MARKOVIAN RANDOM WALK MODELING AND VISUALIZATION OF THE EPIDEMIC SPREAD OF COVID-19

Haluk Akay; George Barbastathis

The SIR model has been applied to model the previous SARS coronavirus epidemic [7] [8] . Variations of the SIR model include the SEIR model where a new state E (exposed) is introduced, or SIS, where recovered agents are susceptible to reinfection. While these models have been shown to act as accurate approximations for the spread of notable infectious diseases [9] , the pandemic nature of CoVID-19 has resulted in policy-driven responses from communities to actively curb spread of the disease, namely quarantining large numbers of individuals testing positive for the virus [10] . This work accounts for this population by extending the model to add a Quarantined state Q that captures the effect of isolating agents who test positive for the virus. By applying the SIR-Q states to a spatio-temporal random walk model, the spread of CoVID-19 can be visualized and the effect of critical demographic and policy variables upon epidemic spreading are evaluated.