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Age structured SIR model for the spread of infectious diseases through indirect contacts

In this article, we discuss an age-structured SIR model in which disease not only spread through direct person to person contacts for e.g. infection due to surface contamination but it can also spread through indirect contacts. It is evident that age also plays a crucial role in SARS virus infection including COVID-19 infection. We formulate our model as an abstract semilinear Cauchy problem in an appropriate Banach space to show the existence of solution and also show the existence of steady states. It is assumed in this work that the population is in a demographic stationary state and show that there is no disease-free equilibrium point as long as there is a transmission of infection due to the indirect contacts in the environment.