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LeJeune L, Ghaffarzadegan N, Childs LM, Saucedo O. Mathematical analysis of simple behavioral epidemic models. Math Biosci 2024; 375:109250. [PMID: 39009074 DOI: 10.1016/j.mbs.2024.109250] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2024] [Revised: 06/26/2024] [Accepted: 07/06/2024] [Indexed: 07/17/2024]
Abstract
COVID-19 highlighted the importance of considering human behavior change when modeling disease dynamics. This led to developing various models that incorporate human behavior. Our objective is to contribute to an in-depth, mathematical examination of such models. Here, we consider a simple deterministic compartmental model with endogenous incorporation of human behavior (i.e., behavioral feedback) through transmission in a classic Susceptible-Exposed-Infectious-Recovered (SEIR) structure. Despite its simplicity, the SEIR structure with behavior (SEIRb) was shown to perform well in forecasting, especially compared to more complicated models. We contrast this model with an SEIR model that excludes endogenous incorporation of behavior. Both models assume permanent immunity to COVID-19, so we also consider a modification of the models which include waning immunity (SEIRS and SEIRSb). We perform equilibria, sensitivity, and identifiability analyses on all models and examine the fidelity of the models to replicate COVID-19 data across the United States. Endogenous incorporation of behavior significantly improves a model's ability to produce realistic outbreaks. While the two endogenous models are similar with respect to identifiability and sensitivity, the SEIRSb model, with the more accurate assumption of the waning immunity, strengthens the initial SEIRb model by allowing for the existence of an endemic equilibrium, a realistic feature of COVID-19 dynamics. When fitting the model to data, we further consider the addition of simple seasonality affecting disease transmission to highlight the explanatory power of the models.
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Affiliation(s)
- Leah LeJeune
- Department of Mathematics, Virginia Tech, 225 Stanger St, Blacksburg, 24061, USA; Center for the Mathematics of Biosystems, Virginia Tech, Blacksburg, 24061, USA.
| | - Navid Ghaffarzadegan
- Department of Industrial and Systems Engineering, Virginia Tech, 7054 Haycock Rd, Falls Church, 22043, USA.
| | - Lauren M Childs
- Department of Mathematics, Virginia Tech, 225 Stanger St, Blacksburg, 24061, USA; Center for the Mathematics of Biosystems, Virginia Tech, Blacksburg, 24061, USA.
| | - Omar Saucedo
- Department of Mathematics, Virginia Tech, 225 Stanger St, Blacksburg, 24061, USA; Center for the Mathematics of Biosystems, Virginia Tech, Blacksburg, 24061, USA.
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2
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St-Onge J, Burgio G, Rosenblatt SF, Waring TM, Hébert-Dufresne L. Paradoxes in the coevolution of contagions and institutions. Proc Biol Sci 2024; 291:20241117. [PMID: 39137891 PMCID: PMC11321847 DOI: 10.1098/rspb.2024.1117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2023] [Revised: 07/04/2024] [Accepted: 07/04/2024] [Indexed: 08/15/2024] Open
Abstract
Epidemic models study the spread of undesired agents through populations, be it infectious diseases through a country, misinformation in social media or pests infesting a region. In combating these epidemics, we rely neither on global top-down interventions, nor solely on individual adaptations. Instead, interventions commonly come from local institutions such as public health departments, moderation teams on social media platforms or other forms of group governance. Classic models, which are often individual or agent-based, are ill-suited to capture local adaptations. We leverage developments of institutional dynamics based on cultural group selection to study how groups attempt local control of an epidemic by taking inspiration from the successes and failures of other groups. Incorporating institutional changes into epidemic dynamics reveals paradoxes: a higher transmission rate can result in smaller outbreaks as does decreasing the speed of institutional adaptation. When groups perceive a contagion as more worrisome, they can invest in improved policies and, if they maintain these policies long enough to have impact, lead to a reduction in endemicity. By looking at the interplay between the speed of institutions and the transmission rate of the contagions, we find rich coevolutionary dynamics that reflect the complexity of known biological and social contagions.
