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GMPH IDM: End of course assessment
R代码代写 isease X is a newly-discovered infectious disease of humans. It is directly transmitted (i.e. without need for vectors).
Disease X is a newly-discovered infectious disease of humans. It is directly transmitted (i.e. without need for vectors). Epidemiological investigations have shown that the disease has the following, important elements of its natural history. After infection, there is an incubation period before people start becoming infectious. However, symptoms do not begin immediately: people can be infectious for some time, before symptoms begin. All infections eventually result in symptoms. Initially, it is believed that all symptoms are mild, and there is no disease-related mortality. Once recovered, it is thought that individuals cannot be reinfected.
For each question, give your answers along with any working or calculations you believe are relevant.
You will submit the responses to these questions in a single document. Upload this along with your R code in any file format as long as we can copy the code in order to run and test it – .R files, or .ipynb files if you have done this in Jupyter notebooks, or if you copy your code into a .txt file that would also be fine. As a backup option you can also copy your code into your main answer document.
Part 1: Model specification R代码代写
1a. Draw the simplest possible model structure capturing the natural history described above. Write down the full governing equations for the model you have drawn. (10 marks)
1b. Emerging data shows that, although the vast majority of infected people have only mild symptoms, a small proportion develops severe illness. Some of these individuals die as a result of the disease, while others recover. Draw an updated model structure to take account of this information. Also write updated governing equations. (10 marks)
1c. Further, epidemiological investigations provide the following information on the natural history of the disease: the incubation period is 5 days on average; people can be infectious for 3 days before developing symptoms; 10% of infections result in severe illness the rest having only mild symptoms; those with mild symptoms recover on average over a week; those with severe illness have a 60% chance of mortality, and survivors recover on average over two weeks.
Use this information to calculate the values of as many parameters as possible, in your model. (10 marks)
Part 2: Model simulation and calibration R代码代写
Information from other countries, where the epidemic is more advanced, suggests that at the peak of the epidemic, roughly 10% of the population has symptoms.
Using R, write code to simulate this epidemic. Calibrate all remaining parameter(s) in your data (those not already determined in Q1b). State your estimated parameter value(s). (20 marks)
What is the value of 0? What proportion of the population ultimately dies from the disease? (10 marks)
Part 3: Interventions
3a. Choose any intervention which could be used against this disease. This could be treatment, vaccination, non-pharmaceutical intervention, or anything else you think is appropriate. Define carefully how your intervention benefits people receiving it or how it impacts the dynamics of the infection (e.g. does it reduce the risk of infection, the risk of death amongst those with severe illness, etc?). Write updated governing equations showing how you would model the impact of this intervention on the epidemic. (20 marks)
3b. Simulate this intervention using R, showing clearly the population benefits of the intervention. (20 marks)