Nonlinear random walks optimize the trade-off between cost and prevention in epidemics lockdown measures: The ESIR model

Contagious diseases can spread quickly in human populations, either through airborne transmission or if some other spreading vectors are abundantly accessible. They can be particularly devastating if the impact on individuals' health has severe consequences on the number of hospitalizations or even deaths. Common countermeasures to contain the epidemic spread include introducing restrictions on human interactions or their mobility in general which are often associated with an economic and social cost. In this paper, we present a targeted model of optimal social distancing on metapopulation networks, named ESIR model, which can effectively reduce the disease spreading and at the same time minimize the impact on human mobility and related costs. The proposed model is grounded in a nonlinear random walk process that considers the finite carrying capacity of the network's metanodes, the physical patches where individuals interact within mobility networks. This latter constraint is modeled as a slack compartment E for the classic SIR model and quantifies the density of vacant spaces to accommodate the diffusing individuals. Formulating the problem as a multi-objective optimization problem shows that when the walkers avoid crowded nodes, the system can rapidly approach Pareto optimality, thus reducing the spreading considerably while minimizing the impact on human mobility as also validated in empirical transport networks. These results envisage ad hoc mobility protocols that can potentially enhance policy making for pandemic control.