Application and analysis of a model with environmental transmission in a periodic environment

The goal of this paper is to introduce a non-autonomous environmental transmission model for most respiratory and enteric infectious diseases to study the impact of periodic environmental changes on related infectious diseases. The transmission and decay rates of pathogens in the environment are set as periodic functions to summarize the influence of environmental fluctuations on diseases. The solutions of the model are qualitatively analyzed, and the equilibrium points and the reference criterion, $R_0$, for judging the infectivity of infectious diseases are deduced. The global stability of the disease-free equilibrium and the uniform persistence of the disease are proved by using the persistence theory. Common infectious diseases such as COVID-19, influenza, dysentery, pertussis and tuberculosis are selected to fit periodic and non-periodic models. Fitting experiments show that the periodic environmental model can respond to epidemic fluctuations more accurately than the non-periodic model. The periodic environment model is reasonable and applicable for seasonal infectious diseases. The response effects of the periodic and non-periodic models are basically the same for perennial infectious diseases. The periodic model can inform epidemiological trends in relevant emerging infectious diseases. Taking COVID-19 as an example, the sensitivity analysis results show that the virus-related parameters in the periodic model have the most significant influence on the system. It reminds us that, even late in the pandemic, we must focus on the viral load on the environment.