Ge Jingwen, Wang Wendi
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China.
Chaos Solitons Fractals. 2022 Aug;161:112294. doi: 10.1016/j.chaos.2022.112294. Epub 2022 Jun 10.
Vaccination coverage is crucial for disease prevention and control. An appropriate combination of compulsory vaccination with voluntary vaccination is necessary to achieve the goal of herd immunity for some epidemic diseases such as measles and COVID-19. A mathematical model is proposed that incorporates both compulsory vaccination and voluntary vaccination, where a decision of voluntary vaccination is made on the basis of game evaluation by comparing the expected returns of different strategies. It is shown that the threshold of disease invasion is determined by the reproduction numbers, and an over-response in magnitude or information interval in the dynamic games could induce periodic oscillations from the Hopf bifurcation. The theoretical results are applied to COVID-19 to find out the strategies for protective immune barrier against virus variants.
疫苗接种覆盖率对于疾病预防和控制至关重要。强制接种与自愿接种的适当结合对于实现针对麻疹和新冠肺炎等一些流行病的群体免疫目标是必要的。提出了一个同时纳入强制接种和自愿接种的数学模型，其中自愿接种的决策是基于通过比较不同策略的预期回报进行博弈评估而做出的。结果表明，疾病入侵阈值由繁殖数决定，动态博弈中幅度或信息区间的过度反应可能会引发霍普夫分岔产生的周期性振荡。将理论结果应用于新冠肺炎，以找出针对病毒变体的保护性免疫屏障策略。
