Mathematical Modelling of HIV-HCV Coinfection Dynamics in Absence of Therapy

Abstract

Globally, it is estimated that of the 36.7 million people infected with human immunodeficiency virus (HIV), 6.3% are coinfected with hepatitis C virus (HCV). Coinfection with HIV reduces the chance of HCV spontaneous clearance. In this work, we formulated and analysed a deterministic model to study the HIV and HCV coinfection dynamics in absence of therapy. Due to chronic stage of HCV infection being long, asymptomatic, and infectious, our model formulation was based on the splitting of the chronic stage into the following: before onset of cirrhosis and its complications and after onset of cirrhosis. We computed the basic reproduction numbers using the next generation matrix method. We performed numerical simulations to support the analytical results. We carried out sensitivity analysis to determine the relative importance of the different parameters influencing the HIV-HCV coinfection dynamics. The findings reveal that, in the long run, there is a substantial number of individuals coinfected with HIV and latent HCV. Therefore, HIV and latently HCV-infected individuals need to seek early treatment so as to slow down the progression of HIV to AIDS and latent HCV to advanced HCV.

Mathematical Modelling of HIV-HCV Co-infection Dynamics in Presence of HIV Therapy

“…We categorized the chronic HCV stage as in [17], that is: latent and advanced HCV, where latent HCV is characterized by a long infectious period during which infection is undiagnosable because there are no or mild symptoms for a long time; and advanced HCV characterized by onset of cirrhosis and its related complications. The total population is divided into eleven distinct compartments, defined as follows: the susceptible, S(t); infected with HIV without AIDS symptoms and not on HIV treatment, I h (t); infected with HIV without AIDS symptoms and are on HIV treatment, I T (t); individuals who have developed AIDS symptoms, Ã(t); acutely HCV-infected, I a (t); latent HCV, I l (t); advanced HCV, B(t); co-infected with HIV and acute HCV, not on HIV treatment, I ha (t); coinfected with HIV and acute HCV, on HIV treatment, I T a (t); co-infected with HIV and latent HCV, not on HIV treatment, I hl (t); and those co-infected with HIV and latent HCV, on HIV treatment, I T l (t).…”

“…The global stability property of the endemic equilibrium of the HIV-only submodel can be investigated using the techniques in [17].…”

“…However, the chronic stage of HCV infection needs to be given a special attention because is very long, asymptomatic and infectious. Recently, Mayanja et al (2020) [17], formulated and analysed a deterministic model to study the HIV and HCV co-infection dynamics in absence of therapy; but with the HCV chronic stage split into two stages i.e. before and after onset of cirrhosis and its complications.…”

“…The dynamics of HIV-HCV co-infection in absence of therapy were dominated by HIV. In this work, we extend the work in [17] by introducing HIV treatment and model the dynamics of HIV-HCV coinfection in presence of HIV treatment. Though HIV and HCV may share other transmission routes, in this work we only considered sexual transmission among sexually active individuals as done in [17].…”

HIV/AIDS-Pneumonia Coinfection Model with Treatment at Each Infection Stage: Mathematical Analysis and Numerical Simulation

“…The Basic Reproduction Number of the Submodel. The basic reproduction number of HIV/AIDS-infected individuals denoted by R H is defined as the average number of secondary infections produced by a single HIV/AIDS infectious individual introduced in a wholly susceptible population during his or her entire infectious period [14,20]. This definition is given for the dynamical system that represents the spread of infection in a population.…”