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Related Experiment Video

Updated: Jun 2, 2026

A Mouse Model for the Transition of Streptococcus pneumoniae from Colonizer to Pathogen upon Viral Co-Infection Recapitulates Age-Exacerbated Illness

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Published on: September 28, 2022

Threshold analysis for a diffusive SIS epidemic model with infection-age.

Salih Djilali¹, Soufiane Bentout², Toshikazu Kuniya³

¹Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University, Chlef, 020000, Algeria.

Mathematical Biosciences

|May 31, 2026

Summary

This study analyzes a diffusive SIS epidemic model. A basic reproduction number (R0) determines if the disease-free state is stable (R0<1) or if endemic states exist (R0>1).

Keywords:

Basic reproduction number Epidemic model Infection age Spatial diffusion

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Area of Science:

Epidemiology
Mathematical Biology
Dynamical Systems

Background:

Investigates a diffusive SIS (Susceptible-Infectious-Susceptible) epidemic model.
Generalizes a previously studied reaction-diffusion model with age structure.
Incorporates Neumann boundary conditions for spatial dynamics.

Purpose of the Study:

Define and analyze the basic reproduction number (R0) for the model.
Determine the conditions for disease eradication or persistence.
Characterize the steady states of the epidemic model.

Main Methods:

Utilizes the next-generation operator to define R0.
Analyzes the asymptotic behavior of model solutions.
Applies techniques from reaction-diffusion theory and dynamical systems.

Main Results:

The basic reproduction number (R0) is rigorously defined.
If R0 < 1, the unique disease-free steady state is globally attractive.
If R0 > 1, at least one non-negative endemic steady state exists.

Conclusions:

The threshold dynamics of the diffusive SIS model are characterized by R0.
The model predicts disease extinction or persistence based on R0.
The study provides insights into the spatial spread and endemicity of infectious diseases.