A multivariate spatiotemporal spread model of COVID-19 using ensemble of ConvLSTM networks

swarna kamal paul; Saikat Jana; Parama Bhaumik

All the observations in the dataset is mapped to a spatial region bounded by predefined latitude and longitude. The spatial region may represent a section of a single country or multiple countries. The region is geospatially divided in M x N grids of equal sizes bounded by calculated latitudes and longitudes. It is assumed that disease spread in locations within a grid is spatially autocorrelated due to its smaller size compared to the whole region. Fig. 1a illustrates a grid bounded by latitudes and longitudes. The box represented by the dotted line is called as frame. The frames have overlapping areas in all 4 direction. The overlap allows flow of spatial influence from neighbouring grids. Each frame is in turn divided into L x L pixels which includes the overlapping area. Each pixel represents a bounded area in geospatial region. The values in each pixel is mapped to certain feature in the bounded geospatial region. Separate frame matrices are constructed for each feature and concatenated through channels. For example, new infection count and population are two features and they represent two separate L x L matrices in a frame concatenated across a third axis. Each pixel in the infection count matrix contains the count of new infections (∆I) in the pixel area in a day. Infection count is distributed both in spatial and temporal dimensions. To reduce the variance, the infection count in a pixel is log transformed and normalized in 0-1 scale. Considering R0 factor of Covid-19 between 2 and 3 it is calculated that 60% of the population (P) in an area needs to get infected to attain herd immunity and reduce further spreading [20] . Similar to the SIR model [14] , the total population P is compartmentalized into susceptible (S) and infected/recovered/deceased (I) group. Susceptible population at any day is calculated as 0.6P − I. In a single day new infection count cannot exceed number of susceptible populations. Thus, a pixel value is calculated as ln(∆I + 1) /ln(S + 2). Total population is distributed spatially in similar fashion and it is assumed time invariant within a short interval. Pixel value of population matrix is calculated as ln(0.6P + 1) /ln(max(0.6P)). Each frame is represented as tensor of dimension T x L x L x C, where T is the total time span and C is number of channels or features. As shown in Fig. 1b each training sample in a frame is generated by sliding a time window size of W+1 by 1, leaving behind a test case sample of time window size of W ′ in the most recent period. Number of training samples in a frame can be calculated as T − W ′ − W − 1. Thus, total number of training samples for all frames can be calculated