Individual risk-aversion responses tune epidemics to critical transmissibility (R = 1)

A model of behavioural response to risk accurately predicts the statistical distribution of COVID-19 infection and reproduction numbers

One clear aspect of behaviour in the COVID-19 pandemic has been people's focus on, and response to, reported or observed infection numbers in their community. We describe a simple model of infectious disease spread in a pandemic situation where people's behaviour is influenced by the current risk of infection and where this behavioural response acts homeostatically to return infection risk to a certain preferred level. This homeostatic response is active until approximate herd immunity is reached: in this domain the model predicts that the reproduction rate R will be centred around a median of 1, that proportional change in infection numbers will follow the standard Cauchy distribution with location and scale parameters 0 and 1, and that high infection numbers will follow a power-law frequency distribution with exponent 2. To test these predictions we used worldwide COVID-19 data from 1st February 2020 to 30th June 2022 to calculate [Formula: see text] confidence interval estimates across countries for these R, location, scale and exponent parameters. The resulting median R estimate was [Formula: see text] (predicted value 1) the proportional change location estimate was [Formula: see text] (predicted value 0), the proportional change scale estimate was [Formula: see text] (predicted value 1), and the frequency distribution exponent estimate was [Formula: see text] (predicted value 2); in each case the observed estimate agreed with model predictions.

The effect of competition between health opinions on epidemic dynamics

Past major epidemic events showed that when an infectious disease is perceived to cause severe health outcomes, individuals modify health behavior affecting epidemic dynamics. To investigate the effect of this feedback relationship on epidemic dynamics, we developed a compartmental model that couples a disease spread framework with competition of two mutually exclusive health opinions (health-positive and health-neutral) associated with different health behaviors. The model is based on the assumption that individuals switch health opinions as a result of exposure to opinions of others through interpersonal communications. To model opinion switch rates, we considered a family of functions and identified the ones that allow health opinions to coexist. Finally, the model includes assortative mixing by opinions. In the disease-free population, either the opinions cannot coexist and one of them is always dominating (mono-opinion equilibrium) or there is at least one stable coexistence of opinions equilibrium. In the latter case, there is multistability between the coexistence equilibrium and the two mono-opinion equilibria. When two opinions coexist, it depends on their distribution whether the infection can invade. If presence of the infection leads to increased switching to a health-positive opinion, the epidemic burden becomes smaller than indicated by the basic reproduction number. Additionally, a feedback between epidemic dynamics and health opinion dynamics may result in (sustained) oscillatory dynamics and a switch to a different stable opinion distribution. Our model captures feedback between spread of awareness through social interactions and infection dynamics and can serve as a basis for more elaborate individual-based models.

Finite-time scaling for epidemic processes with power-law superspreading events

Epidemics unfold by means of a spreading process from each infected individual to a variable number of secondary cases. It has been claimed that the so-called superspreading events of the COVID-19 pandemic are governed by a power-law-tailed distribution of secondary cases, with no finite variance. Using a continuous-time branching process, we demonstrate that for such power-law-tailed superspreading, the survival probability of an outbreak as a function of both time and the basic reproductive number fulfills a "finite-time scaling" law (analogous to finite-size scaling) with universal-like characteristics only dependent on the power-law exponent. This clearly shows how the phase transition separating a subcritical and a supercritical phase emerges in the infinite-time limit (analogous to the thermodynamic limit). We also quantify the counterintuitive hazards posed by this superspreading. When the expected number of infected individuals is computed removing extinct outbreaks, we find a constant value in the subcritical phase and a superlinear power-law growth in the critical phase.