Characteristics of an epidemic outbreak with a large initial infection size

Modeling COVID-19 dynamics in the sixteen West African countries

The current COVID-19 pandemic has caused several damages to the world, especially in public health sector. This study considered a simple deterministic SIR (Susceptible-Infectious-Recovered) model to characterize and predict future course of the pandemic in the West African countries. We estimated specific characteristics of the disease’s dynamics such as its initial conditions, reproduction numbers, true peak, reported peak with their corresponding times, final epidemic size and time-varying attack ratio. Our findings revealed a relatively low proportion of susceptible individuals in the region and in the different countries (1.2 % across West Africa). The detection rate of the disease was also relatively low (0.9 % for West Africa as a whole) and <2 % for most countries, except for Gambia (12.5 %), Cape-Verde (9.5 %), Mauritania (5.9 %) and Ghana (4.4 %). The reproduction number varied between 1.15 (Burkina-Faso) and 4.45 (Niger) and the peak time of the pandemic was between June and July for most countries. Most generally, the peak time of reported cases came a week (7-8 days) after the true peak time. The model predicted 222,100 actual active cases in the region at peak time while the final epidemic size accounted for 0.6 % of the West African population (2,526,700 individuals). Results obtained showed that the COVID-19 pandemic has not severely affected West Africa as noticed in other regions of the world, but current control measures and standard operating procedures should be maintained over time to ensure trends observed and even accelerate the declining trend of the pandemic.

A Model for Highly Fluctuating Spatio-Temporal Infection Data, with Applications to the COVID Epidemic

Spatio-temporal models need to address specific features of spatio-temporal infection data, such as periods of stable infection levels (endemicity), followed by epidemic phases, as well as infection spread from neighbouring areas. In this paper, we consider a mixture-link model for infection counts that allows alternation between epidemic phases (possibly multiple) and stable endemicity, with higher AR1 coefficients in epidemic phases. This is a form of regime-switching, allowing for non-stationarity in infection levels. We adopt a generalised Poisson model appropriate to the infection count data and avoid transformations (e.g., differencing) to alternative metrics, which have been adopted in many studies. We allow for neighbourhood spillover in infection, which is also governed by adaptive regime-switching. Compared to existing models, the observational (in-sample) model is expected to better reflect the balance between epidemic and endemic tendencies, and short-term extrapolations are likely to be improved. Two case study applications involve COVID area-time data, one for 32 London boroughs (and 96 weeks) since the start of the COVID epidemic, the other for a shorter time span focusing on the epidemic phase in 144 areas of Southeast England associated with the Alpha variant. In both applications, the proposed methods produce a better in-sample fit and out-of-sample short term predictions. The spatial dynamic implications are highlighted in the case studies.

COVID-19: Analytic results for a modified SEIR model and comparison of different intervention strategies

The Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model is one of the standard models of disease spreading. Here we analyse an extended SEIR model that accounts for asymptomatic carriers, believed to play an important role in COVID-19 transmission. For this model we derive a number of analytic results for important quantities such as the peak number of infections, the time taken to reach the peak and the size of the final affected population. We also propose an accurate way of specifying initial conditions for the numerics (from insufficient data) using the fact that the early time exponential growth is well-described by the dominant eigenvector of the linearized equations. Secondly we explore the effect of different intervention strategies such as social distancing (SD) and testing-quarantining (TQ). The two intervention strategies (SD and TQ) try to reduce the disease reproductive number, R 0 , to a target value R 0 target < 1 , but in distinct ways, which we implement in our model equations. We find that for the same R 0 target < 1 , TQ is more efficient in controlling the pandemic than SD. However, for TQ to be effective, it has to be based on contact tracing and our study quantifies the required ratio of tests-per-day to the number of new cases-per-day. Our analysis shows that the largest eigenvalue of the linearised dynamics provides a simple understanding of the disease progression, both pre- and post- intervention, and explains observed data for many countries. We apply our results to the COVID data for India to obtain heuristic projections for the course of the pandemic, and note that the predictions strongly depend on the assumed fraction of asymptomatic carriers.

Identifying the number of unreported cases in SIR epidemic models

An SIR epidemic model is analysed with respect to the identification of its parameters and initial values, based upon reported case data from public health sources. The objective of the analysis is to understand the relationship of unreported cases to reported cases. In many epidemic diseases the reported cases are a small fraction of the unreported cases. This fraction can be estimated by the identification of parameters for the model from reported case data. The analysis is applied to the Hong Kong seasonal influenza epidemic in New York City in 1968–1969.

The parameter identification problem for SIR epidemic models: identifying unreported cases

A SIR epidemic model is analyzed with respect to identification of its parameters, based upon reported case data from public health sources. The objective of the analysis is to understand the relation of unreported cases to reported cases. In many epidemic diseases the ratio of unreported to reported cases is very high, and of major importance in implementing measures for controlling the epidemic. This ratio can be estimated by the identification of parameters for the model from reported case data. The analysis is applied to three examples: (1) the Hong Kong seasonal influenza epidemic in New York City in 1968-1969, (2) the bubonic plague epidemic in Bombay, India in 1906, and (3) the seasonal influenza epidemic in Puerto Rico in 2016-2017.

Epidemic characteristics of two classic SIS models with disease-induced death

The epidemic characteristics of two classic SIS epidemic models, including the epidemic size, peak and turning point, are investigated. The two SIS models are with bilinear and standard incidences, respectively. For the SIS models, the susceptible individuals generally can be divided into two classes. One consists of the individuals who had not been infected by the infection, the other are individuals who have been infected and recovered from the infection. Based on this fact, the classic SIS epidemic models need to be reformulated in order to analyze the turning points of the epidemic for various cumulative cases in detail. The obtained results illustrate how to determine the epidemic characteristics of the two models, and demonstrate their dependence on the initial conditions and the relative parameters of the models.