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. 2021 Nov 18;11(1):22497.
doi: 10.1038/s41598-021-01317-z.

Social stress drives the multi-wave dynamics of COVID-19 outbreaks

Innokentiy A Kastalskiy  1   2   3 , Evgeniya V Pankratova  4   5 , Evgeny M Mirkes  4   6 , Victor B Kazantsev  7   4   8 , Alexander N Gorban  7   4   6
Affiliations

Social stress drives the multi-wave dynamics of COVID-19 outbreaks

Innokentiy A Kastalskiy et al. Sci Rep. .

Abstract

The dynamics of epidemics depend on how people's behavior changes during an outbreak. At the beginning of the epidemic, people do not know about the virus, then, after the outbreak of epidemics and alarm, they begin to comply with the restrictions and the spreading of epidemics may decline. Over time, some people get tired/frustrated by the restrictions and stop following them (exhaustion), especially if the number of new cases drops down. After resting for a while, they can follow the restrictions again. But during this pause the second wave can come and become even stronger then the first one. Studies based on SIR models do not predict the observed quick exit from the first wave of epidemics. Social dynamics should be considered. The appearance of the second wave also depends on social factors. Many generalizations of the SIR model have been developed that take into account the weakening of immunity over time, the evolution of the virus, vaccination and other medical and biological details. However, these more sophisticated models do not explain the apparent differences in outbreak profiles between countries with different intrinsic socio-cultural features. In our work, a system of models of the COVID-19 pandemic is proposed, combining the dynamics of social stress with classical epidemic models. Social stress is described by the tools of sociophysics. The combination of a dynamic SIR-type model with the classical triad of stages of the general adaptation syndrome, alarm-resistance-exhaustion, makes it possible to describe with high accuracy the available statistical data for 13 countries. The sets of kinetic constants corresponding to optimal fit of model to data were found. These constants characterize the ability of society to mobilize efforts against epidemics and maintain this concentration over time and can further help in the development of management strategies specific to a particular society.

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Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1
Figure 1
Coronavirus outbreak in China. The dynamics of the SIRSS model is shown in the top panel: Sign, Sres, Sexh, I, and CC = I + R. Fitted COVID data in absolute values (total confirmed and daily new cases: TCC and DNC) are displayed at the bottom. The beginning of the infection spread is characterized by a single wave, followed by a plateau on CC(t). Fractions Sign and Sres quickly interchange with an increase in I(t), and Sexh gradually increases to a relatively low level of ~ 15%.
Figure 2
Figure 2
Earliest coronavirus outbreaks in Europe. Results for Italy (top panel), Germany (center), and United Kingdom (bottom). The dynamics of the epidemic spread are qualitatively similar and are characterized by a profile containing the full first wave and the beginning of the second wave.
Figure 3
Figure 3
Coronavirus outbreaks in countries with a high resistance index. Results for France (top panel), Israel (center), and Spain (bottom). The outbreaks dynamics are characterized by a rapid increase in the Sres fraction during the peak of the first wave and the formation of protracted plateau on CC(t) with low DNC indices. To simulate the spread of COVID in Israel (population is less than 10 million), we take an interval of 100 days. Numerous data corrections in France and Spain for the period April'20–May'20 lead to the minor (practically negligible) discrepancies between the CC and TCC profiles.
Figure 4
Figure 4
Coronavirus outbreaks in countries with a low resistance index. Results for Brazil (top panel), India (center), and Russia (bottom). Trajectories are characterized by a low Sres and a high Sign in comparison with the previous groups. The exhausted fraction of the population Sexh, on the contrary, is quantitatively comparable and evolves in approximately the same scenario. The end of the first wave I(t) smoothly turns into the second one. To simulate the spread of COVID-19 in Brazil and India, which have large populations, intervals of 300 and 400 days were taken, respectively.
Figure 5
Figure 5
Coronavirus outbreaks in countries with extremely high exhaustion rate. Results for Colombia (top panel), Iran (center), and United States (bottom). The main trend here is the rapid accumulation of exhausted people Sexh (up to ~ 50% over a period of 50–150 days, if taken from the peak of the first wave). At the same time, the Sign fraction can remain quite small. The first wave of I(t) rapidly turns into the second one without a significant decline relative to the peak values. The time intervals for the simulations were chosen empirically.
Figure 6
Figure 6
A schematic representation of possible transitions in the SIRSS model. There is a three-stage loop in the S category. Each arrow is associated with a kinetic constant. The rates of transitions “Ignorant → Infected” and “Exhausted → Infected” are also proportional to the infected fraction I, and the rate of transition “Ignorant → Resistant” is proportional to I2 [see the autocatalytic representation and Eqs. (1)–(5)]. Fast transitions are highlighted in red, and slow transitions are highlighted in light blue.
Figure 7
Figure 7
Comparison of coronavirus outbreaks at K3 = 0.01 (left panel) and K3 = 0 (right panel): a case for Germany. The proportion of infected, I, and the number of cases, CC, on the right panel became orders of magnitude higher over time than on the left. Note that the scale for I and CC on the right differs from the left by a factor of 40 (approximately). The second wave on the right will involve almost the entire population.
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