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How to properly incorporate births and deaths in SIR COVID-19 model?

Based on the published article Mathematical analysis of the SIR model for COVID-19 transmission. I am trying to build the following 4 models. However, once I add the births and deaths they seem wrong. I would appreciate any guidance to figure out my mistake. Thank you in advance!!!
POSTED BY: Athanasios Paraskevopoulos
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POSTED BY: Robert Nachbar

I use the following book Mathematical Models in Population Biology and Epidemiology (Texts in Applied Mathematics Book 40) 2nd Edition
POSTED BY: Athanasios Paraskevopoulos

The basic reproduction number R0 is not correct. Martcheva covers this model in her book on pp. 50-51. The notebook below shows how to compute R0 with the next generation matrix method using functions in the CompartmentalModeling paclet.
POSTED BY: Robert Nachbar

Thank you very much for your reply. I am very interested in the models for epidemiology. I have read all your posts in the wolfram community. Do you have any books or resources for me to read?

Thank you in advance!

(ps: I hope Wolfram U will organise daily’s study group on epidemiological models again
POSTED BY: Athanasios Paraskevopoulos
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