Related Experiment Video
Updated: May 19, 2026
07:36
Contact-Free Co-Culture Model for the Study of Innate Immune Cell Activation During Respiratory Virus Infection
Published on: February 28, 2021
Dynamic equilibria in an epidemic model with voluntary vaccinations
Frederick H Chen1, Allin Cottrell
1Department of Economics, Wake Forest University, Winston-Salem, North Carolina, USA. chenfh@wfu.edu
Journal of Biological Dynamics
|August 11, 2012
Summary
Individual vaccination decisions in epidemic models depend on perceived costs and benefits. Low vaccine efficacy can lead to multiple outcomes, influenced by public expectations rather than initial conditions.
Area of Science:
- Epidemiology
- Mathematical Biology
- Public Health
Background:
- Voluntary vaccination dynamics are crucial for epidemic control.
- Individual decisions to vaccinate are often based on cost-benefit analyses.
Purpose of the Study:
- To analyze the dynamics of an epidemic model incorporating voluntary vaccination decisions.
- To investigate the impact of individual economic/game-theoretic approaches on vaccination behavior and epidemic spread.
Main Methods:
- Modeling individual vaccination decisions using a game-theoretic approach.
- Analyzing the resulting epidemic model for steady-state and periodic equilibria.
Main Results:
- Demonstrated coexistence of multiple steady-state and periodic equilibria when vaccine efficacy is low.
- Showed that in cases of multiple steady states, outcomes can depend on agents' expectations, not just initial conditions.
Conclusions:
- Individual cost-benefit assessments of vaccination can lead to complex epidemic dynamics.
- Expectations play a significant role in determining epidemic trajectories when multiple equilibria exist, especially with low vaccine efficacy.
Related Concept Videos
01:25Modeling with Differential Equations
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
01:28Infectious Diseases and Their Occurrence
Infectious diseases appear in populations through various transmission patterns, influenced by pathogen characteristics, population immunity, environmental conditions, and social behavior. Understanding these patterns is essential for effective public health surveillance and intervention. These categories—sporadic, outbreak, epidemic, pandemic, and endemic—help frame the nature and scope of disease events.Sporadic diseases occur irregularly and infrequently, without a predictable temporal or...
01:21Causality in Epidemiology
Causality or causation is a fundamental concept in epidemiology, vital for understanding the relationships between various factors and health outcomes. Despite its importance, there's no single, universally accepted definition of causality within the discipline. Drawing from a systematic review, causality in epidemiology encompasses several definitions, including production, necessary and sufficient, sufficient-component, counterfactual, and probabilistic models. Each has its strengths and...
01:09Pharmacodynamic Models: Additive and Proportional Drug Effect Model
Drug response models describe how pharmacological agents interact with biological systems to produce measurable effects. Baseline responses are inherent physiological activities without a drug significantly influencing the observed pharmacological outcomes. Depending on the drug response model employed, these baseline responses may combine with the drug's effect in either an additive or proportional manner.Additive Drug Response ModelIn the additive model, the drug effect is independent of the...
01:51Vaccinations
Overview
01:18Pharmacodynamic Models: Emax Drug–Concentration Effect Model
The Emax drug-concentration effect model is central to pharmacodynamics in drug discovery and development. This model is predicated on the receptor occupancy theory, which posits that the effect of a drug is directly related to the number of receptors occupied by the drug and the resultant complex formation.The model describes the reversible interaction between a drug (C) and a receptor (R) to form a drug-receptor complex (RC). The kinetics of this interaction are quantified by an equation that...