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The rate of spread of an emerging epidemic is frequently characterized via the doubling time, which is the time it takes for the number of cases to double. This paper explores different ways to estimate doubling time, and investigates the estimation of doubling time in relationship to parameters in the HawkesN model and the SQUIDER (Susceptible, Quarantine, Undetected Infected, Infected, Dead, Exposed, Recovered) model. We observe an approximately exponential relationship between the productivity parameter κ in the HawkesN model and doubling time. We also evaluate the performance of the models in forecasting doubling times and compare to empirical doubling times using daily reported statewide totals for SARS-CoV-2 infections in California, and find that the HawkesN model forecasts doubling times more accurately, with 3.6% smaller root mean squared errors in Spring 2020, 79.4% smaller root mean squared errors in Autumn 2020, and 5.4% smaller root mean squared errors in Summer 2021. The HawkesN and SQUIDER models appear to forecast daily rate doubling times accurately at most times, though the SQUIDER forecasts of daily rate doubling times are far more volatile and thus occasionally have much larger errors, particularly in Fall 2020.
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Fractional Differential Equation Model For COVID-19 Epidemic
An epidemic disease caused by coronavirus has spread all over the world with a strong contagion rate. We present simulations of epidemic models constructed using real data to give a clear perspective and confirmation on the effect of quarantine on the evolution of the infection and the number of infected, recovered, and dead because of this epidemic in South Carolina in a time window (December 1, 2020, to June 1, 2021) when the epidemic was relatively strong. We use CDC data for infected and dead populations covering the period December 1, 2020, to June 1, 2021 in South Carolina to develop models and do simulations. There were no data available for recovered populations in this period. Part of our goal is to estimate the number of recovered for the entire period. The models and results are consistent with the data. The infection and recovery increasing in South Carolina do not show improvement in this period. The number of dead people in this period tended to increase although by small amount. Optimal control methodologies are considered where transmission, recovery, relapse of immunity and death rates are considered as decision variables in minimizing the difference between the real and computed COVID-19 infection and dead data. Effect of quarantine as intervention strategy is also considered as it is critical issue. What we want to show is what could have been the outcome if quarantine had been implemented from the very beginning. The progress of an infection in general is related not only to the present states, but also to its historical states. To account for the effect of past evolution we add fractional differential equations models.
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- PAR ID:
- 10468328
- Publisher / Repository:
- Dynamic Publishers Inc.
- Date Published:
- Journal Name:
- Dynamic systems and applications
- ISSN:
- 1056-2176
- Subject(s) / Keyword(s):
- Optimal control, Reproduction number.
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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