Is it possible to suspend the spread of an epidemic infection? The dynamic Monte Carlo approach

TL;DR

This study uses a dynamic Monte Carlo model to analyze how infection spread depends on risk factors and quarantine measures, revealing conditions for infection die-out and complex oscillatory behaviors.

Contribution

Introduces a dynamic Monte Carlo approach to model epidemic spread, incorporating quarantine states and immunity, highlighting critical thresholds and complex dynamics.

Findings

Infection dies out for sub-critical risk factor values.

Early quarantine off induces oscillatory infection dynamics.

Immunity in individuals affects overall infection spread.

Abstract

We study a dynamics of the epidemiological infection spreading at different values of the risk factor $\beta$ (a control parameter) with the using of dynamic Monte Carlo approach (DMC). In our toy model, the infection transmits due to contacts of randomly moving individuals. We show that the behavior of recovereds critically depends on the $\beta$ value. For sub-critical values $\beta<\beta_{c}\sim 0.6$, the number of infected cases asymptotically converges to zero, such that for a moderate risk factor the infection may disappear with time. Our simulations shown that over time, the properties of such a system asymptotically become close to the critical transition in 2D percolation system. We also analyzed an extended system, which includes two additional parameters: the limits of taking on/off quarantine state. It is found that the early quarantine off does result in the irregular (with positive Lyapunov exponent) oscillatory dynamics of infection. If the lower limit of the quarantine off is small enough, the recovery dynamics acquirers a characteristic nonmonotonic shape with several damped peaks. The dynamics of infection spreading in case of the individuals with immunity is studied too.