A new modelling of the COVID 19 pandemic

Abstract

А model of coronavirus incidence is proposed. Process of disease development is represented as analogue of first- and second order phase transition in physical systems. The model is very simple in terms of the data necessary for the calculations. To verify the proposed model, only data on the current incidence rate are required. However, the determination coefficient of model R2 is very high and exceeds 0.95 for most countries. The model permits the accurate prediction of the pandemics dynamics at intervals of up to 10 days. The ADL(autoregressive distributed lag)-model was introduced in addition to the phase transition model to describe the development of the disease at the exponential phase.The ADL-model allows describing nonmonotonic changes in relative infection over the time, and providing to governments and health care decision makers the possibility to predict the outcomes of their decisions on public health.

Keywords: COVID-19; epidemics; infection disease; mathematics model; modelling.

Fig. 1

The potential function F(x) and the first-order phase transition for patients throughout the United States from 01.01.2020 to 04.12.2020 (total 555,152 cases).

Fig. 2

The dynamics of coronavirus development in different US states. Data is aligned with the start date of the exponential phase of the epidemic in the state, taken as t = 0 (1 - North Dakota, 2 - California, 3 - Illinois, 4 - Wyoming).

Fig. 3

The potential function F(x) and the first-order phase transition for patients in all countries from the WHO registry from 01.01.2020 to 04.08.2020.

Fig. 4

The dynamics of coronavirus disease on the planet. 1 - initial stage of infection (-single country - China), 2 – initial stage of infection, 3 - inhibition of the infection process, 4 - stage of mass infection, 5 - complete infection of the planet.

Fig. 5

The dynamics of coronavirus in the United States. 1 - Initial stage of infection (three states), 2 – inhibition stage of the infection process, 3 - mass infection stage, 4 - complete infection of the country.

Fig. 6

Dynamics of the relative coronavirus incidence for the United States (1 - lag phase; 2 - exponential phase).

Fig. 7

PACF time series for USA (1 PACF; 2 - St. Err.).

Fig. 8

Data for USA (1), the model using data to 04.04.2020 (2) and the forecast (3) according to the model (3) from 04.09.2020 to 04.17.2020.

Fig. 9

The cross-correlation function (CCF) of statistics data and model series for United States. (1 - CCF; 2 - St. Err.).

Fig. 10

Data for Russia (1), the model according to the data until 04.04.2020 (2) and the forecast (3) according to the model from 04.09.2020 to 04.17.2020.