Comparison of a microscopic and a macroscopic age-dependent SIR model

<p>In this work, we compare two structurally different modelling approaches for the simulation of an age-dependent SIR (susceptible, infected, recovered)-type epidemic spread: a microscopic agent-based model and a macroscopic integro-partial differential equation model. Doing so, we put a newly derived mean-field theorem for mixed state-spaces (continuous and discrete) to the test, analytically proving the asymptotic equivalence of the results of both simulations on the aggregate level. Afterwards, both models are executed and compared for abstract scenarios to affirm the derived equivalence. As both models are hereby proven to deliver (asymptotically) the same results, they can be used to supplement each other in terms of structural knowledge of the model, identification and determination of parameters and their values, as well as finally verification and validation.</p

Set-membership estimations for the evolution of infectious diseases in heterogeneous populations

The paper presents an approach for set-membership estimation of the state of a heterogeneous population in which an infectious disease is spreading. The population state may consist of susceptible, infected, recovered, etc. groups, where the individuals are heterogeneous with respect to traits, relevant to the particular disease. Set-membership estimations in this context are reasonable, since only vague information about the distribution of the population along the space of heterogeneity is available in practice. The presented approach comprises adapted versions of methods which are known in estimation and control theory, and involve solving parametrized families of optimization problems. Since the models of disease spreading in heterogeneous populations involve distributed systems (with non-local dynamics and endogenous boundary conditions), these problems are non-standard. The paper develops the needed theoretical instruments and a solution scheme. SI and SIR models of epidemic diseases are considered as case studies and the results reveal qualitative properties that may be of interest.Austrian Science Foundation (FWF