Question

3. Consider the following data (table 1) reported during an outbreak of bubonic plague in Eyam, England. It can be described by the SIR model without demographics. (2) \frac{dS}{dt} = -\beta SI, \frac{dI}{dt} = \beta SI - \gamma I, \frac{dR}{dt} = \gamma I, where $S(0) = 254$ and $I(0) = 7$. (a) For $\beta = 0.0134$ and $\gamma = 2.19$ plot the model and the data. TABLE 1. Bubonic plague from year 1666. Date (1666) Susceptibles Infectives July 3/4 235 14.5 July 19 201 22 August 3/4 153.5 29 August 19 121 21 September 3/4 108 8 September 19 97 8 October 20 83 0 (b) Explain why this is not a good model by researching the way bubonic plague is transmitted. Write a more realistic model for this outbreak and plot its solutions.

          3. Consider the following data (table 1) reported during an outbreak of bubonic plague in Eyam, England. It can be described by the SIR model without demographics.
(2)
\frac{dS}{dt} = -\beta SI,
\frac{dI}{dt} = \beta SI - \gamma I,
\frac{dR}{dt} = \gamma I,
where $S(0) = 254$ and $I(0) = 7$.
(a) For $\beta = 0.0134$ and $\gamma = 2.19$ plot the model and the data.
TABLE 1. Bubonic plague from year 1666.
Date (1666) Susceptibles Infectives
July 3/4 235 14.5
July 19 201 22
August 3/4 153.5 29
August 19 121 21
September 3/4 108 8
September 19 97 8
October 20 83 0
(b) Explain why this is not a good model by researching the way bubonic plague is transmitted. Write a more realistic model for this outbreak and plot its solutions.

3. Consider the following data (table 1) reported during an outbreak of bubonic plague in Eyam, England. It can be described by the SIR model without demographics.
(2)
(dS)/(dt) = -βSI,
(dI)/(dt) = βSI - γI,
(dR)/(dt) = γI,
where S(0) = 254 and I(0) = 7.
(a) For β = 0.0134 and γ = 2.19 plot the model and the data.
TABLE 1. Bubonic plague from year 1666.
Date (1666) Susceptibles Infectives
July 3/4 235 14.5
July 19 201 22
August 3/4 153.5 29
August 19 121 21
September 3/4 108 8
September 19 97 8
October 20 83 0
(b) Explain why this is not a good model by researching the way bubonic plague is transmitted. Write a more realistic model for this outbreak and plot its solutions.

Added by Rebecca T.

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