Problem set 8 built on the virus and patient model created in ps7. The main things to look at are comparisons of patients with different medication regimens. In part 2, we look at the results of patients prescribed ‘guttagonal’ with a control group that receives no medication.
In part five, we see that there are very similar looking graphs for two groups of patients: group A receives one prescription followed by a delay a second prescription, while the second group, B, receives two anti-virals simultaneously. What the graph does not show is that all 100 patients in group A are virus free by the end of the trial, but group B has 20-25 patients with single digit virus counts remaining.
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 |
# 6.00 Problem Set 8 # # Name: Casey # Collaborators: # Time: ~8hr import numpy import random import pylab from ps7 import * # # PROBLEM 1 # class ResistantVirus(SimpleVirus): """ Representation of a virus which can have drug resistance. """ def __init__(self, maxBirthProb, clearProb, resistances, mutProb): """ Initialize a ResistantVirus instance, saves all parameters as attributes of the instance. maxBirthProb: Maximum reproduction probability (a float between 0-1) clearProb: Maximum clearance probability (a float between 0-1). resistances: A dictionary of drug names (strings) mapping to the state of this virus particle's resistance (either True or False) to each drug. e.g. {'guttagonol':False, 'grimpex',False}, means that this virus particle is resistant to neither guttagonol nor grimpex. mutProb: Mutation probability for this virus particle (a float). This is the probability of the offspring acquiring or losing resistance to a drug. """ # TODO assert 0 < maxBirthProb < 1 and 0 < clearProb < 1 and 0 < mutProb < 1 assert isinstance(resistances, dict) self.maxBirthProb = maxBirthProb self.clearProb = clearProb self.resistances = resistances self.mutProb = mutProb def isResistantTo(self, drug): """ Get the state of this virus particle's resistance to a drug. This method is called by getResistPop() in Patient to determine how many virus particles have resistance to a drug. drug: The drug (a string) returns: True if this virus instance is resistant to the drug, False otherwise. """ # TODO # resistances: A dictionary of drug names (strings) return self.resistances[drug] def reproduce(self, popDensity, activeDrugs): """ Stochastically determines whether this virus particle reproduces at a time step. Called by the update() method in the Patient class. If the virus particle is not resistant to any drug in activeDrugs, then it does not reproduce. Otherwise, the virus particle reproduces with probability: self.maxBirthProb * (1 - popDensity). If this virus particle reproduces, then reproduce() creates and returns the instance of the offspring ResistantVirus (which has the same maxBirthProb and clearProb values as its parent). For each drug resistance trait of the virus (i.e. each key of self.resistances), the offspring has probability 1-mutProb of inheriting that resistance trait from the parent, and probability mutProb of switching that resistance trait in the offspring. For example, if a virus particle is resistant to guttagonol but not grimpex, and `self.mutProb` is 0.1, then there is a 10% chance that that the offspring will lose resistance to guttagonol and a 90% chance that the offspring will be resistant to guttagonol. There is also a 10% chance that the offspring will gain resistance to grimpex and a 90% chance that the offspring will not be resistant to grimpex. popDensity: the population density (a float), defined as the current virus population divided by the maximum population activeDrugs: a list of the drug names acting on this virus particle (a list of strings). returns: a new instance of the ResistantVirus class representing the offspring of this virus particle. The child should have the same maxBirthProb and clearProb values as this virus. Raises a NoChildException if this virus particle does not reproduce. """ # TODO # if not resistant to a drug in activeDrugs: don't reproduce # else: reproduce with birthProb and clearProb resistant = False newResistances = self.resistances # if no active drugs, go to random.random() if len(activeDrugs) > 0: for i in activeDrugs: if self.isResistantTo(i): resistant = True if resistant: for k,v in self.resistances.items(): if random.random() < self.mutProb: # reverse resistance in newResistances newResistances[k] = not v else: return NoChildException() if random.random() < self.maxBirthProb * (1 - popDensity): return ResistantVirus(self.maxBirthProb, self.clearProb, newResistances, self.mutProb) else: return NoChildException() #a = ResistantVirus(.99, .25, {'guttagonal': True, 'grimpex': True}, .99) #b = a.reproduce(.1, ['grimpex']) #print b.resistances class Patient(SimplePatient): """ Representation of a patient. The patient is able to take drugs and his/her virus population can acquire resistance to the drugs he/she takes. """ def __init__(self, viruses, maxPop): """ Initialization function, saves the viruses and maxPop parameters as attributes. Also initializes the list of drugs being administered (which should initially include no drugs). viruses: the list representing the virus population (a list of SimpleVirus instances) maxPop: the maximum virus population for this patient (an integer) """ # TODO assert isinstance(viruses, list) assert isinstance(maxPop, int) self.viruses = viruses self.maxPop = maxPop def addPrescription(self, newDrug): """ Administer a drug to this patient. After a prescription is added, the drug acts on the virus population for all subsequent time steps. If the newDrug is already prescribed to this patient, the method has no effect. newDrug: The name of the drug to administer to the patient (a string). postcondition: list of drugs being administered to a patient is updated """ # TODO # should not allow one drug being added to the list multiple times # if