Lab Session 3:Using Maple to Explore S-I-R Models (D

LAB SESSION 3:USING MAPLE TO EXPLORE S-I-R MODELS (D. Kirschner)

GOALS for LAB: *********WORK IN TEAMS of TWO PEOPLE

1) We are going to develop an S-I-R type model to model HIV spread. 2) Decide a specific question that we want to ask 3) Once we have done that, we are go code it up on Maple and run simulations.

STEPS: 1) We first need to develop the model. What do we know about HIV spread? i) Who are the susceptible people? ii) Should we consider birth/death processes? iii) How many infected classes are there? iv) How large is our population? v) Are we considering interactions which are heterosexual, homosexual or both? vi) How long do individuals remain in each compartment of the model?

2) .Follow the modeling outline carefully to set up the model. i) decide on the dependent variables in your model (i.e. S, I, etc…) ii) draw a picture of the interactions and dynamics effecting each variable iii) determine in words these interactions for rate change equations for each population involved iv)choose mathematical expressions describing each term a) find steady states…should be at least 2: the uninfected & the epidemic state. Can you find the Jacobean and plug in your uninfected state and b) try to find the eigenvalues? This should give you an Ro. v) choose initial values for each of the population variable vi)try to choose parameter values for the parameters vii)Using the code from the MAPLE lab we did yesterday (called lecture2.mws) viii)code up the equations using the EXACT syntax that is shown there changing the variable names and parameters names and equations to be those of your model. viii)Vary the parameters and see what parameters lead you to epidemic or clearance ix) try to figure out how print out (i.e. graph) prevalence of disease (number of cases/total population) as a measure of how bad the epidemic can get when you vary parameter values

3) OK, for you more ADVANCED people who get up this part quickly, answer this Question using a modified model (i.e. how would you modify the model to include Vaccination?) x)What if we had a vaccine to prevent HIV infection. How many people would we need to vaccinate to eradicate the epidemic?

GOOD LUCK AND HAVE FUN!!!