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

Bhalchandra S Pujari; Snehal M Shekatkar

One of the most celebrated models to study epidemics is the SIR model, and its subsequent variations [6] [7] [8] . This model distributes the total population into compartments for Susceptible, Infected and Recovered individuals, and a set of coupled differential equations describes the movement of population from one compartment to another. Although the model has been used extensively it fails to account for the demographic details and spatial heterogeneity. Several remedies have been proposed to overcome this limitation. For example, 'fully-mixed' assumption can be replaced with network of con-tacts between individuals 9,10 . In the last few days network based SIR-type models were also used to predict the spread of ongoing epidemic of COVID-19 coronavirus 11, 12 . Many studies have used the transmission dynamics of virus in metapopulation patches where the total population is subdivided into a number of discrete patches, each of which is treated as being well-mixed 13 . Bolker et al. 14 used such a model to demonstrate the effectiveness of vaccination against measles outbreak. Arino and van den Driessche 15,16 have proposed a model in which the population of a city is coupled with other cities via a mobility parameter that describes the net rate of intercity migration 16 . Lloyd and Jansen 17 also used metapopulation of n-patches to epidemics' dynamics to see the patterns of synchrony in outbreaks. A more involved model with cross-patch infection was investigated for various cases by Muroya et al. 18 , who looked at the global stability of an endemic.