Optimal control and differential game solutions for social distancing in response to epidemics of infectious diseases on networks

Abstract

Summary In this paper, the problem of social distancing in the spread of infectious diseases in the human network is extended by optimal control and differential game approaches. Hear, SEAIR model on simulation network is used. Total costs for both approaches are formulated as objective functions. SEAIR dynamics for group k that contacts with k individuals including susceptible, exposed, asymptomatically infected, symptomatically infected and improved or safe individuals is modeled. A novel random model including the concept of social distancing and relative risk of infection using Markov process is proposed. For each group, an aggregate investment is derived and computed using adjoint equations and maximum principle. Results show that for each group, investments in the differential game are less than investments in an optimal control approach. Although individuals' participation in investment for social distancing causes to reduce the epidemic cost, the epidemic cost according to the second approach is too much less than the first approach.

Game-Theoretic Frameworks for Epidemic Spreading and Human Decision-Making: A Review

“…Decision making consists of the choices of individuals and the strategies of stakeholders at different hierarchical levels. Decision models considered in the existing literature mainly consider two types of decision-makers: a central planner [12,13,25,27,28,54,57,66,73,75,81,82,87,97,98,103,107,108,112,122,136,[139][140][141][142]144,146,148], which works for social benefits by conducting mechanism design and/or applying enforceable measures directly to the general public, and a collection of individuals with various types Fig. 1 Schematic illustration of the human-in-the-loop epidemic framework consisting of epidemic processes and decision models Fig.…”

“…1 Schematic illustration of the human-in-the-loop epidemic framework consisting of epidemic processes and decision models Fig. 2 A taxonomic summary of well-known epidemic models and their connection [2,13,16,21,27,30,35,36,50,56,59,65,66,114,127,129,130,145] who have their own goals. Considering only one central planner simplifies the case in the real world and allows modelers to focus on a particular aspect of decision making amid the epidemic and derive results that explain certain phenomena.…”

“…For example, [66] uses a weight coefficient w i j ∈ [0, 1] to describe the intensity of the interaction between individual i and j. In epidemic models that do not capture the complete topology (e.g., the 6)), the reduced interaction between individuals is modeled by a scaled infection rate αβ, where α ∈ [0, 1] is the scaling factor and β is the normal infection rate when there is no intervention [12,27,75,103,107,114]. For example, in [75], α captures how well people practice social distancing.…”

“…Timing plays a significant role in the coupling between the epidemic spreading processes and the decision models. Depending on when decisions are made, decision-making can be categories into pre-epidemic decision-making [20,51,53,57,97,112,123,130], during-epidemic decision-making [2,3,16,21,25,27,28,30,31,34,[54][55][56]59,66,73,81,82,84,87,97,107,108,114,120,122,127,129,139,142,145], and post-epidemic decision-making [19,66,106,142]. Pre-epidemic decision-making refers to the decisions made before an epidemic happens or at the beginning of the pandemic.…”

A compartmental model that predicts the effect of social distancing and vaccination on controlling COVID-19

“…The concept of social distancing as a nonpharmaceutical action to reduce and control the spread of an epidemic was studied by Reluga 14 . According to optimal control and differential game approaches, the impact of social distancing in the spread of infectious diseases on the network was studied in 2020 15 .…”