The social dynamics of COVID-19

Abstract

We add a simple dynamic process for adaptive "social distancing" measures to a standard SIR model of the COVID pandemic. With a limited attention span and in the absence of a consistent long-term strategy against the pandemic, this process leads to a sweeping of an instability, i.e. fluctuations in the effective reproduction number around its bifurcation value of $R_{eff}=1$ . While mitigating the pandemic in the short-run, this process remains intrinsically fragile and does not constitute a sustainable strategy that societies could follow for an extended period of time.

Keywords: COVID pandemic; SIR model; Social interaction.

Fig. 1

Simulation of SIR model showing the evolution of the number of currently infected and the cumulative number of all individuals that have been exposed to the pathogen since the start of the pandemic. The inlet shows the cumulative number of fatalities.

Fig. 2

Dynamics of new infections with different reproduction rates $R$, assuming “social distancing” measures are imposed, when $I_t$ reaches one million (note the semi-logarithmic scale of the graph).

Fig. 3

The reproduction rate of COVID-19 reported by the German Robert Koch Institute (Germany’s national public health institute). The numbers displayed are 7-day moving averages with elements of nowcasting, i.e., corrections for known delays in reporting and diagnosis.

Fig. 4

Typical trajectory of a SIR model with social dynamics. The main frame shows the number of infected individuals; the inlet depicts the effective reproduction rate averaged over two weeks. Parameters are: ${\alpha }_0=0.25$, ${\alpha }_1=100$, ${\alpha }_2=175$, ${\alpha }_3=15$, ${\alpha }_4=20$, and $T=30$.