Abstract
Networks and graphs offer a suitable and powerful framework for studying the spread of infection in human and animal populations. In the case of a heterogeneous population, the social contact network has a pivotal role in the analysis of directly transmitted infectious diseases. The literature presents several works where network-based models encompass realistic features (such as contacts networks or host–pathogen biological data), but analytical results are nonetheless scarce. As a significant example, in this paper, we develop a multi-group version of the epidemiological SEIR population-based model. Each group can represent a social subpopulation with the same habits or a group of geographically localized people. We consider also heterogeneity in the weighting of contacts between two groups. As a simple application, we propose a simple control algorithm in which we optimize the connection weights in order to minimize the combination between an economic cost and a social cost. Some numerical simulations are also provided.
Highlights
Environmental Science and Policy Department, Università degli Studi di Milano, 20133 Milan, Italy; Matematica”, and of the ADAMSS Center of the Università degli Studi di Milano (Italy)
The epidemiological modeling of infectious disease transmission has a long history in mathematical biology, for humans [1,2,3,4,5,6,7], animals [3,8] and plants [9,10,11]
Without any interaction with other nodes, within a deterministic approach of the compartmental models, with continuous time t, the epidemic dynamics can be described by the system of differential equations in (1): Ṡ(t) = −λ S(t)
Summary
The transmission of infectious diseases raises many important questions. The spatial component of many transmission systems has been recognized to be of pivotal importance in the recent years. Spatially heterogeneous interventions must be included in the model, and it is essential to properly represent the transmission pattern. A reasonable hypothesis may consider that the spatial aspects of transmission heavily influence the aggregation characteristic of epidemic influence. We need to investigate data by using models that include such spatial connections. The understanding of human mobility and the developing of qualitative and quantitative theories is of key importance for the modeling and for the comprehension of human infectious disease dynamics on geographical scales of different size
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