Data Fitting of a Dynamic Model of Hbv Based on Acute Patient Cases in the United States with its Optimal Control and Prevention Strategies

Abstract

According to the World Health Organization statistics, the world will add 1.5 million hepatitis B patients every year; the medical community has not yet studied the effective thing to eliminate HBV; it is only through some means to prevent and control. In this paper, based on the epidemiological characteristics of HBV infectious disease, an infection-age structure model is constructed that is more suitable for the actual situation. This main purpose of the model is to explain the different duration of HBV transmission, and it is transmitted by horizontal and vertical transmission. Real data of acute hepatitis B patients in the United States from 2013 to 2021 are collected for data fitting, and optimal parameters are obtained. The most sensitive parameter values are obtained, and the corresponding control measures are formulated. The necessary conditions for the optimal control of HBV are obtained through Pontryagin's Maximum Principle, and the number of HBV patients is effectively controlled. At the same time, we study the effectiveness of different strategies for the prevention and treatment of HBV in combination with the actual situation. Finally, through the cost-effectiveness analysis, we conclude that the earlier implementation of hepatitis B vaccination prevention is the most cost-effective measure.

Note:
Funding Declaration: This research is supported by the National Natural Science Foundation of China (Nos. 12326335, 12326341), and the Natural Science Foundation of Xinjiang (No. 2022D01A198).

Conflicts of Interest: None

Keywords: HBV, Infection-age, Optimal control, Cost-effectiveness, Data fitting