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Motivated by the need for novel robust approaches to modelling the Covid-19epidemic, this paper treats a population of $N$ individuals as an inhomogeneousrandom social network (IRSN). The nodes of the network represent differenttypes of individuals and the edges represent significant social relationships.An epidemic is pictured as a contagion process that changes daily, triggered onday $0$ by a seed infection introduced into the population. Individuals' socialbehaviour and health status are assumed to be random, with probabilitydistributions that vary with their type. First a formulation and analysis isgiven for the basic SI ("susceptible-infective") network contagion model, whichfocusses on the cumulative number of people that have been infected. The mainresult is an analytical formula valid in the large $N$ limit for the state ofthe system on day $t$ in terms of the initial conditions. The formula involvesonly one-dimensional integration. Next, more realistic SIR and SEIR networkmodels, including "removed" (R) and "exposed" (E) classes, are formulated.These models also lead to analytical formulas that generalize the results forthe SI network model. The framework can be easily adapted for analysis ofdifferent kinds of public health interventions, including vaccination, socialdistancing and quarantine. The formulas can be implemented numerically by analgorithm that efficiently incorporates the fast Fourier transform. Finally anumber of open questions and avenues of investigation are suggested, such asthe framework's relation to ordinary differential equation SIR models and agentbased contagion models that are more commonly used in real world epidemicmodelling.

COVID-19: Analytics Of Contagion On Inhomogeneous Random Social Networks