A quantitative method to project the probability of the end of an epidemic: Application to the COVID-19 outbreak in Wuhan, 2020

Exact calculation of end-of-outbreak probabilities using contact tracing data

A key challenge for public health policymakers is determining when an infectious disease outbreak has finished. Following a period without cases, an estimate of the probability that no further cases will occur in future (the end-of-outbreak probability) can be used to inform whether or not to declare an outbreak over. An existing quantitative approach (the Nishiura method), based on a branching process transmission model, allows the end-of-outbreak probability to be approximated from disease incidence time series, the offspring distribution and the serial interval distribution. Here, we show how the end-of-outbreak probability under the same transmission model can be calculated exactly if data describing who-infected-whom (the transmission tree) are also available (e.g. from contact tracing studies). In that scenario, our novel approach (the traced transmission method) is straightforward to use. We demonstrate this by applying the method to data from previous outbreaks of Ebola virus disease and Nipah virus infection. For both outbreaks, the traced transmission method would have determined that the outbreak was over earlier than the Nishiura method. This highlights that collection of contact tracing data and application of the traced transmission method may allow stringent control interventions to be relaxed quickly at the end of an outbreak, with only a limited risk of outbreak resurgence.

Modeling the effects of Prophylactic behaviors on the spread of SARS-CoV-2 in West Africa

Various general and individual measures have been implemented to limit the spread of SARS-CoV-2 since its emergence in China. Several phenomenological and mechanistic models have been developed to inform and guide health policy. Many of these models ignore opinions about certain control measures, although various opinions and attitudes can influence individual actions. To account for the effects of prophylactic opinions on disease dynamics and to avoid identifiability problems, we expand the SIR-Opinion model of Tyson et al. (2020) to take into account the partial detection of infected individuals in order to provide robust modeling of COVID-19 as well as degrees of adherence to prophylactic treatments, taking into account a hybrid modeling technique using Richard's model and the logistic model. Applying the approach to COVID-19 data from West Africa demonstrates that the more people with a strong prophylactic opinion, the smaller the final COVID-19 pandemic size. The influence of individuals on each other and from the media significantly influences the susceptible population and, thus, the dynamics of the disease. Thus, when considering the opinion of susceptible individuals to the disease, the view of the population at baseline influences its dynamics. The results are expected to inform public policy in the context of emerging and re-emerging infectious diseases.

A COVID-19 Infection Model Considering the Factors of Environmental Vectors and Re-Positives and Its Application to Data Fitting in Japan and Italy

COVID-19, which broke out globally in 2019, is an infectious disease caused by a novel strain of coronavirus, and its spread is highly contagious and concealed. Environmental vectors play an important role in viral infection and transmission, which brings new difficulties and challenges to disease prevention and control. In this paper, a type of differential equation model is constructed according to the spreading functions and characteristics of exposed individuals and environmental vectors during the virus infection process. In the proposed model, five compartments were considered, namely, susceptible individuals, exposed individuals, infected individuals, recovered individuals, and environmental vectors (contaminated with free virus particles). In particular, the re-positive factor was taken into account (i.e., recovered individuals who have lost sufficient immune protection may still return to the exposed class). With the basic reproduction number R0 of the model, the global stability of the disease-free equilibrium and uniform persistence of the model were completely analyzed. Furthermore, sufficient conditions for the global stability of the endemic equilibrium of the model were also given. Finally, the effective predictability of the model was tested by fitting COVID-19 data from Japan and Italy.

The modeling and analysis of the COVID-19 pandemic with vaccination and isolation: a case study of Italy

The global spread of COVID-19 has not been effectively controlled. It poses a significant threat to public health and global economic development. This paper uses a mathematical model with vaccination and isolation treatment to study the transmission dynamics of COVID-19. In this paper, some basic properties of the model are analyzed. The control reproduction number of the model is calculated and the stability of the disease-free and endemic equilibria is analyzed. The parameters of the model are obtained by fitting the number of cases that were detected as positive for the virus, dead, and recovered between January 20 and June 20, 2021, in Italy. We found that vaccination better controlled the number of symptomatic infections. A sensitivity analysis of the control reproduction number has been performed. Numerical simulations demonstrate that reducing the contact rate of the population and increasing the isolation rate of the population are effective non-pharmaceutical control measures. We found that if the isolation rate of the population is reduced, a short-term decrease in the number of isolated individuals can lead to the disease not being controlled at a later stage. The analysis and simulations in this paper may provide some helpful suggestions for preventing and controlling COVID-19.

COVID-19 cases with a contact history: A modeling study of contact history-stratified data in Japan

The purpose of the present study was to develop a transmission model of COVID-19 cases with and without a contact history to understand the meaning of the proportion of infected individuals with a contact history over time. We extracted epidemiological information regarding the proportion of coronavirus disease 2019 (COVID-19) cases with a contact history and analyzed incidence data stratified by the presence of a contact history in Osaka from January 15 to June 30, 2020. To clarify the relationship between transmission dynamics and cases with a contact history, we used a bivariate renewal process model to describe transmission among cases with and without a contact history. We quantified the next-generation matrix as a function of time; thus, the instantaneous (effective) reproduction number was calculated for different periods of the epidemic wave. We objectively interpreted the estimated next-generation matrix and replicated the proportion of cases with a contact p(t) over time, and we examined the relevance to the reproduction number. We found that p(t) does not take either the maximum or minimum value at a threshold level of transmission with R(t)=1.0. With R(t) < 1 (subcritical level), p(t) was a decreasing function of R(t). Qualitatively, the minimum p(t) was seen in the domain with R(t) > 1. An important future implication for use of the proposed model is to monitor the success of ongoing contact tracing practice. A decreasing signal of p(t) reflects the increasing difficulty of contact tracing. The present study findings indicate that monitoring p(t) would be a useful addition to surveillance.

Spatiotemporal pattern recognition and dynamical analysis of COVID-19 in Shanghai, China

Shanghai suffered a large outbreak of Omicron mutant of COVID-19 at the beginning of March 2022. To figure out the spatiotemporal patterns of the epidemic, a retrospective statistical investigation, coupled with a dynamic model, is implemented in this study. The hotspots of SARS-CoV-2 transmissions are identified, and strong aggregative effects in the decay stage are found. Besides, the visualization of disease diffusion is provided to show how COVID-19 disease invades all districts of Shanghai in the early stage. Furthermore, the calculations from the dynamic model manifest the effect of detections to suppress the epidemic dissemination. These results reveal the strategies to improve the spatial control of disease.