Müller J
Universität Tübingen, Germany.
Math Biosci. 1997 Jan 15;139(2):133-54. doi: 10.1016/s0025-5564(96)00140-x.
A SIRS model with vaccination is considered. The vaccination is assumed to have side effects (for simplicity, these side effects are modeled as a probability of becoming ill because of vaccination). It is the interest of the total population to minimize the prevalence of disease; hence, the vaccination rate that minimizes the prevalence will be determined. In Section 2, the individual is considered: an individual tries to minimize his or her own risk. This angle of approach results in a vaccination rate dependent on the prevalence of the disease. The bifurcations of this system are analyzed, and the optimal vaccination coverage for the individual is computed. This coverage is then compared with the optimal vaccination coverage for the total population: it is found that they disagree for some parameter sets.
考虑一个带有疫苗接种的SIRS模型。假设疫苗接种有副作用（为简单起见，这些副作用被建模为因接种疫苗而患病的概率）。使疾病流行率最小化符合总人口的利益；因此，将确定使流行率最小化的疫苗接种率。在第2节中，考虑个体情况：个体试图使自身风险最小化。这种研究角度导致疫苗接种率取决于疾病的流行率。分析了该系统的分岔情况，并计算了个体的最优疫苗接种覆盖率。然后将此覆盖率与总人口的最优疫苗接种覆盖率进行比较：发现对于某些参数集，它们并不一致。
