Modeling visceral leishmaniasis and tuberculosis co-infection dynamics

Abstract

The co-infection of visceral leishmaniasis (VL) and tuberculosis (TB) patients pose a major public health challenge. In this study, we develop a mathematical model to study the transmission dynamics of VL and TB co-infection by first analyzing the VL and TB sub-models separately. The dynamics of these sub-models and the full co-infection model are determined based on the reproduction number. When the associated reproduction number (R1) for the TB-only model and (R2) for the VL-only are less than unity, the model exhibits backward bifurcation. If max{R1,R2}=R1, then the TB-VL co-infection model exhibits backward bifurcation for values of R1. Furthermore, if max{R1,R2}=R2, and by choosing the transmission probability, βL as the bifurcation parameter, then the phenomenon of backward bifurcation occurs for values of R2. Consequently, the full model, whose associated reproduction number is R0, also exhibits backward bifurcation when R0=1. The equilibrium points and their stability for the models are determined and analyzed based on the magnitude of the respective reproduction numbers. Finally, some numerical simulations are presented to show the reliability of our theoretical results.

Dual Antitubercular and Antileishmanial Profiles of Quinoxaline Di-N-Oxides Containing an Amino Acidic Side Chain

“…Furthermore, tuberculosis may cause progression of latent leishmaniasis to the clinical stage, while visceral leishmaniasis can also reactivate latent tuberculosis. Thus, pulmonary tuberculosis and leishmaniasis (as well as other parasitic diseases) have been shown to be risk factors for each other [ 10 ] and due to their geographical overlap, co-infections are very common [ 11 , 12 , 13 , 14 ]. The low level of development of the countries with the highest prevalence of both infections makes the simultaneous treatment of these diseases difficult.…”

Modeling and analysis of visceral leishmaniasis dynamics using fractional‐order operators: A comparative study

“…Intensive studies over the years revealed that mathematical modeling and simulation can play a significant role in understanding the reasons for diverse infectious diseases, thereby predicting the possible cure. It is needless to say that mathematical modeling of VL has a rich history wherein numerous reports exist on the classical, fractional, statistical, machine learning models, and so forth [1][2][3][4][5][6][7][8][9]. In addition, it was acknowledged that the fractional calculus can offer deep insights into the dynamics of VL, leading to more accurate model and effective treatment strategies.…”