Kinetic Monte Carlo model for the COVID-19 epidemic: Impact of mobility restriction on a COVID-19 outbreak

As the coronavirus disease 2019 (COVID-19) spreads worldwide, epidemiological models have been employed to evaluate possible scenarios and gauge the efficacy of proposed interventions. Considering the complexity of disease transmission dynamics in cities, stochastic epidemic models include uncertainty in their treatment of the problem, allowing the estimation of the probability of an outbreak, the distribution of epidemic magnitudes, and their expected duration. In this sense, we propose a kinetic Monte Carlo epidemic model that focuses on demography and on age-structured mobility data to simulate the evolution of the COVID-19 outbreak in the capital of Brazil, Brasilia, under several scenarios of mobility restriction. We show that the distribution of epidemic outcomes can be divided into short-lived mild outbreaks and longer severe ones. We demonstrate that quarantines have the effect of reducing the probability of a severe outbreak taking place but are unable to mitigate the magnitude of these outbreaks once they happen. Finally, we present the probability of a particular trajectory in the epidemic progression resulting in a massive outbreak as a function of the cumulative number of cases at the end of each quarantine period, allowing for the estimation of the risk associated with relaxing mobility restrictions at a given time.

Figure 1

Schematics of the KMC model. Individuals (black squares) are able to move in a grid by jumping to nearby sites. When a susceptible (S) individual and an infected (I) one meet, the susceptible may become exposed (E) with probability $p_t$. Exposed individuals turn infectious with a rate of $1/{\tau }_{\mathrm{inc}}$ and infectious individuals are removed (either cured or dead) with rate $1/{\tau }_{\inf }$.

Figure 2

(a) Average number of active infectious individuals as a function of time for different quarantine scenarios and $p_t=0.30$. The shaded area corresponds to one standard deviation. (b) Histograms showing the distribution of peaks of the infection curves in the $p_t=0.30$ case. The inset shows in details the distribution in the 0.02% to 0.15% population range.

Figure 3

(a) Distribution of the number of days for peaks in the infection curves to be reached in the case of simulations that resulted in large outbreaks. (b) Average attack rate taken from simulations that produced large outbreaks as a function of time for the different mobility restriction scenarios.

Figure 4

(a) Average reproduction number as a function of time for simulations with still active infections after quarantine. Time starts counting from the seventh day after the end of quarantine in each scenario. (b) Cumulative conditional probability of an outbreak resulting in $>90$% infected individuals as a function of the cumulative number of cases at the end of quarantine. (c) Probability of at most 1% of the population being infected as a function of quarantine duration. (d) Distribution of the total number of deaths for simulations with different periods of quarantine.