Projecting the Pandemic Trajectory through Modeling the Transmission Dynamics of COVID-19

Stochastic compartmental models of the COVID-19 pandemic must have temporally correlated uncertainties

Compartmental models are an important quantitative tool in epidemiology, enabling us to forecast the course of a communicable disease. However, the model parameters, such as the infectivity rate of the disease, are riddled with uncertainties, which has motivated the development and use of stochastic compartmental models. Here, we first show that a common stochastic model, which treats the uncertainties as white noise, is fundamentally flawed since it erroneously implies that greater parameter uncertainties will lead to the eradication of the disease. Then, we present a principled modelling of the uncertainties based on reasonable assumptions on the contacts of each individual. Using the central limit theorem and Doob’s theorem on Gaussian Markov processes, we prove that the correlated Ornstein–Uhlenbeck (OU) process is the appropriate tool for modelling uncertainties in the infectivity rate. We demonstrate our results using a compartmental model of the COVID-19 pandemic and the available US data from the Johns Hopkins University COVID-19 database. In particular, we show that the white noise stochastic model systematically underestimates the severity of the Omicron variant of COVID-19, whereas the OU model correctly forecasts the course of this variant. Moreover, using an SIS model of sexually transmitted disease, we derive an exact closed-form solution for the final distribution of infected individuals. This analytical result shows that the white noise model underestimates the severity of the pandemic because of unrealistic noise-induced transitions. Our results strongly support the need for temporal correlations in modelling of uncertainties in compartmental models of infectious disease.

Evolving trend change during the COVID-19 pandemic

Coronavirus disease (COVID-19) has caused unimaginable damage to public health and socio-economic structures worldwide; thus, an epidemiological depiction of the global evolving trends of this disease is necessary. As of March 31, 2022, the number of cases increased gradually over the four waves of the COVID-19 pandemic, indicating the need for continuous countermeasures. The highest total cases per million and total deaths per million were observed in Europe (240,656.542) and South America (2,912.229), despite these developed countries having higher vaccination rates than other continents, such as Africa. In contrast, the lowest of the above two indices were found in undeveloped African countries, which had the lowest number of vaccinations. These data indicate that the COVID-19 pandemic is positively related to the socio-economic development level; meanwhile, the data suggest that the vaccine currently used in these continents cannot completely prevent the spread of COVID-19. Thus, rethinking the feasibility of a single vaccine to control the disease is needed. Although the number of cases in the fourth wave increased exponentially compared to those of the first wave, ~43.1% of deaths were observed during the first wave. This was not only closely linked to multiple factors, including the inadequate preparation for the initial response to the COVID-19 pandemic, the gradual reduction in the severity of additional variants, and the protection conferred by prior infection and/or vaccination, but this also indicated the change in the main driving dynamic in the fourth wave. Moreover, at least 12 variants were observed globally, showing a clear spatiotemporal profile, which provides the best explanation for the presence of the four waves of the pandemic. Furthermore, there was a clear shift in the trend from multiple variants driving the spread of disease in the early stage of the pandemic to a single Omicron lineage predominating in the fourth wave. These data suggest that the Omicron variant has an advantage in transmissibility over other contemporary co-circulating variants, demonstrating that monitoring new variants is key to reducing further spread. We recommend that public health measures, along with vaccination and testing, are continually implemented to stop the COVID-19 pandemic.