Mathematical modeling of infectious disease

Abstract

Within the last couple of months, the COVID-19 epidemic has determined our public and private life with travel restrictions, lockdown, social distancing, working from home, hygiene rules etc. The daily news informed about reproduction rates and the numbers of current confirmed COVID-19 cases. The media prominently advertised the strategy stay at home in order to flatten the curve.

In this joint talk, we present two mathematical modeling strategies for infectious disease. In the first part, we consider a classical compartment approach which splits the population into different groups, for example Susceptible, Infected, Recovered (SIR model). The evolution of the numbers in each compartment can be described mathematically in form of a system of coupled ordinary differential equations. The transition rates between the different compartments (e.g. infection rate, recovery rate) can be adjusted through available data. For the modeling of the COVID-19 epidemic in Italy and Germany, the SIDHARTE version of a compartment model has been developed¹ in order to simulate and predict the spread of the epidemic and to model possible countermeasures.

In the second part of the talk, the spreading of the disease on a graph representing a smaller population sample is presented. In this model the graph represents a hospital or other institution in which a COVID-19 outbreak could be harmful. In this model we are particularly interested in finding a suitable test strategy, which is one way to apply control to the system. In general is the question of the right control mechanisms to flatten the curve or slow the spread of virus still an open one.