Modeling and Optimal Control for Resource Allocation in the Epidemic Monitoring of a Multi-group Population

In the last 3 years, the entire world has been facing the sanitary emergency due to the SARS-CoV2; it has been stressed the mutual interdependence of the human populations, as well as the strong impact of specific conditions, such as age, work, habits, on the disease spread among subgroups of a given population. Moreover, the high percentage of asymptomatic individuals, especially among young subjects, improves the infection spread among groups with higher probability of fatal consequences. The vaccination campaign has strongly contributed to reduce mortality, so bringing the epidemic scenario probably closer to the endemic state. Nevertheless, the loss of the vaccination protection, the appearance of new variants and the mixing of moving people require a surveillance action to reduce new virus waives. By suitable modeling and optimal control design, this paper addresses the planning of a swab test campaign for the surveillance of the disease spread within a given multi-group population, when resource limitation and distinctive epidemiological characteristics of the subgroups are present. The proposed approach, applied on a case study in which the population is split into four groups, stresses the importance of a suitable tuned swab test campaign, saving a significant number of infections (and therefore of human lives), by scheduling the surveillance effort on the different populations. The determination of this kind of control is useful not only in the endemic condition, but also as general surveillance strategy at the beginning of an epidemic spread, with limitations in material and logistic resources.