A Dynamical Framework for Modeling Fear of Infection and Frustration with Social Distancing in COVID-19 Spread

Abstract

In this paper, we introduce a novel modeling framework for incorporating fear of infection and frustration with social distancing into disease dynamics. We show that the resulting SEIR behavior-perception model has three principal modes of qualitative behavior-no outbreak, controlled outbreak, and uncontrolled outbreak. We also demonstrate that the model can produce transient and sustained waves of infection consistent with secondary outbreaks. We fit the model to cumulative COVID-19 case and mortality data from several regions. Our analysis suggests that regions which experience a significant decline after the first wave of infection, such as Canada and Israel, are more likely to contain secondary waves of infection, whereas regions which only achieve moderate success in mitigating the disease's spread initially, such as the United States, are likely to experience substantial secondary waves or uncontrolled outbreaks.

Long-term regulation of prolonged epidemic outbreaks in large populations via adaptive control: a singular perturbation approach

“…By A1-A4, we have p(t) ≡ p e . Hence, LaSalle's condition is satisfied and global stability follows for (7). Hence, the endemic steady state of the system (6) is globally asymptotically stable.…”

“…Viewing the system from this angle, we note that the infective compartment ( 6) is a PI controller tracking the error between the growth rate of infectives c s β and the removal rate γ with a state-dependent gain I. (In the transformed coordinates (7), p is a linear PI controller). In other words, the system is trying to stabilize β to a level ensuring that the infection stays at a QSS, i.e., İ = 0.…”

“…COVID-19, a highly contagious disease, has been spreading between continents and has already claimed more than 2.5 million lives globally during its first year. Unsurprisingly, this has sparked a renewed interest in the dynamical modeling and analysis of infectious diseases, particularly in the control theory and dynamical systems communities [1][2][3][4][5][6][7][8][9].…”

“…They describe the pandemic as an interaction between two dynamical processes, namely the compartmental component which corresponds to the dynamics of disease, and the regulatory component which corresponds to dynamics of the meta-effects of the disease. The latter dynamics have been referred to by multiple names such as "dynamics of fear" [7,17], "information transmission" [18], "behavior dynamics" [19], "reactive social distancing" [20], and the population observation of the infection level [6].…”

A Multilayer Network Model of the Coevolution of the Spread of a Disease and Competing Opinions

“…She et al 65 examined an opinion model with continuous-valued opinions to study the beliefs of different communities about the severity of disease spread with both cooperative and antagonistic opinion spreading. Epstein et al 19 used compartmental models to study the fear of infection and the fear of vaccines, and Johnston et al 38 examined the fear of infection and frustration with physical distancing.…”