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. 2023 Oct 26;18(10):e0288024.
doi: 10.1371/journal.pone.0288024. eCollection 2023.

Computational analysis of control of hepatitis B virus disease through vaccination and treatment strategies

Azhar Iqbal Kashif Butt  1   2 , Muhammad Imran  2   3 , Javeria Aslam  2 , Saira Batool  4 , Saira Batool  2
Affiliations

Computational analysis of control of hepatitis B virus disease through vaccination and treatment strategies

Azhar Iqbal Kashif Butt et al. PLoS One. .

Abstract

Hepatitis B disease is an infection caused by a virus that severely damages the liver. The disease can be both acute and chronic. In this article, we design a new nonlinear SVEICHR model to study dynamics of Hepatitis B Virus (HBV) disease. The aim is to carry out a comprehensive mathematical and computational analysis by exploiting preventive measures of vaccination and hospitalization for disease control. Mathematical properties of proposed model such as boundedness, positivity, and existence and uniqueness of the solutions are proved. We also determine the disease free and endemic equilibrium points. To analyze dynamics of HBV disease, we compute a biologically important quantity known as the reproduction number R0 by using next generation method. We also investigate the stability at both of the equilibrium points. To control the spread of disease due to HBV, two feasible optimal control strategies with three different cases are presented. For this, optimal control problem is constructed and Pontryagin maximum principle is applied with a goal to put down the disease in the population. At the end, we present and discuss effective solutions obtained through a MATLAB code.

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Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Fig 1
Fig 1. Flow diagram.
HBV disease transmission through compartments.
Fig 2
Fig 2. Local stability at DEF.
Behavior of state variables for R0 < 1 and for R0 > 1.
Fig 3
Fig 3. Optimal control variable and corresponding cost functional.
The cost functional has reached to its minimum with the optimal vaccine rate β4.
Fig 4
Fig 4. Optimized state variables.
Figure shows state variables before and after optimization. A decrease in the infected and carrier individuals is noticed with the implemented vaccine strategy.
Fig 5
Fig 5. Optimal control variables and corresponding cost functional.
The figure shows optimal controllers that have minimized the cost functional with treatment strategy.
Fig 6
Fig 6. Optimized state variables.
Figure shows state variables before and after optimization. A remarkable decrease in the exposed, infected and carrier individuals is noticed with the implemented treatment strategy.
Fig 7
Fig 7. Optimal control variables and corresponding cost functional.
Figure shows the optimal vaccine and treatment rates that have minimized the cost functional.
Fig 8
Fig 8. Optimized state variables.
Figure shows optimal behaviour of state variables before and after optimization. A remarkable decrease in the exposed, infected and carrier individuals is noticed under the strategy when both vaccination rate and treatment rates are considered together as control variables.
See this image and copyright information in PMC

References

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