Compartment models have been proposed in the 1920s as a model for the spread of an infectious disease in a society, in a famous article by Kermack and MacKendrick. The mathematical frame of the original model was a system of partial differential equations. Under reasonable assumptions on the type of interactions, these partial differential equations are reduced to systems of ordinary differential equations that consist of the nowadays widely used Susceptible-Infectious-Removed model and its variations. Discrete versions of these systems are analyzed in terms of difference equations, network models, agent-based models, and appropriate numerical methods. Furthermore, uncertainties are incorporated via stochastic versions in all cases.
The present Research Topic aims to explore areas of social interactions that could be described by compartmental models.
The earliest example of problems solved by compartmental models, beyond epidemiology, is in the area of computer viruses and the spread of rumors and opinions in a society. Recent applications cover areas such as substance abuse, eating disorders, and peer group interactions.
Compartmental models can be solved on complex interacting networks. For example, network topology has been successfully incorporated into SIR epidemic models which could then be analytically or numerically solved according to the complexity of the considered network.
The Research Topic is open to manuscripts that cover technical aspects of social interaction problems and answers questions such as why one would be interested in building a model for physical or social phenomena.
The aim would be to use the model to explain observed facts and to oversee consequences for adopting mitigation measures.
For example, in the case of epidemiology, the model allows estimating the timing of the peak of an epidemic, and the timing of its end. Furthermore, models predict the effects of vaccination campaigns and non-pharmaceutical control measures, and hence they serve as a tool to control the spread and adverse effects of the disease.
Compartment models have been proposed in the 1920s as a model for the spread of an infectious disease in a society, in a famous article by Kermack and MacKendrick. The mathematical frame of the original model was a system of partial differential equations. Under reasonable assumptions on the type of interactions, these partial differential equations are reduced to systems of ordinary differential equations that consist of the nowadays widely used Susceptible-Infectious-Removed model and its variations. Discrete versions of these systems are analyzed in terms of difference equations, network models, agent-based models, and appropriate numerical methods. Furthermore, uncertainties are incorporated via stochastic versions in all cases.
The present Research Topic aims to explore areas of social interactions that could be described by compartmental models.
The earliest example of problems solved by compartmental models, beyond epidemiology, is in the area of computer viruses and the spread of rumors and opinions in a society. Recent applications cover areas such as substance abuse, eating disorders, and peer group interactions.
Compartmental models can be solved on complex interacting networks. For example, network topology has been successfully incorporated into SIR epidemic models which could then be analytically or numerically solved according to the complexity of the considered network.
The Research Topic is open to manuscripts that cover technical aspects of social interaction problems and answers questions such as why one would be interested in building a model for physical or social phenomena.
The aim would be to use the model to explain observed facts and to oversee consequences for adopting mitigation measures.
For example, in the case of epidemiology, the model allows estimating the timing of the peak of an epidemic, and the timing of its end. Furthermore, models predict the effects of vaccination campaigns and non-pharmaceutical control measures, and hence they serve as a tool to control the spread and adverse effects of the disease.