Modeling the impact of hospitalization-induced behavioral changes on SARS-COV-2 spread in New York City

TL;DR

This work develops a multi-group behavioral-epidemiology framework to quantify how hospitalization-induced and peer-influence-driven behavioral changes alter SARS-CoV-2 transmission in New York City. The authors analyze a general $n$-group model and a tractable two-group case, deriving existence and stability results for disease-free equilibria in terms of the control reproduction number $\mathbb{R}_c$ and the influence ratio $\Gamma$. They calibrate the two-group model with NYC first-wave hospitalization data, validate via second-wave predictions, and compare to a behavior-free variant, showing that explicit behavioral heterogeneity is essential for accurate trajectories and burden forecasts. Global sensitivity analysis highlights key drivers of peak hospitalizations and mortality (notably $\beta_a$, $\beta_i$, $\theta_{l,1}$, and $\sigma_e$), and simulations reveal that hospitalization-driven behavior changes generally have a larger impact on outcomes than peer influence alone, with timing and efficacy of NPIs critically shaping the pandemic's course. Overall, the study demonstrates the value of incorporating behavioral heterogeneity and hospitalization-linked risk perception into epidemic forecasts and policy planning.

Abstract

A novel behavior-epidemiology model, which considers $n$ heterogeneous behavioral groups based on level of risk tolerance and distinguishes behavioral changes by social and disease-related motivations (such as peer-influence and fear of disease-related hospitalizations), is developed. In addition to rigorously analyzing the basic qualitative features of this model, a special case is considered where the total population is stratified into two groups: risk-averse (Group 1) and risk-tolerant (Group 2). The two-group behavior model has three disease-free equilibria in the absence of disease, and their stability is analyzed using standard linearization and the properties of Metzler-stable matrices. Furthermore, the two-group model was calibrated and validated using daily hospitalization data for New York City during the first wave, and the calibrated model was used to predict the data for the second wave. Numerical simulations of the calibrated two-group behavior model showed that while the dynamics of the SARS-CoV-2 pandemic during the first wave was largely influenced by the behavior of the risk-tolerant individuals, the dynamics during the second wave was influenced by the behavior of individuals in both groups. It was also shown that disease-motivated behavioral changes had greater influence in significantly reducing SARS-CoV-2 morbidity and mortality than behavior changes due to the level of peer or social influence or pressure. Finally, it is shown that the initial proportion of members in the community that are risk-averse (i.e., the proportion of individuals in Group 1 at the beginning of the pandemic) and the early and effective implementation of non-pharmaceutical interventions have major impacts in reducing the size and burden of the pandemic (particularly the total SARS-CoV-2 mortality in New York City during the second wave).

Figures (21)

• Figure 1: Flow diagram of the heterogeneous $n-$group behavior model \ref{['eq:fullmodel']}, illustrating the disease dynamics (top panel) and the influence dynamics with $n$ behavioral groups (bottom panel).
• Figure 2: Profile of the effective contact rate modification parameter ($c_i^A(t)$), as a function of the proportion of the population that is hospitalized ($I_h(t)/N(t)$), for various values of $a_i$ (the modification parameter for the hospitalization-induced behavior change by individuals in group $i$). Blue, orange, green, and red curves represent, respectively, the case with $a_i=$ 0, 2,200, 6,000, and 30,000.
• Figure 3: Simulations of the 2-group behavior model \ref{['eq:n2model']}, showing the profile of the total number of infected individuals (top) and the total number of individuals in the community, stratified by behavioral group ($N_1(t)$ and $N_2(t)$)(bottom), as a function of time for various initial conditions. Column (a): $c^B_{12}=0.5,c^B_{21}=0.25$ ($\Gamma=2>1$). Column (b): $c^B_{12}=0.25, c^B_{21}=0.5$ ($\Gamma=0.5<1$). Column (c): $c^B_{12}=c^B_{21}=0.5$ ($\Gamma=1$). In all panels, all other parameter values used in these simulations are as given in Tables \ref{['tab:fixedparams']} and \ref{['tab:fittedparams_full']}, but with $\theta_l=1$, $\beta_a=0.1$, and $\beta_i=0.05$ (so that, $\mathbb{R}_c=0.78<1$). These simulations show that when $\mathbb{R}_c<1$, solutions of model \ref{['eq:n2model']} converge to G1DFE if $\Gamma>1$ (see Figure(a)), G2DFE if $\Gamma<1$ (see Figure(b)), and G3DFE if $\Gamma=1$ (see Figure(c)), in line with Theorems \ref{['thm:LASG1DFE']}-\ref{['thm:LASG3DFE']}.
• Figure 4: Simulations of the 2-group behavior model \ref{['eq:n2model']}, showing the profile of the total number of infected individuals (top) and the total number of individuals in the community, stratified by behavioral group ($N_1(t)$ and $N_2(t)$)(bottom), as a function of time for various initial conditions. Column (a): $c^B_{12}=0.5,c^B_{21}=0.25$ ($\Gamma=2>1$). Column (b): $c^B_{12}=0.25, c^B_{21}=0.5$ ($\Gamma=0.5<1$). Column (c): $c^B_{12}=c^B_{21}=0.5$ ($\Gamma=1$). In all panels, all other parameter values used in these simulations are as given in Tables \ref{['tab:fixedparams']} and \ref{['tab:fittedparams_full']}, but with $\theta_l=1$, $\beta_a=1$, and $\beta_i=0.5$ (so that, $\mathbb{R}_c=7.8>1$). These simulations show that when $\mathbb{R}_c>1$, solutions of the 2-group model \ref{['eq:n2model']} converge to the extinction equilibrium (TDFE), regardless of the value of $\Gamma$.
• Figure 5: Stability regions of different disease-free equilibria of the 2-group behavior model \ref{['eq:n2model']}, as determined by the values of the control reproduction number $\mathbb{R}_c$ and the relative influence ratio $\Gamma$. This figure shows that the 2-group behavior model \ref{['eq:n2model']} has a bifurcation at $\mathbb{R}_c=1$ and a separatrix at $\Gamma=1$.

Theorems & Definitions (10)

• Theorem 2.1
• proof
• Definition 3.1
• Definition 3.2
• Definition 3.3
• Theorem 3.4
• Theorem 3.5
• Theorem 3.6
• proof
• Proposition B.1