  Approaches to the calculation of the full state vector of a larger
epidemiological model for the spread of COVID-19 in Sweden at the initial time
instant from available data and with a simplified dynamical model are proposed
and evaluated. The larger epidemiological model is based on a continuous Markov
chain and captures the demographic composition of and the transport flows
between the counties of Sweden. Its intended use is to predict the outbreak
development in temporal and spatial coordinates as well as across the
demographic groups. It can also support evaluating and comparing of prospective
intervention strategies in terms of e.g. lockdown in certain areas or isolation
of specific age groups. The simplified model is a discrete time-invariant
linear system that has cumulative infectious incidence, infected population,
asymptomatic population, exposed population, and infectious pressure as the
state variables. Since the system matrix of the model depends on a number
transition rates, structural properties of the model are investigated for
suitable parameter ranges. It is concluded that the model becomes unobservable
for some parameter values. Two contrasting approaches to the initial state
estimation are considered. One is a version of Rauch-Tung-Striebel smoother and
another is based on solving a batch nonlinear optimization problem. The
benefits and shortcomings of the considered estimation techniques are analyzed
and compared on synthetic data for several Swedish counties.
