Age-Structured SIR Model for the Spread of Infectious Diseases Through Indirect Contacts.

Area of Science:

• Epidemiology
• Mathematical Biology
• Public Health

Background:

• Age is a critical factor in SARS and COVID-19 transmission dynamics.
• Disease spread occurs through both direct person-to-person and indirect environmental contacts.
• Existing models may not fully capture the interplay of age structure and indirect transmission routes.

Purpose of the Study:

• To develop and analyze an age-structured SIR model accounting for both direct and indirect disease transmission.
• To mathematically prove the existence of solutions and steady states for the proposed model.
• To investigate the impact of indirect transmission on disease dynamics, particularly the absence of a disease-free equilibrium.

Main Methods:

• Formulation of an age-structured SIR model as an abstract semilinear Cauchy problem in a Banach space.
• Mathematical analysis to demonstrate the existence of model solutions and steady states.
• Numerical simulations to assess the influence of indirect contacts on infected population density.

Main Results:

• The model demonstrates that indirect transmission prevents a disease-free equilibrium point in a stationary population.
• Analysis confirms the existence of solutions and steady states under the model's assumptions.
• Numerical results illustrate how indirect contacts affect the density of infected individuals.

Conclusions:

• Indirect transmission pathways are significant and can maintain disease presence, even in a stationary population.
• The age structure and indirect contacts are crucial components for accurate infectious disease modeling.
• Further research using this model can inform targeted public health interventions.