An epidemic model for non-first-order transmission kinetics

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Dynamics

Background:

• Compartmental models, like the Susceptible-Infectious-Removed (SIR) scheme, are fundamental in epidemiology for modeling disease spread using ordinary differential equations.
• The standard SIR model relies on a first-order rate law for transmission, assuming disease spread is directly proportional to the infectious agent concentration.

Purpose of the Study:

• To challenge the universal applicability of the first-order rate law in SIR models.
• To propose and validate a modified SIR model incorporating mixed-order kinetics for disease transmission.
• To provide a more realistic mathematical framework for understanding and managing epidemics.

Main Methods:

• Developed a modified compartmental SIR model based on mixed-order chemical reaction kinetics.
• Derived a general rate law applicable to non-first-order transmission kinetics.
• Applied and validated the modified model using early-phase COVID-19 pandemic data from 127 countries.

Main Results:

• The modified epidemic model demonstrated superior realism compared to the classic first-order kinetics SIR model when analyzing COVID-19 data.
• Identified two key coefficients: transmission rate constant (k), useful for evaluating control measures, and transmission reaction order (n), reflecting intrinsic epidemic properties.
• The proposed rate law is broadly applicable to disease transmission exhibiting mixed-kinetics and heterogeneous mechanisms.

Conclusions:

• The modified SIR model with mixed-order kinetics offers a more accurate representation of epidemic spread than traditional models.
• The model's parameters (k and n) provide valuable insights into disease dynamics and the effectiveness of interventions.
• Early analysis using this modified model can aid in timely epidemic insight and the development of effective control strategies at the onset of outbreaks.