[SOLVED] R BIOS3036 Computer Modelling in Science: Applications

BIOS3036 Computer Modelling in Science: Applications
AMR Model Fitting Practical
Dov Stekel

Semester 1 2019/20

Week 10 Patch 4

This practical is assessed. In this practical you will fit an AMR model to data using any techniques you see fit.

The model is given by the equations:

S is the concentration of sensitive bacteria (CFU/l), R is the concentration of resistant bacteria and A is the concentration of antibiotic. r is the maximal growth rate, N is the total population equal to R+S, Nmax is the carrying capacity, ES and ER are the effects of antibiotic on growth of sensitive and resistant bacteria respectively, S and R are the death rates of sensitive and resistant bacteria respectively, is the rate of horizontal gene transfer, is the fitness cost of carrying resistance genes and A is the decay rate of antibiotics. In the E equations, Emax is the maximal antibiotic inhibition, H is a Hill coefficient equal to 2, and MICS and MICR are the minimal inhibitory concentrations of antibiotic on the sensitive and resistant strains respectively.

The data you are given are placed in the file amrdata.txt

They represent samples from the slurry tank each week. At the start of the experiment, a large volume of antibiotic is added to the tank, and the antibiotic decays in time. No further antibiotic is added. Each week, the microbiologists cultured 100 bacterial strains, and worked out how many of them are resistant to the antibiotic. The first column is the time in hours, and the second column is the number of resistant strains of the 100 isolates tested. This can be thought of as equal to:

100 R/(R+S)

You will need to estimate three parameter values from the data:

, the horizontal transfer rate
, the fitness cost of carrying the resistance
A, the rate of decay of the antibiotic

You have the following information about these three parameters:

is expected to be small, but could be anywhere between 10-2 and 10-11
must be bigger than 0 and less than 1
A is the rate of decay (1 / mean lifetime of antibiotics).. It is thought that the mean life time is about 2-3 weeks, based on other studies, but might be outside this range in slurry as the chemical conditions are different.

For the sake of this exercise, the other parameters are fully known. They can be assumed to be:

Parameter
Value
r maximal growth rate
0.5 h-1
Nmax carrying capacity
107 CFU/L
S death rate sensitive
0.025 h-1
R death rate resistant
0.025 h-1
Emax maximal inhibition
2
H hill coefficient
2
MICS MIC sensitive
8 g/L
MICR MIC resistant
2000 g/L
S(0) initial sensitive population
9 x 106 CFU/L
R(0) initial resistant population
105 CFU/L
A(0) initial antibiotic concentration
5.6 g/L

This practical is completely open. You can investigate fit to the model data as you see appropriate. The write up should be relevant and concise.

The patch will be marked according to the following criteria:

Quality of implementation of model [20%]
Quality of fitting model to data / parameter estimates including description of details of investigations, choice of methods and interpretation of results [50%]
Quality of write up, including written description, clarity of code and good use of plots [20%]
Evidence of reading or use of techniques beyond the lecture material [10%]

Please create a single pdf with your write-ups for patches 3 and 4 for uploading onto Moodle by the deadline.