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Affiliation(s)
- Jonathan St-Onge
- Vermont Complex Systems Center, University of Vermont, Burlington, VT, USA
| | - Giulio Burgio
- Departament d’Enginyeria Informatica i Matematiques, Universitat Rovira i Virgili, Tarragona43007, Spain
| | - Samuel F. Rosenblatt
- Vermont Complex Systems Center, University of Vermont, Burlington, VT, USA
- Department of Computer Science, University of Vermont, Burlington, VT, USA
| | - Timothy M. Waring
- School of Economics, University of Maine, Orono, ME, USA
- Mitchell Center for Sustainability Solutions, University of Maine, Orono, ME, USA
| | - Laurent Hébert-Dufresne
- Vermont Complex Systems Center, University of Vermont, Burlington, VT, USA
- Department of Computer Science, University of Vermont, Burlington, VT, USA
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Evangelou N, Cui T, Bello-Rivas JM, Makeev A, Kevrekidis IG. Tipping points of evolving epidemiological networks: Machine learning-assisted, data-driven effective modeling. CHAOS (WOODBURY, N.Y.) 2024; 34:063128. [PMID: 38865091 DOI: 10.1063/5.0187511] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Accepted: 04/20/2024] [Indexed: 06/13/2024]
Abstract
We study the tipping point collective dynamics of an adaptive susceptible-infected-susceptible (SIS) epidemiological network in a data-driven, machine learning-assisted manner. We identify a parameter-dependent effective stochastic differential equation (eSDE) in terms of physically meaningful coarse mean-field variables through a deep-learning ResNet architecture inspired by numerical stochastic integrators. We construct an approximate effective bifurcation diagram based on the identified drift term of the eSDE and contrast it with the mean-field SIS model bifurcation diagram. We observe a subcritical Hopf bifurcation in the evolving network's effective SIS dynamics that causes the tipping point behavior; this takes the form of large amplitude collective oscillations that spontaneously-yet rarely-arise from the neighborhood of a (noisy) stationary state. We study the statistics of these rare events both through repeated brute force simulations and by using established mathematical/computational tools exploiting the right-hand side of the identified SDE. We demonstrate that such a collective SDE can also be identified (and the rare event computations also performed) in terms of data-driven coarse observables, obtained here via manifold learning techniques, in particular, Diffusion Maps. The workflow of our study is straightforwardly applicable to other complex dynamic problems exhibiting tipping point dynamics.
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Affiliation(s)
- Nikolaos Evangelou
- Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Tianqi Cui
- Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Juan M Bello-Rivas
- Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Alexei Makeev
- Faculty of Computational Mathematics and Cybernetics, Moscow State University, 119991 Moscow, Russia
| | - Ioannis G Kevrekidis
- Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
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Cheng T, Zou X. Modelling the impact of precaution on disease dynamics and its evolution. J Math Biol 2024; 89:1. [PMID: 38709376 DOI: 10.1007/s00285-024-02100-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2023] [Revised: 02/15/2024] [Accepted: 04/18/2024] [Indexed: 05/07/2024]
Abstract
In this paper, we introduce the notion of practically susceptible population, which is a fraction of the biologically susceptible population. Assuming that the fraction depends on the severity of the epidemic and the public's level of precaution (as a response of the public to the epidemic), we propose a general framework model with the response level evolving with the epidemic. We firstly verify the well-posedness and confirm the disease's eventual vanishing for the framework model under the assumption that the basic reproduction numberR 0 < 1 . ForR 0 > 1 , we study how the behavioural response evolves with epidemics and how such an evolution impacts the disease dynamics. More specifically, when the precaution level is taken to be the instantaneous best response function in literature, we show that the endemic dynamic is convergence to the endemic equilibrium; while when the precaution level is the delayed best response, the endemic dynamic can be either convergence to the endemic equilibrium, or convergence to a positive periodic solution. Our derivation offers a justification/explanation for the best response used in some literature. By replacing "adopting the best response" with "adapting toward the best response", we also explore the adaptive long-term dynamics.
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Affiliation(s)
- Tianyu Cheng
- Department of Mathematics, University of Western Ontario, London, ON, N6A 5B7, Canada
| | - Xingfu Zou
- Department of Mathematics, University of Western Ontario, London, ON, N6A 5B7, Canada.
