Coupling multiscale within-host dynamics and between-host transmission with recovery (SIR) dynamics

Area of Science:

• Epidemiology
• Mathematical Biology
• Virology

Background:

• Multiscale models are crucial for understanding viral infectious diseases by connecting within-host dynamics to population-level transmission.
• Existing models often simplify the complex interplay between individual infection processes and large-scale epidemic spread.

Purpose of the Study:

• To develop and analyze two novel multiscale models coupling within-host infection dynamics with a susceptible-infected-recovered (SIR) framework.
• To investigate how within-host parameters influence between-host transmission dynamics and epidemic outcomes for influenza and Ebola.

Main Methods:

• Development of two multiscale mathematical models integrating within-host viral load with a between-host SIR model.
• Stability analysis of equilibrium points to identify endemic scenarios and bifurcations.
• Numerical simulations to illustrate model predictions for influenza and Ebola virus dynamics.

Main Results:

• The first model (influenza) identified two equilibrium points in the SIR model, indicating endemic states with persistent susceptible and infected populations.
• The between-host system exhibits two bifurcations, dependent on the within-host basic reproduction number and infected population size at equilibrium.
• The second model (Ebola) highlighted the transient inhibitory effect of antibodies on viral replication, impacting the pre-outbreak time window.

Conclusions:

• Multiscale modeling provides a robust framework for understanding viral disease transmission dynamics.
• Disease-induced transmission rates effectively bridge within-host and between-host scales.
• Model insights are critical for predicting epidemic potential and informing public health strategies for diseases like influenza and Ebola.