Introduction to Group-Structured-Epidemic Model

The spread of an infectious disease in a population is a random process when considering a small group of individuals. However, to a great group of individuals, the use of deterministic behavior is better. Based on these facts, in the literature, there were proposed stochastic and deterministic epidemic models. This work proposes a mixed compartmental epidemic model that allows stratifying the population into groups, considers demographic and environmental variability, presents an approximation to stochastic effects, and contemplates the network effects. The proposed model has a compact form to assist in the synthesis of the control law and parameters estimation strategies. Its objective is to overcome the difficulties encountered when used purely deterministic or purely stochastic models. In the end, to detail and verify the functioning of the proposed model, we present a set of flowcharts and simulations.

Controlling epidemic diseases based only on social distancing level: General case.

The COVID-19 outbreak is an epidemic disease caused by the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). When a new virus emerges, generally, little is known about it, and no vaccines or other pharmaceutical interventions are available. In the case of a person-to-person transmission virus with no vaccines or other pharmaceutical interventions, the only way to control the virus outbreak is by keeping a sustained physical distancing between the individuals. However, to adjust the level of the physical distancing accurately can be so complicated. Any level above the necessary can compromise the economic activity, and any level below can collapse the health care system. This work proposes a controller to keep the number of hospitalized individuals below a limit, and a new group-structured model to describe the COVID-19 outbreak. The proposed controller is robust to the uncertainties in the parameters of the model and keeps the number of infected individuals controlled only by adjusting the social distancing level. Numerical simulations, to show the behavior of the proposed controller and model, are done.