scholarly journals Effect of Control on the Mathematical Model of Hepatitis B Virus with Infective Migrant

2020 ◽  
pp. 58-70
Author(s):  
Folahan S. Akinboro ◽  
T. O. Oluyo ◽  
O. O. Kehinde ◽  
S. Alao
Keyword(s):  
Mathematical Model ◽  
Hepatitis B Virus ◽  
Hepatitis B ◽  
Control Strategy ◽  
Transmission Dynamics ◽  
Optimal Control Strategy ◽  
Control Variables ◽  
B Virus ◽  
Implicit Finite Difference ◽  
The Mathematical Model

The transmission dynamics of Hepatitis B Virus in a population with infective immigrant is presented with the inclusion of an optimal control strategy to curtail the spread of the virus. To understand the spread of this infection, we develop a mathematical model with control variables of migrant screening and public sensitization. The optimality system is characterized using Pontryagin’s maximum principle and solve numerically with an implicit finite difference method.  Result of the numerical simulation is presented to illustrate the feasibility of this control strategy. The analysis reveals that combination of both control variables could be the most fruitful way to reduce the incidence of Hepatitis B virus.

scholarly journals Mathematical Modeling of Transmission Dynamics and Optimal Control of Vaccination and Treatment for Hepatitis B Virus

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Ali Vahidian Kamyad ◽  
Reza Akbari ◽  
Ali Akbar Heydari ◽  
Aghileh Heydari
Keyword(s):  
Optimal Control ◽  
Hepatitis B Virus ◽  
Hepatitis B ◽  
Public Health Problem ◽  
Hbv Infection ◽  
Optimal Control Strategy ◽  
B Virus ◽  
Existence And Stability ◽  
Steady State Solutions ◽  
Disease Free

Hepatitis B virus (HBV) infection is a worldwide public health problem. In this paper, we study the dynamics of hepatitis B virus (HBV) infection which can be controlled by vaccination as well as treatment. Initially we consider constant controls for both vaccination and treatment. In the constant controls case, by determining the basic reproduction number, we study the existence and stability of the disease-free and endemic steady-state solutions of the model. Next, we take the controls as time and formulate the appropriate optimal control problem and obtain the optimal control strategy to minimize both the number of infectious humans and the associated costs. Finally at the end numerical simulation results show that optimal combination of vaccination and treatment is the most effective way to control hepatitis B virus infection.

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