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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.
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Optimal Epidemic Control with Nonmedical and Medical Interventions
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.
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- PAR ID:
- 10558696
- Publisher / Repository:
- NSF Public Access Repository (NSF-PAR)
- Date Published:
- Journal Name:
- Mathematics
- Volume:
- 12
- Issue:
- 18
- ISSN:
- 2227-7390
- Page Range / eLocation ID:
- 2811
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/math12182811
