Abstract
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 trade-off 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.
Highlights
Infectious diseases still pose a serious medical challenge worldwide, with millions of deaths per year estimated to be directly related to infectious diseases
The outbreak of new diseases such as severe acute respiratory syndrome (SARS), Middle East respiratory syndrome (MERS), the rise of Ebola, and, most recently, the COVID-19 pandemic represent a few examples of significant problems that the public healthcare system and medical science research need to address
In contrast to classical SIRS models [43,44], where populations are divided into three groups, we formulate a three-level modified SEIR model (SusceptibleInfected-Recovered-Susceptible) with one virus circulated in a population of size N
Summary
Infectious diseases still pose a serious medical challenge worldwide, with millions of deaths per year estimated to be directly related to infectious diseases. The influenza A (H1N1) virus has the potential to develop into the first influenza pandemic of the twenty-first century [4], accompanied by seasonal influenza accompanies [5] Another important issue is the rate of the pathogen’s spread and the network of contacts for each resident in the population. We establish a hierarchical control-theoretic model to design disease control strategies through quarantine measures to mitigate the impact of epidemics on society. This approach has been motivated by the initial stage of the COVID-19 propagation in China and Italy.
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