Effect of Intervention of Vaccination and Treatment on the Transmission Dynamics of HBV Disease: A Mathematical Model Analysis

Abstract

Hepatitis B is a globally infectious disease. It is pretty contagious and can be transmitted by blood or bodily fluids, through things like sharing razors and toothbrushes. It has been called the silent killer because it is asymptomatic, one might have the virus but not know until it manifests itself until much later. Since people do not give attention, it will develop into cirrhosis and hepatocellular carcinoma that leads to liver transplantation and death. This nature of HBV disease motivated us to perform this work. Mathematical modeling of HBV transmission is an interesting research area. In this paper, we present characteristics of HBV virus transmission in the form of a mathematical model. We proposed and analyzed a compartmental nonlinear deterministic mathematical model SEACTR for transmission dynamics and control of hepatitis B virus disease. In this model, we used force infection which takes the contact rate of susceptible population and transmission probability into account. We proved that the solution of the considered dynamical system is positive and bounded. The model is studied qualitatively using the stability theory of differential equations and the effective reproductive number which represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. The sensitivity index shows that the transfer rate from exposed class to acute infective class and transfer rate from exposed class to chronic infective class are the most dominant parameters contributing to the transmission of HBV. On the one hand, the vaccination rate and treatment rate are the parameters that suppress the transmission of the disease the most, and enhancing the vaccination rate for newborns and treatment for chronically infected individuals is very effective to stop the transmission of HBV. The combined efforts of vaccination, effective treatment, and interruption of transmission make elimination of the infection plausible and may eventually lead to the eradication of the virus.

Appraisal and Simulation on Codynamics of Pneumonia and Meningitis with Vaccination Intervention: From a Mathematical Model Perspective

“…Definition . the normalized forward sensitivity index of a variable meningitis and pneumonia reproduction number denoted by the symbol ℛ eff that depends differentially on a parameter ξ is defined as SI( p ) = ∂ℛ eff / ∂ξ ∗ ξ / ℛ eff [ 2 , 17 ].…”

“…where Y ∈ ℝ m be the components of noninfected individuals and W ∈ ℝ n be the components of infected individuals including treated class and E 0 p = ðY * , 0Þ denotes the diseasefree equilibrium point of dynamical system (2). Assume (i) For ðdY/dtÞ = GðY, 0Þ, Y * is globally asymptotically stable (GAS) (ii) HðY, WÞ = BW − H ˇðY , WÞ, H ˇðY , WÞ ≥ 0 for ðY, WÞ ∈ Ω 1 where B = D W HðY * , 0Þ is an M-matrix, i.e., the off diagonal elements of B are nonnegative and Ω 1 is the region in which the system makes biological sense.…”

“…In other words, the term “epidemiology” has its roots in the study of the experiences of a population. Despite the fact that many definitions have been provided, the one that best encapsulates the fundamental ideas and public health perspective of epidemiology is: “Epidemiology is the study of the prevalence and causes of health-related conditions or incidents in particular populations, as well as the application of this information to the prevention or treatment of health issues” [ 1 , 2 ]. In epidemiology, the frequency and distribution of health events in a population are studied.…”

“…By the term “frequency,” we not only mean the number of health events, such as the number of cases of meningitis or diabetes in a population, but also the correlation between that number and the size of the population [ 2 , 3 ].…”

Coinfection Dynamics of HBV-HIV/AIDS with Mother-to-Child Transmission and Medical Interventions

“…Recently, numerous scholars are concentrated on the study of the transmission dynamics of a particular and coinfection of various diseases and how the diseases might be effectively managed and potentially eliminated. Wodajo and Mekonnen [20] proposed a mathematical model to study the dynamics of hepatitis B virus infection under the administration of vaccination and treatment, where HBV infection is transmitted in two ways through vertical and horizontal transmission. Their results show that the combined efforts of vaccination, effective treatment, and interruption of transmission make elimination of the infection plausible and may eventually lead to the eradication of the virus.…”