Population-induced oscillations in blended SI-SEI epidemiological models

Area of Science:

• Epidemiology
• Mathematical Biology
• Population Dynamics

Background:

• Standard compartmental models in epidemiology, such as SI-SEI, are crucial for understanding disease spread.
• These models often incorporate population dynamics, including exponential and logistic growth, which can affect disease transmission.
• The specific form of the incidence function (e.g., mass action vs. bilinear) is a key factor in model behavior.

Purpose of the Study:

• To investigate the impact of population growth patterns on epidemiological models.
• To determine the minimal conditions required to generate sustained oscillations in disease dynamics.
• To analyze the role of incidence form and delays in disease progression within SI-SEI models.

Main Methods:

• Analysis of blended SI-SEI (Susceptible-Infectious-Exposed-Infectious) models.
• Consideration of both exponential and logistic population growth dynamics.
• Examination of 'true mass action' and bilinear incidence functions.

Main Results:

• Global system stability is achieved with 'true mass action' incidence under both exponential and logistic population growth.
• Sustained oscillations emerge when bilinear incidence is used.
• Oscillations necessitate exponentially growing populations, bilinear incidence, and a delay in individuals entering the infective state.

Conclusions:

• The incidence function and population growth significantly influence disease dynamics in SI-SEI models.
• Bilinear incidence, coupled with exponential population growth and a delay in infectivity, is the minimal requirement for sustained oscillations.
• Understanding these minimal dynamical ingredients is key for predicting and managing infectious disease outbreaks.