lab10.desc

# lab10.desc - LAB#10 SIR Model of a Disease Goal Model a...

This preview shows pages 1–2. Sign up to view the full content.

LAB #10 SIR Model of a Disease Goal : Model a disease and investigate its spread under certain conditions. Use graphs generated by pplane (and its many options) to estimate various quantities. Required tools : Matlab routine pplane and its graphing options. Discussion The SIR model is a mathematical model of the spread of an infectious disease satisfying the following assumptions: (i) the disease is short lived and rarely fatal (ii) the disease is spread by contact between individuals (iii) individuals who recover develop immunity. If S ( t ) ,I ( t )and R ( t ) represent the number of S usceptible, I nfected and R ecovered individuals in a population, then it can be shown that with the above assumptions, the system of equations modeling this disease satisﬁes: dS dt = - aSI dI dt = aSI - bI dR dt = bI ( * ) where a and b are positive constants. Because the total population N remains constant (at least in the short term), for small values of t ,wehave N = S ( t )+ I ( t )+ R ( t )( ** ) If we know S ( t )and I ( t ), we also know R ( t ). Hence the 3 rd equation in ( *

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

lab10.desc - LAB#10 SIR Model of a Disease Goal Model a...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online