Time-continuous and time-discrete SIR models revisited: theory and applications

Cross-Risk Between Tuberculosis and COVID-19 in East Java Province, Indonesia: An Analysis of Tuberculosis and COVID-19 Surveillance Registry Period 2020-2022

INTRODUCTION

Tuberculosis (TB) and COVID-19 are highly transmissible diseases and pose a serious risk to public health. Unfortunately, information on cross-risk between the two diseases was still sparse. Our main objective was to estimate the excess risk among TB patients in getting COVID-19 infection and vice versa.

METHODS

The study design was a series of analyses of existing data from TB and COVID-19 registries in East Java Province, Indonesia. The study period was from January 2020 to June 2022. Case-by-case data for this study were obtained from the registration systems for TB and COVID-19 in separate databases. In comparing risk across different groups, adjusting for differences in risk factors that influence the outcome was essential. We overcame this problem by employing a standardized morbidity ratio.

RESULTS

Among 92,424 newly diagnosed TB patients, 1,326 were subsequently infected with COVID-19 during the study period, compared with 1,679 expected. The standardized morbidity ratio (95% confidence interval) was 72.61% (60.19%, 85.03%). Among 635,946 newly diagnosed COVID-19-infected patients, 987 subsequently got active TB during the study period against 1,679 expected. The standardized morbidity ratio (95% confidence interval) was 55.33% (49.24%, 61.42%).

CONCLUSION

There was no evidence of excess risk in either direction, the excess risk among TB patients in getting COVID-19 infection and vice versa.

Novel Approach for Identification of Basic and Effective Reproduction Numbers Illustrated with COVID-19

This paper presents a novel numerical technique for the identification of effective and basic reproduction numbers, Re and R0, for long-term epidemics, using an inverse problem approach. The method is based on the direct integration of the SIR (Susceptible-Infectious-Removed) system of ordinary differential equations and the least-squares method. Simulations were conducted using official COVID-19 data for the United States and Canada, and for the states of Georgia, Texas, and Louisiana, for a period of two years and ten months. The results demonstrate the applicability of the method in simulating the dynamics of the epidemic and reveal an interesting relationship between the number of currently infectious individuals and the effective reproduction number, which is a useful tool for predicting the epidemic dynamics. For all conducted experiments, the results show that the local maximum (and minimum) values of the time-dependent effective reproduction number occur approximately three weeks before the local maximum (and minimum) values of the number of currently infectious individuals. This work provides a novel and efficient approach for the identification of time-dependent epidemics parameters.

Analysis and simulation of a stochastic COVID-19 model with large-scale nucleic acid detection and isolation measures: A case study of the outbreak in Urumqi, China in August, 2022

In this paper, a stochastic COVID-19 model with large-scale nucleic acid detection and isolation measures is proposed. Firstly, the existence and uniqueness of the global positive solution is obtained. Secondly, threshold criteria for the stochastic extinction and persistence in the mean with probability one are established. Moreover, a sufficient condition for the existence of unique ergodic stationary distribution for any positive solution is also established. Finally, numerical simulations are carried out in combination with real COVID-19 data from Urumqi, China and the theoretical results are verified.

