I am using the book Manual Mathematical Biology, it is a similar question to the one in the book

I am supposed to set up ‘discrete-time’ or ‘continuous’ equations for the system, and computing their BRN.

Set up SEIR diagrams, explain the meaning of all variables and parameters for the following infection systems smallpox-type pathogen (with life-long immunity) spreading in a homogeneous community with natural mortality - u (mu) , disease-specific mortality uD (mu subscript D), where fraction 0<f<1 of total population is vaccinated (fully protected). Sketch and discuss the resulting dynamic patterns of diseases spread. Explain what happens in the long run (t-> infinity), is there and ‘endemic’ state? Explain the effect of vaccination (f=0 vs. f>0) on disease

patterns.

Latency period 10 days

Infectious period 7 days

Natural Resistance level 0.9

Contact rate 2.7/day