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Song Y, Yang Q. Revisiting the Modularity-Disease transmission Link: Uncovering the importance of intra-modular structure. J Theor Biol 2024; 583:111772. [PMID: 38442844 DOI: 10.1016/j.jtbi.2024.111772] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2023] [Revised: 02/17/2024] [Accepted: 02/22/2024] [Indexed: 03/07/2024]
Abstract
Studies have shown that the internal structure of modules is hardly important for the spread of epidemics. However, most of these studies have assumed that intra-module connectivity and inter-module connectivity do not affect each other. In reality, changes in the internal structure of modules may affect inter-module links and thus change the modularity of the entire network. Therefore, we have developed a theoretical network model with adjustable modularity to investigate the impact of this situation on disease transmission. Our findings indicate that the intra-module structure plays a crucial role in disease outbreaks. Changes in intra-module structure lead to significant numerical changes in peak prevalence and duration of disease. This implies that the potential impact of changes in exposure patterns within modules should also be considered when investigating the exact impact of modular social networks on disease burden.
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Affiliation(s)
- Yan Song
- School of Business and Management, Shanghai international Studies University, 200083 Shanghai, China
| | - Qian Yang
- School of Business and Management, Shanghai international Studies University, 200083 Shanghai, China.
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Levin SA, Weber EU. Polarization and the Psychology of Collectives. PERSPECTIVES ON PSYCHOLOGICAL SCIENCE 2024; 19:335-343. [PMID: 37555427 DOI: 10.1177/17456916231186614] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/10/2023]
Abstract
Achieving global sustainability in the face of climate change, pandemics, and other global systemic threats will require collective intelligence and collective action beyond what we are currently experiencing. Increasing polarization within nations and populist trends that undercut international cooperation make the problem even harder. Allegiance within groups is often strengthened because of conflict among groups, leading to a form of polarization termed "affective." Hope for addressing these global problems will require recognition of the commonality in threats facing all groups collective intelligence that integrates relevant inputs from all sources but fights misinformation and coordinated, cooperative collective action. Elinor Ostrom's notion of polycentric governance, involving centers of decision-making from the local to the global in a complex interacting framework, may provide a possible pathway to achieve these goals.
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Affiliation(s)
- Simon A Levin
- Department of Ecology and Evolutionary Biology, Princeton University
| | - Elke U Weber
- Department of Psychology and School of Public and International Affairs, Princeton University
- Andlinger Center for Energy and the Environment, Princeton University
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Lim TY, Xu R, Ruktanonchai N, Saucedo O, Childs LM, Jalali MS, Rahmandad H, Ghaffarzadegan N. Why Similar Policies Resulted In Different COVID-19 Outcomes: How Responsiveness And Culture Influenced Mortality Rates. Health Aff (Millwood) 2023; 42:1637-1646. [PMID: 38048504 DOI: 10.1377/hlthaff.2023.00713] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/06/2023]
Abstract
In the first two years of the COVID-19 pandemic, per capita mortality varied by more than a hundredfold across countries, despite most implementing similar nonpharmaceutical interventions. Factors such as policy stringency, gross domestic product, and age distribution explain only a small fraction of mortality variation. To address this puzzle, we built on a previously validated pandemic model in which perceived risk altered societal responses affecting SARS-CoV-2 transmission. Using data from more than 100 countries, we found that a key factor explaining heterogeneous death rates was not the policy responses themselves but rather variation in responsiveness. Responsiveness measures how sensitive communities are to evolving mortality risks and how readily they adopt nonpharmaceutical interventions in response, to curb transmission. We further found that responsiveness correlated with two cultural constructs across countries: uncertainty avoidance and power distance. Our findings show that more responsive adoption of similar policies saves many lives, with important implications for the design and implementation of responses to future outbreaks.