Trade-Off between COVID-19 Pandemic Prevention and Control and Economic Stimulus

The coronavirus disease 2019 (COVID-19) pandemic has posed a severe threat to public health and economic activity. Governments all around the world have taken positive measures to, on the one hand, contain the epidemic spread and, on the other hand, stimulate the economy. Without question, tightened anti-epidemic policy measures restrain people's mobility and deteriorate the levels of social and economic activity. Meanwhile, loose policy measures bring little harm to the economy temporarily but could accelerate the transmission of the virus and ultimately wreck social and economic development. Therefore, these two kinds of governmental decision-making behaviors usually conflict with each other. With the purpose of realizing optimal socio-economic benefit over the full duration of the epidemic and to provide a helpful suggestion for the government, a trade-off is explored in this paper between the prevention and control of the epidemic, and economic stimulus. First, the susceptible-infectious-recovered (SIR) model is introduced to simulate the epidemic dynamics. Second, a state equation is constructed to describe the system state variable-the level of socio-economic activity dominated by two control variables. Specifically, these two variables are the strengths of the measures taken for pandemic prevention and control, and economic stimulus. Then, the objective function used to maximize the total socio-economic benefit over the epidemic's duration is defined, and an optimal control problem is developed. The statistical data of the COVID-19 epidemic in Wuhan are used to validate the SIR model, and a COVID-19 epidemic scenario is used to evaluate the proposed method. The solution is discussed in both static and dynamic strategies, according to the knowledge of the epidemic's duration. In the static strategy, two scenarios with different strengths (in terms of anti-epidemic and economic stimulus measures) are analyzed and compared. In the dynamic strategy, two global optimization algorithms, including the dynamic programming (DP) and Pontryagin's minimum principle (PMP), respectively, are used to acquire the solutions. Moreover, a sensitivity analysis of model parameters is conducted. The results demonstrate that the static strategy, which is independent of the epidemic's duration and can be easily solved, is capable of finding the optimal strengths of both policy measures. Meanwhile, the dynamic strategy, which generates global optimal trajectories of the control variables, can provide the path that leads to attaining the optimal total socio-economic benefit. The results reveal that the optimal total socio-economic benefit of the dynamic strategy is slightly higher than that of the static strategy.

Adaptive SIR model with vaccination: simultaneous identification of rates and functions illustrated with COVID-19

An Adaptive Susceptible-Infected-Removed-Vaccinated (A-SIRV) epidemic model with time-dependent transmission and removal rates is constructed for investigating the dynamics of an epidemic disease such as the COVID-19 pandemic. Real data of COVID-19 spread is used for the simultaneous identification of the unknown time-dependent rates and functions participating in the A-SIRV system. The inverse problem is formulated and solved numerically using the Method of Variational Imbedding, which reduces the inverse problem to a problem for minimizing a properly constructed functional for obtaining the sought values. To illustrate and validate the proposed solution approach, the present study used available public data for several countries with diverse population and vaccination dynamics—the World, Israel, The United States of America, and Japan.

Time-discrete SIR model for COVID-19 in Fiji

Using the data provided by Fiji's ministry of health and medical services, we apply an implicit time-discrete SIR (susceptible people–infectious people–removed people) model that tracks the transmission and recovering rate at time, t to predict the trend of the coronavirus disease 2019 (COVID-19) pandemic in Fiji. The model implied time-varying transmission and recovery rates were calculated from 4 May 2021 to 9 October 2021. The estimator functions for these rates were determined, and a short-term (30 days) forecast was done. The model was validated with observed values of the active and recovered cases from 11 October 2021 to 9 December 2021. Statistical results reveal a good fit of profiles between model simulated and the reported COVID-19 data. The gradual decrease of the time-varying basic reproduction number with values below one towards the end of the study period suggest the government's success in controlling the epidemic. The mean reproduction number for the second wave of COVID-19 in Fiji was estimated as 2.7818. The results from this study can be used by researchers, the Fijian government, and the relevant health policy makers in making informed decisions should a third COVID-19 wave occur.

Inverse problem for adaptive SIR model: Application to COVID-19 in Latin America

This work presents a method for solving an Adaptive Susceptible-Infected-Removed (A-SIR) epidemic model with time-dependent transmission and removal rates. Available COVID-19 data as of March 2021 are used for identifying the rates from an inverse problem. The estimated rates are used to solve the adaptive SIR system for the spread of the infectious disease. This method simultaneously solves the problem for the time-dependent rates and the unknown functions of the A-SIR system. Presented results show the spread of COVID-19 in the World, Argentina, Brazil, Colombia, Dominican Republic, and Honduras. Comparisons of the reported affected by the disease individuals from the available real data and the values obtained with the A-SIR model demonstrate how well the model simulates the dynamic of the infectious disease.