Data-driven dynamical analysis of an age-structured model: A graph-theoretic approach

Abstract

The dynamics of the propagation and outspread of infectious diseases are eminently intricate, mainly due to the heterogeneity of the host individuals. In this paper, an age-stratified SEIR (susceptible-exposed-infected-recovered) epidemiological model incorporating saturated treatment function and heterogeneous contact rates is developed to study infectious disease transmission dynamics among various age groups. The expression for the basic reproduction number $R_0$ and conditions for the global stability of the system have been derived by a recently developed graph-theoretic (GT) approach. Digraph reduction creates a GT version of the Gauss elimination method for computing the $R_0$. The global dynamics results have been formed by constructing the Lyapunov function using a GT approach. The endemic equilibrium exists uniquely if $R_0>1$, whereas the disease-free equilibrium is observed to be globally stable if $R_0\le 1$. The numerical simulations are demonstrated by extracting the daily reported COVID-19 cases for the second wave in Italy. The age-dependent contact matrix for the Republic of Italy (data sourced from the POLYMOD study) is computed via paper–diary methodology (PDM) grounded on a population-prospective survey in European countries. Our numerical findings imply that (i) for the age group (20–49) years and (50–69) years, the number of infected persons is quite double as compared with the exposed cases; (ii) approximately 50% of positive cases lies in (20–69) years age group; (iii) for the (00–19) years age group, only half of the exposed individuals got infected; and (iv) a consistent graph is detected for the age group of (70–99) years in both cases; it shows that almost all the exposed got infected.