A model for the spread of infectious diseases compatible with case data

Area of Science:

• Epidemiology and Public Health
• Mathematical Modeling of Infectious Diseases
• Biostatistics

Background:

• Current epidemiological models struggle to align with laboratory-confirmed case data, especially when asymptomatic infections are prevalent.
• Traditional compartmental models often assume instantaneous recovery, which does not reflect real-world disease progression.
• Estimating infection rates from observed data is an ill-posed problem for existing models.

Purpose of the Study:

• To derive a novel epidemiological model that incorporates a delay between infection and recovery.
• To develop a method for reconciling model predictions with observed case data, addressing the challenge of asymptomatic and untested infections.
• To provide a simple, accurate tool for epidemic prediction and analysis.

Main Methods:

• Derived a first-principles epidemiological model featuring a time delay between the newly infected (N) and recovered (R) populations.
• Developed a data-driven approach by solving for ratios of observed quantities, specifically analyzing the behavior of log(N(t)/R(t)).
• Incorporated the effects of social behavior and interventions into the epidemiological model.

Main Results:

• Demonstrated that the ratio log(N(t)/R(t)) should exhibit a linear relationship over time, providing a simple prediction tool.
• Validated the model's accuracy through hindcasting using real-world epidemic data from China and Italy.
• Showed that epidemic suppression can be achieved with low infection rates (<5%) through social measures, challenging traditional herd immunity concepts for deadly diseases.

Conclusions:

• The derived epidemiological model with infection-recovery delays offers improved compatibility with observed case data.
• The log(N(t)/R(t)) linear trend provides a robust and simple method for epidemic forecasting and analysis.
• The model successfully integrates social behavior, highlighting its importance in controlling epidemics without widespread infection or vaccination.