The behavioral spillover effect: Modeling behavioral interdependencies in multi-pathogen dynamics

TL;DR

This work introduces the behavioral spillover concept, analyzing how endogenous risk response to one pathogen can indirectly suppress or reshape the spread of another in a two-disease setting with no cross-immunity. It extends a behavioral SEIR framework to a two-pathogen SIRS-like system (SIRSb), parameterized by a spillover strength $s$ and a risk-feedback function $m_i=\exp(-k\widetilde{I}_i)$, and examines no spillover ($s=0$), perfect spillover ($s=1$), and imperfect spillover ($0<s<1$). Through numerical simulations and analytical results, the paper characterizes equilibria, stability conditions, and thresholds for coexistence or exclusion, revealing regimes where one disease dominates or where both persist at reduced levels. It also provides identifiability analyses (structural and practical) to assess which parameters can be inferred from data, highlighting limitations such as identifiability of the immunity period and of perceived-prevalence initial conditions. The findings have practical implications for public health strategies, illustrating how interventions aimed at a high-$R_0$ pathogen can transiently suppress others and how behavioral coupling shapes epidemic waves, while outlining directions for empirical validation and model extensions with heterogeneity and vaccination dynamics.

Abstract

During the recent pandemic, a rise in COVID-19 cases was followed by a decline in influenza. In the absence of cross-immunity, a potential explanation for the observed pattern is behavioral: non-pharmaceutical interventions (NPIs) designed and promoted for one disease also reduce the spread of others. We study short-term and long-term dynamics of two pathogens where NPIs targeting one pathogen indirectly influence the spread of another - a phenomenon we term behavioral spillover. We examine how perceived risk of and response to one disease substantially alters the spread of other pathogens, revealing how waves of different pathogens emerge over time as a result of behavioral interdependencies and human response. Our analysis identifies the parameter space where two diseases simultaneously co-exist, and where shifts in prevalence occur. Our findings are consistent with observations from the COVID-19 pandemic, where NPIs contributed to significant declines in infections such as influenza, pneumonia, and Lyme disease.

Figures (7)

• Figure 1: US Confirmed weekly cases of COVID-19 (blue, left y-axis) and Influenza A and B (red, right y-axis). Source: based on CDC Influenza data CDC_FluView_YYYY and Johns Hopkins Dashboard COVID-19 data dong2020interactive.
• Figure 2: SIRS model with waning immunity and behavioral response for disease $A$ and disease $B$. The system of differential equations for this flow-diagram are represented in System \ref{['eqn:SIRS']} with functions for $\beta_i$ in Table \ref{['table:beta-v2']} and $m_i$ in Equation \ref{['eq:e']}. Solid arrows represent flow of individuals. Dashed lines represent flow of information.
• Figure 3: Dynamics with three levels of spillover and three values of the basic reproduction number of disease $B$. For (a), (d) and (g), there is no spillover, $s=0$; for (b), (e), (h), there is imperfect spillover, $s=0.5$; and for (c), (f), (i), there is perfect spillover, $s=1$. For (a)-(c), $\mathcal{R}_{0,B}=2.9$; for (d)-(f), $\mathcal{R}_{0,B}=2$; and for (g)-(i) $\mathcal{R}_{0,B}=1.3$). Other parameters as in Table \ref{['table:params']} with $\mathcal{R}_{0,A}=3$.
• Figure 4: Persistence and dominance of diseases across one year. (a) Persistence of both diseases (purple) or only disease $A$ (red), which has the higher basic reproduction number. (b) Percentage of the first year that disease $B$ prevalence is above disease $A$ prevalence. For $\mathcal{R}_{0,A}=\mathcal{R}_{0,B}=3$ the diseases produce independent, identical outbreaks so neither are considered dominant. Dots correspond to combination of spillover ($s$) and basic reproduction number of disease $B$ ($\mathcal{R}_{0,B}$) used for plots in Figure \ref{['fig:dyanmics_spillover']}. Note that for $\mathcal{R}_{0,A}=\mathcal{R}_{0,B}=3$, the strains are independent and identical, regardless of the level of spillover, so neither are considered dominant.
• Figure 5: Approximated and analytical persistence of diseases. (a) Approximated threshold for co-existence of both diseases as determined in Theorem \ref{['thm:approximation']}. (b) Analytically based computation of persistence of both diseases (purple) or only disease $A$ (red), which has the higher basic reproduction number. Dots correspond to combination of spillover ($s$) and basic reproduction number of disease $B$ ($\mathcal{R}_{0,B}$) used for plots in Figure \ref{['fig:dyanmics_spillover']}.

Theorems & Definitions (5)

• Theorem 1
• Theorem 2
• Theorem 3
• Theorem 4
• Theorem 5