""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

"That sounds fine. I wanted to share with you what I have completed on the problem, currently I am stuck at this point

C=Contact Rate=2.7/day

q- Probability to Stay Latent- 10-1/10=.90 q=.90

r-Probability to Stay Infected- 7-1/7= r=.86 r=.90

s-Probability to Stay Immune-Infinity/All Life s=1

p=Probability to Survive Infectious Contact (1-p)=Susceptibility 1-p=.33 p=.66

Probability of Infection/Infectious contact 0.9/2.7=.33 Susceptibility=.33

Recovery rate= 1-r= 1-.9=.10

Attached is the handout with similar questions

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

"That sounds fine. I wanted to share with you what I have completed on the problem, currently I am stuck at this point

C=Contact Rate=2.7/day

q- Probability to Stay Latent- 10-1/10=.90 q=.90

r-Probability to Stay Infected- 7-1/7= r=.86 r=.90

s-Probability to Stay Immune-Infinity/All Life s=1

p=Probability to Survive Infectious Contact (1-p)=Susceptibility 1-p=.33 p=.66

Probability of Infection/Infectious contact 0.9/2.7=.33 Susceptibility=.33

Recovery rate= 1-r= 1-.9=.10

Attached is the handout with similar questions