Lattice Model of Mitigated Epidemic

Abstract

We study a statistical lattice model of a mitigated epidemic. The level of mitigation, defined by measures to slow down the spread of the infection, is characterized by the infection transmissivity. It is determined by people’s mobility, frequency of contacts, and probability to catch the virus from a contact. In the absence of testing the infected people are isolated for a finite period of time during which they are symptomatic. In the presence of testing, people become isolated a soon as they are tested positive. We compute time dependence of daily new infections as function of transmissivity, initial infection, and testing. The duration of the epidemic increases rapidly with the increased level of mitigation while the number of people falling sick daily decreases. Testing, regardless of the level, has little effect on the duration of the epidemic. The total number of people who contract the disease over the lifetime of the epidemic depends weakly on its duration. It does not change significantly for the homogeneous testing of the population at the level below 10% daily.