Hierarchical Epidemic Model on Structured Population: Diffusion Patterns and Control Policies

Computation. 2022. Vol. 10. No. 2. Article 31.

Gubar E., Taynitskiy V., Fedyanin D., Petrov I.

In the current study, we define a hierarchical epidemic model that helps to describe the
propagation of a pathogen in a clustered human population. The estimation of a novel coronavirus
spreading worldwide leads to the idea of the hierarchical structure of the epidemic process. Thus,
the propagation process is divided into three possible levels: a city, a country, and a worldwide. On
each level, the pathogen propagation process is based on the susceptible-exposed-infected-recovered
(SEIR) model. We thus formulate a modified transmission model of infected individuals between
levels. The control of the pathogen’s spread can be seen as an optimal control problem. A tradeoff
exists between the cost of active virus propagation and the design of appropriate quarantine
measures. Each level of the hierarchy is defined by its network. A series of numerical experiments
was conducted to corroborate the obtained results.

Keywords: optimal control, epidemic models, SIR epidemic, compartment epidemic models