An epidemic model with infector and exposure dependent severity

Area of Science:

• Mathematical epidemiology
• Stochastic modeling
• Public health

Background:

• Existing epidemic models often simplify disease severity.
• Understanding the impact of varying infectiousness is crucial for effective control strategies.
• The role of pre-outbreak vaccination in modulating epidemic trajectories requires further investigation.

Purpose of the Study:

• To define and analyze a stochastic epidemic model incorporating both mild and severe infectiousness.
• To investigate the influence of pre-outbreak vaccination on epidemic dynamics and outcomes.
• To provide approximations for early and main epidemic phases and the final epidemic size.

Main Methods:

• Development of a stochastic epidemic model with two distinct infectious states.
• Application of branching processes for approximating the initial epidemic phase.
• Utilizing laws of large numbers and central limit theorems for analyzing the main epidemic phase and final outcome.
• Conducting simulations and numerical analyses to validate approximations and explore parameter effects.

Main Results:

• The initial epidemic phase can be approximated by a branching process.
• The main epidemic phase and final outcome admit normal approximations.
• Critical vaccination coverage for preventing large outbreaks is derived.
• Vaccination may paradoxically increase the proportion of mildly infected individuals.

Conclusions:

• The proposed stochastic model and its approximations offer valuable insights into epidemic dynamics.
• Branching process and normal approximations are effective even for finite communities.
• Vaccination strategies require careful consideration due to potential counterintuitive effects on infection severity distribution.