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Formation of the COVID19 infection cluster and effectiveness of contact trace to suppress it are analyzed with computer simulation using an agent-based model. Some parameters are reported from clinical studies like incubation period(lognormal distribution with mean 5.6 days and SD 3.9 days) [1,2]. For these parameters, Monte Carlo sampling using these distribution functions are done. Parameters unknown for the COVID19 infection are assumed appropriately, for example, time interval being infective after infection be one third of pre-symptomatic or asymptomatic period, and check its effect with sensitivity analysis.
Simulations are made for systems with N agents in a closed system contacting with each other randomly among agents except ones in symptomatic state. Initially, there are one just-infected agent in pre-symptomatic state and (N-1) susceptible agents. Systems with N=1000 are simulated, but ones with smaller (more than a few) or larger N show statistically the same behavior. For a given number of basic reproduction, R0, contacting probability and infection probability are determined so that they realize the given R0 in average. Typical value of R0 used in the simulations are 2.5. For the contact trace, a privacy-preserving proximity trace[3] is simulated. When an agent found to be COVID19 positive, send alerts to agents contacted previous some interval and ask to be isolated for some period.
Sensitivity analysis for the model parameters are made, and the followings are observed:
(1) Time delay between symptomatic to alert, and basic reproduction number influence strongly on peak value of infected rate.
(2) Rate of asymptomatic agent affects on it.
(3) Effect of contact alert does not change if alert interval, that is, time interval of contact alert, and isolating time of alert receivers are longer than about one week. Contact alert does not work if these times are less than four days.
(4) Effect of contact alert is proportional to square of rate of agent with contact alert application.