# Epidemic Models on Networks

Mathematical theory of epidemiology starts with the work of Kermack and McKendrick, “Contributions to the Mathematical Theory of Epidemics” (1927). The basic model is structured as a subdivision of a population into “Susceptible”, “Infected” and “Recovered/Removed” individuals. The passage from the Susceptible compartment to the Infected compartment is via the “infectious force” that is proportional to the product of the numbers of people in both departments. This approach brings in nonlinearity into the model and leads to a number of interesting features.
In recent years, the study of epidemic models evolved in different directions both in terms of mathematical tools and in view of applications to social interactions and to computer networks.

The original model for the spread of epidemics, which leads to ordinary differential equations fails to represent the spatial dynamics. Its generalization to partial differential equations represents the spread via diffusion but it is insufficient to reflect current human mobility patterns. Studies of epidemics on networks aim to explain the spread of an epidemic in a society or between societies via interactions through the nodes of a network. Current human mobility patterns are mostly long distance travels, as hopping between nodes of a graph. The study of epidemics on networks is of current interest in view of its applications and its mathematical challenges. Epidemic models are used not only for the spread of contagious diseases, but also for the study of various social interactions.

In the last decade, the use of networks in modelling the spread of an infectious disease has been a growing field and it attracts a great deal of interdisciplinary interest from fields as disparate as biology, mathematics, physics and social sciences. The underlying reason is that these epidemic models can be used not only for the analysis of the spread of contagious diseases but also for the study of various social interactions.
This Research Topic will present recent research results in "Epidemic Models on Networks". We welcome papers using network tools with real world applications, across diverse areas.

Keywords: Epidemic Models, Network Models, Mobility Patterns, Social Networks, SIR Models.

Important Note: All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.

Mathematical theory of epidemiology starts with the work of Kermack and McKendrick, “Contributions to the Mathematical Theory of Epidemics” (1927). The basic model is structured as a subdivision of a population into “Susceptible”, “Infected” and “Recovered/Removed” individuals. The passage from the Susceptible compartment to the Infected compartment is via the “infectious force” that is proportional to the product of the numbers of people in both departments. This approach brings in nonlinearity into the model and leads to a number of interesting features.
In recent years, the study of epidemic models evolved in different directions both in terms of mathematical tools and in view of applications to social interactions and to computer networks.

The original model for the spread of epidemics, which leads to ordinary differential equations fails to represent the spatial dynamics. Its generalization to partial differential equations represents the spread via diffusion but it is insufficient to reflect current human mobility patterns. Studies of epidemics on networks aim to explain the spread of an epidemic in a society or between societies via interactions through the nodes of a network. Current human mobility patterns are mostly long distance travels, as hopping between nodes of a graph. The study of epidemics on networks is of current interest in view of its applications and its mathematical challenges. Epidemic models are used not only for the spread of contagious diseases, but also for the study of various social interactions.

In the last decade, the use of networks in modelling the spread of an infectious disease has been a growing field and it attracts a great deal of interdisciplinary interest from fields as disparate as biology, mathematics, physics and social sciences. The underlying reason is that these epidemic models can be used not only for the analysis of the spread of contagious diseases but also for the study of various social interactions.
This Research Topic will present recent research results in "Epidemic Models on Networks". We welcome papers using network tools with real world applications, across diverse areas.

Keywords: Epidemic Models, Network Models, Mobility Patterns, Social Networks, SIR Models.

Important Note: All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.

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## Topic Editors

 10 September 2021 Abstract 08 January 2022 Manuscript

## Participating Journals

Manuscripts can be submitted to this Research Topic via the following journals:

## Topic Editors

 10 September 2021 Abstract 08 January 2022 Manuscript

## Participating Journals

Manuscripts can be submitted to this Research Topic via the following journals:

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