On a quarantine model of coronavirus infection and data analysis

Abstract

Attempts to curb the spread of coronavirus by introducing strict quarantine measures apparently have different effect in different countries: while the number of new cases has reportedly decreased in China and South Korea, it still exhibit significant growth in Italy and other countries across Europe. In this brief note, we endeavour to assess the efficiency of quarantine measures by means of mathematical modelling. Instead of the classical SIR model, we introduce a new model of infection progression under the assumption that all infected individual are isolated after the incubation period in such a way that they cannot infect other people. Disease progression in this model is determined by the basic reproduction number R 0 (the number of newly infected individuals during the incubation period), which is different compared to that for the standard SIR model. If R 0 > 1, then the number of latently infected individuals exponentially grows. However, if R 0 < 1 (e.g. due to quarantine measures and contact restrictions imposed by public authorities), then the number of infected decays exponentially. We then consider the available data on the disease development in different countries to show that there are three possible patterns: growth dynamics, growthdecays dynamics, and patchy dynamics (growth-decay-growth). Analysis of the data in China and Korea shows that the peak of infection (maximum of daily cases) is reached about 10 days after the restricting measures are introduced. During this period of time, the growth rate of the total number of infected was gradually decreasing. However, the growth rate remains exponential in Italy. Arguably, it suggests that the introduced quarantine is not sufficient and stricter measures are needed.

Immuno-epidemiological model of two-stage epidemic growth

“…Quarantine model. Another epidemiological model was introduced in [16], in order to take into account removal of infected individuals to quarantine when the incubation period is finished and they manifest disease symptoms:…”

Coronavirus – Scientific insights and societal aspects

“…Thus, the M-day was reached 12 days after the Q-day in China and after 10 days in South Korea. These two examples are hardly sufficient to draw general conclusions but they allow to work out a working hypothesis, for instance about the importance of the time lag [11].…”

“…Most of the new cases were imported to have been brought from abroad by the citizens returning after international travel. Quarantine models [8,11] present all three regimes: exponential growth, exponential decay, and constant number of daily cases (linear growth of the total number of infected) [11]. One can expect the transition to the decay and stabilization modes after the M-day.…”

Forecasting Models for Coronavirus (COVID-19): A Survey of the State-of-the-Art

“…The social media and web search correlate with the number of daily COVID cases. Keeping this in mind few researchers has taken datasets from Google, Baidu search engines [43,44] , mobile phones [45,46], newspapers [51] and various websites [47][48][49] like Github [50] over a particular duration of time. Analysis of these datasets is done by various techniques as discussed before i.e.…”