Modelling epidemic spread is definitely an important and actual question of applied mathematics. Among the possible methods of describing this process, the current topic is about certain random graphs, in which individuals form groups in two layers, corresponding to a simple model in which everyone lives in a household, and goes to another community (workplace, school) every day. Given the households, the other communities can be formed randomly. Even in this simple model there are various open questions about estimating the parameters of the epidemics about the necessary information for a good estimator. For example, we can ask whether it is sufficient to know the total number of infected individuals, or we also need the number of household with a given number (proportion) of infected individuals.
The goal of the project are as follows: (1) studying the literature of parameter estimation of epidemic spread on two-layer graphs; (2) develop new methods for parameter estimation, either in some specific cases, or more generally; (3) develop and use computer simulations to check that the proposed methods work properly, or to understand this problem in more details.
Hivatkozások
Kiss., I.Z, Miller, J.C., Simon, P.L., Mathematics of Epidemics on Networks; From Exact to Approximate Models, Springer, Interdisciplinary Applied Mathematics 46, (2017).
Ball F, Shaw L. Estimating the within-household infection rate in emerging SIR epidemics among a community of households. J Math Biol. 2015 Dec;71(6-7):1705-35.