Modelling the Effect of Treatment and Infected Immigrants on the Spread of Hepatitis C Virus Disease with Acute and Chronic Stages

Abstract

This paper examines the effect of Treatment and Infected Immigrants on the spread of Hepatitis C Virus (HCV) disease with Acute and Chronic stages. A nonlinear mathematical model for the problem is proposed and analysed qualitatively using the stability theory of the differential equations. The results show that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Globally, the disease free equilibrium is not stable due existence of forward bifurcation at threshold parameter equal to unity. However the disease becomes more endemic due to the presence of infected immigrants in the community. It is also shown that in the presence of treatment, the rate of infected immigrants (acute and chronic) decreases and consequently the treated infected individuals decreases continuously. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the treatment and infected immigrants on the spread of the disease with acute and chronic stages.

A Mathematical Framework for Modeling the Spread of HIV-disease within two Different Age Classes

“…For R 0 > 1, we obtain from mathematical analysis a quadratic equation in i 1 1 . It has been proven that the existence of an endemic equilibrium depends on the existence of at least one real positive value for i 1 1 . The stability analysis of endemic equilibrium produces that if the Routh-Hurwitz criterion are satisfied, then the endemic equilibrium E * is locally asymptotically stable.…”

“…We determine the basic reproduction number R 0 using the next generation matrix method at Disease-Free Equilibrium [12]. According to this method, R 0 is defined as the effective number of secondary infections caused by typical infected individual during his/her entire period of infectioussness [1,4]. Let X be the vector of infected classes:…”

“…HIV-AIDS is usually transmitted in three different ways, namely the sexual contact, blood transfusion, mother-to-child exchanges during pregnancy, childbirth and breastfeeding. Many mathematical models are used to study the impact of preventive control strategies on the spread of HIV-AIDS in given populations [1,3,5,6,[9][10][11][12][13][14]. Some of these models have shown that a change in risky behavior is necessary to prevent the spread of HIV-AIDS, even in the presence of a treatment [2,8].…”

Modelling and Simulating a Transmission of COVID-19 Disease: Niger Republic Case

“…We determine the basic reproductive number by using the next generation matrix method [ [4], [10]] at Disease Free Equilibrium. The basic reproductive number R 0 is defined as the effective number of secondary infections caused by typical infected individual during his/her entire period of infectioussness [ [5], [3]]. Let X be vector of infected classes:…”

Mathematical Analysis of Control Strategies of HCV in a Community with Inflow of Infected Immigrants

“…Mathematical modelling of the spread of infectious diseases continues to become an important tool in understanding the dynamics of diseases and in decision making processes regarding diseases intervention programs for disease in many countries. For instance, [3] formulated and analysed a mathematical model on the effect of Treatment and Infected Immigrants on the spread of Hepatitis C Virus disease at Acute and Chronic stages. [4] considered SEI (Susceptible-Exposed-Infective) epidemic model with acute and chronic stages.…”