# Data fitting and optimal control strategies for HBV acute patient cases in the United States

## TL;DR

This paper models HBV transmission in the US and finds that early vaccination is the most cost-effective way to control the spread of the virus.

## Contribution

A novel dynamic model with infection-age structure is proposed to analyze HBV transmission and control strategies.

## Key findings

- A mixed approach with vaccination, medication, and health assessments effectively controls HBV transmission.
- Early vaccination with a single-dose vaccine is the most cost-effective strategy.
- The model incorporates age heterogeneity in horizontal and vertical transmission modes.

## Abstract

Infection with Hepatitis B Virus (HBV) has been a serious public health issue worldwide. It caused more than one million fatalities per year. The mathematical modelling of the disease allows better understanding of the transmission of the disease and help the government policy makers to choose the best control strategies. With this inspiration, we proposed a novel dynamic model by incorporating infection-age structure to imitate the transmission of HBV, especially the age heterogeneity in horizontal and vertical (mother-to-child) transmission modes. We also discussed its impact on control measures and analyzed the dynamics of waning immunity and reinfection. We conducted sensitivity analysis to evaluate the effectiveness of each control measure. Our research concentrates on HBV acute patient cases in the United States data from Centre for Disease Control and Prevention (CDC). Our findings show that a mixed approach by including vaccination, medication and periodic health assessments can effectively control HBV transmission. Among these measures, we found that early vaccination with a single-dose vaccine of US$50 is the most cost-effective control strategy.