Multi-city modeling of epidemics using spatial networks: Application to 2019-nCov (COVID-19) coronavirus in India

Bhalchandra S Pujari; Snehal M Shekatkar

The accurate estimation of the parameter D which is related to the migration is unavailable. Thus, to check its effect on the epidemic, we vary it and observe the behaviour of the time t max at which the infection maximum occurs for each city. The results are shown in Fig 4 with initial infection only at Delhi. D = 0 corresponds to quarantining Delhi from the rest of the nodes, and hence only Delhi has finite t max while for others t max is undefined. For D > 0, infection spreads to other nodes, and understandably very small values of D result in very large values of t max . Upon increasing D, the value of t max decreases rapidly as more fraction of individuals migrate among the cities. Interestingly, for each node except the initially infected one, there exists a critical value of D at which this trend reverses and t max starts increasing again. We can understand this unexpected behaviour with the following argument. When D is very high, it is analogous to having all the population wellmixed. As a result, too many infected individuals migrate from node to node to infect any one node effectively. In other words, too few infected individuals remain in any given city compared to low D. As a result, even the initially infected node takes long time to get maximally infected, and peaks for all the cities appear simultaneously.