Models for the simple epidemic

Area of Science:

• Epidemiology
• Mathematical Modeling
• Computational Simulation

Background:

• Epidemic modeling relies on both stochastic and deterministic approaches.
• Understanding the relationship between these models is crucial for accurate disease spread predictions.
• Previous research suggested potential equivalence under certain conditions.

Purpose of the Study:

• To formulate and compare discrete and continuous time stochastic and deterministic models for simple epidemics.
• To investigate the practical significance of the equivalence conjecture between stochastic and deterministic models.
• To determine the influence of initial conditions on model convergence.

Main Methods:

• Development of discrete and continuous time stochastic and deterministic epidemic models.
• Comparative analysis of model outputs using simulation studies.
• Assessment of convergence properties based on varying initial susceptible and infective populations.

Main Results:

• The equivalence between stochastic and deterministic models has limited practical importance for large initial susceptible populations.
• The number of initial infectives significantly affects the convergence of stochastic and deterministic models.
• Discrete stochastic models converge to their continuous counterparts as the time step diminishes.

Conclusions:

• Initial conditions, particularly the number of infectives, are critical factors in epidemic model selection and interpretation.
• Discrete stochastic models offer a practical and accurate approach to simulating simple epidemics.
• The convergence of discrete to continuous models supports the validity of discrete-time simulations in epidemiology.