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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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There are several resources listed in the SOURCE METADATA section of the CompartmentalModeling home page. The three books about mathematical epidemiology modeling are my primary general references. For specific topics, diseases, or models I go to the published scientific literature. Google Scholar is helpful for that.
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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