A modified Susceptible-Infected-Recovered model for observed under-reported incidence data

Area of Science:

• Epidemiology
• Mathematical Modeling
• Infectious Disease Dynamics

Background:

• Traditional Susceptible-Infected-Recovered (SIR) models struggle with incomplete case reporting.
• Unobserved infections complicate accurate assessment of disease transmission.
• Accurate estimation requires accounting for the fraction of undetected cases.

Purpose of the Study:

• To derive differential-integral equations for observed incidence data under fixed underreporting.
• To develop a stochastic model for disease incidence based on reported cases.
• To estimate transmission rates and asymptomatic fractions for Coronavirus 2019 in American countries.

Main Methods:

• Derivation of differential-integral equations for observed incidence.
• Development of a stochastic model for conditional disease incidence distribution.
• Bayesian Markov Chain Monte-Carlo (MCMC) sampling for parameter estimation.

Main Results:

• Identifiable parameters for the derived differential equation system.
• Estimation of transmission rates and asymptomatic fractions for eight American countries (Jan 2020 - May 2021).
• Significant variation in reported case fractions observed across countries (e.g., USA: 0.3-0.6, Brazil: 0.2-0.4).

Conclusions:

• The developed model provides a robust framework for analyzing infectious diseases with underreporting.
• Underreporting significantly impacts disease surveillance and requires careful consideration.
• The fraction of reported cases varied substantially across the studied American nations during the early COVID-19 pandemic.