers leishmaniasis as the sixthmost important endemic disease in the world [5], and it is distributed around the world in 90 countries [6], most of which are developing countries associated withmalnutrition, population displacement, poor housing, a weak immune system, and lack of financial resources [6].WHOestimated that from about 900,000 to 1.3 million new cases of leishmaniasis are reported per year [1, 2, 6, 7]; of these, approximately 0.2–0.4 million are of visceral leishmaniasis (VL) [6, 7]. The spread of the disease is linked to environmental changes such as deforestation, building of dams, irrigation schemes, and urbanization [7]. © The