Waiting time to infectious disease emergence

Area of Science:

• Epidemiology
• Mathematical Biology
• Public Health

Background:

• Emerging infectious diseases require sustained transmission chains.
• The transition to sustained transmission may not align with a system becoming supercritical.
• Predicting the timing of major outbreaks is complex.

Purpose of the Study:

• To analyze the delay time to disease emergence after a system becomes supercritical.
• To model the transition from sporadic to sustained disease transmission.
• To identify key parameters influencing epidemic emergence.

Main Methods:

• Utilized a dynamic bifurcation approach to model disease emergence.
• Employed an SIR (Susceptible-Infectious-Recovered) model with time-varying transmission.
• Incorporated external random infections into the model.
• Derived an analytic density function for bifurcation delay times.

Main Results:

• The derived analytic density function for delay times aligns with stochastic simulations.
• Key parameters influencing emergence delay include infection introduction rate and changes in the basic reproductive ratio.
• The system can become supercritical without immediate widespread infection.

Conclusions:

• Disease emergence is a dynamic bifurcation phenomenon with a characteristic delay.
• The rate of infection introduction and the dynamics of the basic reproductive ratio are critical for predicting emergence.
• Findings can enhance early-warning systems for forecasting disease risk.