本次英国代写主要为医学建模相关的限时测试
MAT009/MA4609 Healthcare Modelling
1（i）提供以下术语的定义：
•豁免权
•潜伏期
•传染期
•潜伏期[15％]
（ii）考虑一种非致命的传染性儿童疾病，即感染儿童
会从疾病中恢复过来。跟踪方程的微分方程模型
这种疾病在儿童人群中传播的动态是为了
根据以下假设进行开发：
•有固定数量的儿童，n。
•S表示人口中易感儿童的数量。
•I表示人口中被感染儿童的数量。
•R表示人口中恢复的儿童数量。
•b是感染率（SI接触导致新感染的比例
感染）
•r表示每单位时间的恢复率。
清楚说明您所做的任何假设，得出（但不解决）
捕获S，I和R的变化率的必要方程式。
[20％]
（iii）陈述传染性儿童期传播的必要条件
流行病并简要描述卫生官员的方式
可能会尝试减少地方性流行的机会。
[15％]
（iv）现在假设人口不是固定的。让你成为平均值
每单位时间人口中儿童的出生/到达率，v为比率
每单位时间离开人口的儿童数量。推导新的方程式
（但不能解决）S，I和R的变化率。
[20％]
（v）进一步的观察表明，儿童实际上可以反复抓到
疾病，因此在易感和感染状态之间移动。建立在您的
回答上述第（iv）部分，得出新的方程式（但不求解）
S和I的变化率。
[15％]
（vi）建议并简要描述可用于以下目的的替代OR方法
更实际地模拟传染性儿童疾病的传播。
1 (i) Provide definitions for the following terms:
• Immunity
• Latent period
• Infectious period
• Incubation period [15%]
(ii) Consider a non-fatal contagious childhood disease, whereby infected children
will recover from the illness. A differential equation model to track the
dynamics of the spread of such a disease within a population of children is to
be developed with the following assumptions:
• There is a fixed size population of children, n.
• S denotes the number of susceptible children in the population.
• I denotes the number of infected children in the population.
• R denotes the number of recovered children in the population.
• b is the infection rate (the proportion of SI contacts which lead to a new
infection)
• r denotes the recovery rate per unit time.
Clearly stating any assumptions you make, derive (but do not solve) the
necessary equations to capture the rate of change of S, I and R.
[20%]
(iii) State the required conditions for the spread of the contagious childhood
disease to become endemic and briefly describe ways in which health officials
might try to reduce the chances of an endemic.
[15%]
(iv) Now assume that the population is not of a fixed size. Let u be the average
birth/arrival rate of children into the population per unit time and v be the rate
of children leaving the population per unit time. Derive the new equations
(but do not solve) for the rate of change of S, I and R.
[20%]
(v) Further observations suggest that children can in fact repeatedly catch the
illness, thus moving between susceptible and infected states. Building on your
answer to part (iv) above, derive the new equations (but do not solve) for the
rate of change of S and I.
[15%]
(vi) Suggest and briefly describe an alternative OR method that could be used to
more realistically model the spread of a contagious childhood disease.