The time dependent SIR model is extended to simulate infection across spatial boundaries. We used New Jersey data as an example to test the extended SIR model. Infection from neighboring counties are modelled by connectivity matrix where each pair of neighboring counties has an element in the connectivity matrix. The magnitude of this matrix element represents the degree to which the infected from one county can affect the susceptible in one of its neighboring counties. Simulated result from the extended spatial SIR model is compared with observed new COVID-19 cases measured in the 21 counties in New Jersey. The extended model has to solve 84 simulated functions simultaneously and the large number of parameters involved in the spatial SIR model are auto tuned using genetic algorithm.
Spatial simulation of COVID-19 new cases development