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Affiliation(s)
- Tse Yang Lim
- Tse Yang Lim, Harvard University, Boston, Massachusetts
| | - Ran Xu
- Ran Xu, University of Connecticut, Storrs, Connecticut
| | | | - Omar Saucedo
- Omar Saucedo, Virginia Tech, Blacksburg, Virginia
| | | | | | - Hazhir Rahmandad
- Hazhir Rahmandad, Massachusetts Institute of Technology, Cambridge, Massachusetts
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Morsky B, Magpantay F, Day T, Akçay E. The impact of threshold decision mechanisms of collective behavior on disease spread. Proc Natl Acad Sci U S A 2023; 120:e2221479120. [PMID: 37126702 PMCID: PMC10175758 DOI: 10.1073/pnas.2221479120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2022] [Accepted: 03/27/2023] [Indexed: 05/03/2023] Open
Abstract
Humans are a hyper-social species, which greatly impacts the spread of infectious diseases. How do social dynamics impact epidemiology and what are the implications for public health policy? Here, we develop a model of disease transmission that incorporates social dynamics and a behavior that reduces the spread of disease, a voluntary nonpharmaceutical intervention (NPI). We use a "tipping-point" dynamic, previously used in the sociological literature, where individuals adopt a behavior given a sufficient prevalence of the behavior in the population. The thresholds at which individuals adopt the NPI behavior are modulated by the perceived risk of infection, i.e., the disease prevalence and transmission rate, costs to adopt the NPI behavior, and the behavior of others. Social conformity creates a type of "stickiness" whereby individuals are resistant to changing their behavior due to the population's inertia. In this model, we observe a nonmonotonicity in the attack rate as a function of various biological and social parameters such as the transmission rate, efficacy of the NPI, costs of the NPI, weight of social consequences of shirking the social norm, and the degree of heterogeneity in the population. We also observe that the attack rate can be highly sensitive to these parameters due to abrupt shifts in the collective behavior of the population. These results highlight the complex interplay between the dynamics of epidemics and norm-driven collective behaviors.
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Affiliation(s)
- Bryce Morsky
- Department of Mathematics, Florida State University, Tallahassee, FL32306
- Department of Mathematics & Statistics, Queen’s University, Kingston, ONK7L 3N6, Canada
- Department of Biology, University of Pennsylvania, Philadelphia, PA19104
| | - Felicia Magpantay
- Department of Mathematics & Statistics, Queen’s University, Kingston, ONK7L 3N6, Canada
| | - Troy Day
- Department of Mathematics & Statistics, Queen’s University, Kingston, ONK7L 3N6, Canada
| | - Erol Akçay
- Department of Biology, University of Pennsylvania, Philadelphia, PA19104
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Rahmandad H, Xu R, Ghaffarzadegan N. A missing behavioural feedback in COVID-19 models is the key to several puzzles. BMJ Glob Health 2022; 7:bmjgh-2022-010463. [PMID: 36283733 PMCID: PMC9606737 DOI: 10.1136/bmjgh-2022-010463] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2022] [Accepted: 09/22/2022] [Indexed: 11/11/2022] Open
Affiliation(s)
| | - Ran Xu
- Department of Allied Health Sciences, University of Connecticut, Storrs, Connecticut, USA
| | - Navid Ghaffarzadegan
- Department of Industrial and Systems Engineering, Virginia Tech, Falls Church, Virginia, USA
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Abstract
Behavioral responses influence the trajectories of epidemics. During the COVID-19 pandemic, nonpharmaceutical interventions (NPIs) reduced pathogen transmission and mortality worldwide. However, despite the global pandemic threat, there was substantial cross-country variation in the adoption of protective behaviors that is not explained by disease prevalence alone. In particular, many countries show a pattern of slow initial mask adoption followed by sharp transitions to high acceptance rates. These patterns are characteristic of behaviors that depend on social norms or peer influence. We develop a game-theoretic model of mask wearing where the utility of wearing a mask depends on the perceived risk of infection, social norms, and mandates from formal institutions. In this model, increasing pathogen transmission or policy stringency can trigger social tipping points in collective mask wearing. We show that complex social dynamics can emerge from simple individual interactions and that sociocultural variables and local policies are important for recovering cross-country variation in the speed and breadth of mask adoption. These results have implications for public health policy and data collection.
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