Abstract
The paper presents the results of sensitivity-based identifiability analysis of the COVID-19 pandemic spread models in the Novosibirsk region using the systems of differential equations and mass balance law. The algorithm is built on the sensitivity matrix analysis using the methods of differential and linear algebra. It allows one to determine the parameters that are the least and most sensitive to data changes to build a regularization for solving an identification problem of the most accurate pandemic spread scenarios in the region. The performed analysis has demonstrated that the virus contagiousness is identifiable from the number of daily confirmed, critical and recovery cases. On the other hand, the predicted proportion of the admitted patients who require a ventilator and the mortality rate are determined much less consistently. It has been shown that building a more realistic forecast requires adding additional information about the process such as the number of daily hospital admissions. In our study, the problems of parameter identification using additional information about the number of daily confirmed, critical and mortality cases in the region were reduced to minimizing the corresponding misfit functions. The minimization problem was solved through the differential evolution method that is widely applied for stochastic global optimization. It has been demonstrated that a more general COVID-19 spread compartmental model consisting of seven ordinary differential equations describes the main trend of the spread and is sensitive to the peaks of confirmed cases but does not qualitatively describe small statistical datasets such as the number of daily critical cases or mortality that can lead to errors in forecasting. A more detailed agent-oriented model has been able to capture statistical data with additional noise to build scenarios of COVID-19 spread in the region.
Highlights
Many mathematical models in biology, medicine, physics and chemistry, as well as sociology are described by systems of differential equations, whether they be ordinary (Kermack, McKendrick, 1927), partial (Habtemariam et al, 2008), or stochastic differential ones (Lee et al, 2020)
In the present study, sensitivity-based identifiability analysis has been performed for the COVID-19 pandemic spread models based on systems of differential equations
The analysis has shown that the virus contagiousness is consistently identified based on the number of new daily diag noses, critical cases, and recoveries
Summary
Many mathematical models in biology (epidemiology, im munology, pharmacokinetics, systems biology), medicine (tomography), physics and chemistry (meteorology, chemical kinetics), as well as sociology are described by systems of differential equations, whether they be ordinary (Kermack, McKendrick, 1927), partial (Habtemariam et al, 2008), or stochastic differential ones (Lee et al, 2020). Assume that additional information on diagnoses, critical cases, and mortality on fixed days is available: 86 Вавиловский журнал генетики и селекции / Vavilov Journal of Genetics and Breeding математических моделей распространения эпидемии COVID-19 25
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