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

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

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