Search for: All records

In this study, we investigate different epidemic control scenarios through theoretical analysis and numerical simulations. To account for two important types of control at the early ascending stage of an outbreak, nonmedical interventions, and medical treatments, a compartmental model is considered with the first control aimed at lowering the disease transmission rate through behavioral changes and the second control set to lower the period of infectiousness by means of antiviral medications and other forms of medical care. In all experiments, the implementation of control strategies reduces the daily cumulative number of cases and successfully “flattens the curve”. The reduction in the cumulative cases is achieved by eliminating or delaying new cases. This delay is incredibly valuable, as it provides public health organizations with more time to advance antiviral treatments and devise alternative preventive measures. The main theoretical result of the paper, Theorem 1, concludes that the two optimal control functions may be increasing initially. However, beyond a certain point, both controls decline (possibly causing the number of newly infected people to grow). The numerical simulations conducted by the authors confirm theoretical findings, which indicates that, ideally, around the time that early interventions become less effective, the control strategy must be upgraded through the addition of new and improved tools, such as vaccines, therapeutics, testing, air ventilation, and others, in order to successfully battle the virus going forward. 

Control and prevention strategies are indispensable tools for managing the spread of infectious diseases. This paper examined biological models for the post-vaccination stage of a viral outbreak that integrate two important mitigation tools: social distancing, aimed at reducing the disease transmission rate, and vaccination, which boosts the immune system. Five different scenarios of epidemic progression were considered: (ⅰ) the no control scenario, reflecting the natural evolution of a disease without any safety measures in place, (ⅱ) the reconstructed scenario, representing real-world data and interventions, (ⅲ) the social distancing control scenario covering a broad set of behavioral changes, (ⅳ) the vaccine control scenario demonstrating the impact of vaccination on epidemic spread, and (ⅴ) the both controls concurrently scenario incorporating social distancing and vaccine controls simultaneously. By comparing these scenarios, we provided a comprehensive analysis of various intervention strategies, offering valuable insights into disease dynamics. Our innovative approach to modeling the cost of control gave rise to a robust computational algorithm for solving optimal control problems associated with different public health regulations. Numerical results were supported by real data for the Delta variant of the COVID-19 pandemic in the United States. 

Abstract A novel optimization algorithm for stable parameter estimation and forecasting from limited incidence data for an emerging outbreak is proposed.The algorithm combines a compartmental model of disease progression with iteratively regularized predictor-corrector numerical scheme aimed at the reconstruction of case reporting ratio, transmission rate, and effective reproduction number.The algorithm is illustrated with real data on COVID-19 pandemic in the states of Georgia and New York, USA.The techniques of functional data analysis are applied for uncertainty quantification in extracted parameters and in future projections of new cases. 

In the absence of reliable information about transmission mechanisms for emerging infectious diseases, simple phenomenological models could provide a starting point to assess the potential outcomes of unfolding public health emergencies, particularly when the epidemiological characteristics of the disease are poorly understood or subject to substantial uncertainty. In this study, we employ the modified Richards model to analyze the growth of an epidemic in terms of 1) the number of times cumulative cases double until the epidemic peaks and 2) the rate at which the intervals between consecutive doubling times increase during the early ascending stage of the outbreak. Our theoretical analysis of doubling times is combined with rigorous numerical simulations and uncertainty quantification using synthetic and real data for COVID-19 pandemic. The doubling-time approach allows to employ early epidemic data to differentiate between the most dangerous threats, which double in size many times over the intervals that are nearly invariant, and the least transmissible diseases, which double in size only a few times with doubling periods rapidly growing.