Dynamics of an epidemic controlled by isolation and quarantine: A probability-based deterministic model

Area of Science:

• Epidemiology
• Mathematical Biology
• Public Health

Background:

• Understanding epidemic dynamics is crucial for effective public health interventions.
• Isolation and quarantine are key strategies for controlling infectious disease spread.
• Deterministic modeling provides a framework for analyzing epidemic control performance.

Purpose of the Study:

• To explore epidemic dynamics under isolation and quarantine control strategies.
• To develop explicit, closed-form equations for key epidemic control metrics.
• To analyze the combined effects of isolation and quarantine on epidemic outcomes.

Main Methods:

• Employed a deterministic mathematical model based on probability principles.
• Derived analytical solutions for final epidemic size under isolation.
• Developed empirical relations for other control scenarios and metrics.
• Modeled intervention strength, speed, and imperfect implementation.

Main Results:

• Developed explicit equations for final epidemic size, maximum prevalence, and epidemic duration.
• Derived an analytical solution for small final sizes under isolation.
• Provided empirical relations for other intervention combinations and scenarios.
• Accounted for quarantine of susceptible individuals and imperfect interventions.

Conclusions:

• The study provides a quantitative framework for evaluating isolation and quarantine strategies.
• The derived equations can inform public health policy for epidemic control.
• Modeling intervention parameters like strength, speed, and imperfectness enhances predictive accuracy.