Research Institute of Economy, Trade and Industry (RIETI), Chiyoda, Tokyo, Japan.
Graduate School of Economics, University of Tokyo, Bunkyo, Tokyo, Japan.
PLoS One. 2024 Apr 9;19(4):e0299813. doi: 10.1371/journal.pone.0299813. eCollection 2024.
Many countries have experienced multiple waves of infection during the COVID-19 pandemic. We propose a novel but parsimonious extension of the SIR model, a CSIR model, that can endogenously generate waves. In the model, cautious individuals take appropriate prevention measures against the virus and are not exposed to infection risk. Incautious individuals do not take any measures and are susceptible to the risk of infection. Depending on the size of incautious and susceptible population, some cautious people lower their guard and become incautious-thus susceptible to the virus. When the virus spreads sufficiently, the population reaches "temporary" herd immunity and infection subsides thereafter. Yet, the inflow from the cautious to the susceptible eventually expands the susceptible population and leads to the next wave. We also show that the CSIR model is isomorphic to the SIR model with time-varying parameters.
许多国家在 COVID-19 大流行期间经历了多波感染。我们提出了一种新颖但简约的 SIR 模型扩展，即 CSIR 模型，该模型可以内生地产生波。在该模型中，谨慎的个体采取适当的预防措施来对抗病毒，不会接触到感染风险。不谨慎的个体不采取任何措施，容易受到感染风险的影响。根据不谨慎和易感人群的规模，一些谨慎的人会放松警惕，变得不谨慎，从而容易感染病毒。当病毒传播足够多时，人群会达到“暂时”的群体免疫力，此后感染会消退。然而，谨慎人群向易感人群的流动最终会扩大易感人群，并导致下一波感染。我们还表明，CSIR 模型与具有时变参数的 SIR 模型同构。
