Simple Approximations for Epidemics with Exponential and Fixed Infectious Periods

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Dynamics

Background:

• Analytical approximations offer insights into epidemic dynamics but often rely on unrealistic assumptions, such as exponentially distributed infectious periods.
• Existing models primarily focus on the classic susceptible-infected-recovered (SIR) framework, limiting applicability to diverse epidemiological scenarios.

Purpose of the Study:

• To derive approximations for the entire epidemic curve, accommodating various infectious period distributions.
• To extend the sech-squared approximation to epidemics with arbitrary infectious period distributions (finite second moment).
• To approximate the dynamics of strong epidemics (R₀ ≫ 1) and highlight the significance of early estimation of infectious period distributions.

Main Methods:

• Development of analytical approximations for epidemic curves.
• Extension of the sech-squared approximation to incorporate fixed and gamma-distributed infectious periods.
• Approximation of epidemic time courses for strong epidemic scenarios (R₀ ≫ 1).

Main Results:

• The sech-squared approximation is successfully extended to handle arbitrary infectious period distributions with a finite second moment.
• Approximations for the whole epidemic curve are derived, improving upon existing models.
• The study demonstrates the critical importance of estimating infectious period distributions early in strong epidemics for accurate forecasting.

Conclusions:

• The derived approximations provide a more realistic framework for understanding epidemic dynamics beyond the exponential distribution assumption.
• Accurate estimation of infectious period distributions is vital for effective epidemic control and prediction, particularly in the early stages of strong outbreaks.