patient has no drug list: make one # if newDrug on list: don't add # else: add drug assert isinstance(newDrug, str) try: if newDrug in self.drugs: return self.drugs.append(newDrug) except AttributeError: self.drugs = [] self.drugs.append(newDrug) def getPrescriptions(self): """ Returns the drugs that are being administered to this patient. returns: The list of drug names (strings) being administered to this patient. """ # TODO try: return self.drugs except AttributeError: return [] def getResistPop(self, drugResist): """ Get the population of virus particles resistant to the drugs listed in drugResist. drugResist: Which drug resistances to include in the population (a list of strings - e.g. ['guttagonol'] or ['guttagonol', 'grimpex']) returns: the population of viruses (an integer) with resistances to all drugs in the drugResist list. """ # TODO assert isinstance(drugResist, list) count = 0 for i in drugResist: count += self.viruses.count(i) return count def update(self): """ Update the state of the virus population in this patient for a single time step. update() should execute these actions in order: - Determine whether each virus particle survives and update the list of virus particles accordingly - The current population density is calculated. This population density value is used until the next call to update(). - Determine whether each virus particle should reproduce and add offspring virus particles to the list of viruses in this patient. The listof drugs being administered should be accounted for in the determination of whether each virus particle reproduces. returns: the total virus population at the end of the update (an integer) """ # TODO survive_list = [] for i in range(0, len(self.viruses)): if not self.viruses[i].doesClear(): survive_list.append(self.viruses[i]) # debug print "survive list: ", len(survive_list) self.viruses = survive_list # update the pop density now_density = self.getTotalPop() / float(self.maxPop) # for each virus particle, reproduce or not new_viruses = [] for i in range(0, len(self.viruses)): virus = self.viruses[i] a = virus.reproduce(now_density, self.getPrescriptions()) if isinstance(a, ResistantVirus): new_viruses.append(a) # debug print "new viruses: ", len(new_viruses) self.viruses = self.viruses + new_viruses # return total virus pop as an int return self.getTotalPop() # # PROBLEM 2 # def simulationWithDrug(): """ Runs simulations and plots graphs for problem 4. Instantiates a patient, runs a simulation for 150 timesteps, adds guttagonol, and runs the simulation for an additional 150 timesteps. total virus population vs. time and guttagonol-resistant virus population vs. time are plotted """ # TODO a = ResistantVirus(0.1, 0.05, {'guttagonal': False}, 0.005) viruses = [a]*100 trialPatient = Patient(viruses, 1000) controlPatient = Patient(viruses, 1000) guttagonal = [] control = [] for i in range(0, 150): guttagonal.append(trialPatient.update()) control.append(controlPatient.update()) trialPatient.addPrescription('guttagonal') for i in range(0, 150): guttagonal.append(trialPatient.update()) control.append(controlPatient.update()) pylab.plot(guttagonal, 'r-', label='guttagonal prescribed') pylab.plot(control, 'b-', label='without medication') pylab.xlabel("Time") pylab.ylabel("Virus count") pylab.legend(loc='best') pylab.title("Virus when drugs applied at time 150") pylab.show() #simulationWithDrug() ''' virus *was* dying off before we get to timestep 150 was not resistant to empty activeDrugs ''' # # PROBLEM 3 # def simulationDelayedTreatment(stepsDelayed, numTrials): """ Runs simulations and make histograms for problem 5. Runs multiple simulations to show the relationship between delayed treatment and patient outcome. Histograms of final total virus populations are displayed for delays of 300, 150, 75, 0 timesteps (followed by an additional 150 timesteps of simulation). """ # TODO # run 30 trials for each scenario # displays histograms of final virus counts as four colored bars virusPops = [] a = ResistantVirus(0.1, 0.05, {'guttagonal': True}, 0.005) viruses = [a]*100 for k in range(0, numTrials): # reset patients for each trial myPatients = [] for i in range(0, len(stepsDelayed)): a = Patient(viruses, 1000) myPatients.append(a) # run through all steps with delayed prescriptions # capture final viral counts statsStep = [] counter = 0 for i in range(0, max(stepsDelayed)+150): if counter in stepsDelayed: myPatients[stepsDelayed.index(counter)].addPrescription('guttagonal') for j in myPatients: j.update() counter += 1 # one final result for each patient each trial for z in myPatients: statsStep.append(z.getTotalPop()) print statsStep virusPops.append(statsStep) # for hist to work, list should convert to numpy.array() virusPops = numpy.array(virusPops) ''' README 100 trials shows 389 patients free of virus and 11 with 1 virus left needs legend and axis labels ''' stepsDelayed = [str(i) for i in stepsDelayed] # convert ints in list to strs pylab.hist(virusPops, 8, histtype='bar', color=['blue', 'red', 'green', 'purple'], label=stepsDelayed) pylab.xlabel('Virus cells remaining') pylab.ylabel('Patients') pylab.title('Outcomes for delayed treatment') pylab.legend() # labels won't appear without it pylab.show() #simulationDelayedTreatment([0,75,150,300], 100) # # PROBLEM 4 # def simulationTwoDrugsDelayedTreatment(stepsDelayed, numTrials): """ Runs simulations and make histograms for problem 6. Runs multiple simulations to show the relationship between administration of multiple drugs and patient outcome. Histograms of final total virus populations are displayed for lag times of 150, 75, 0 timesteps between adding drugs (followed by an additional 150 timesteps of simulation). """ # TODO # run 30 trials for each scenario # plot virusPops = [] a = ResistantVirus(0.1, 0.05, {'guttagonal': False, 'grimpex': False}, 0.005) viruses = [a]*100 for k in range(0, numTrials): # reset patients for each trial myPatients = [] for i in range(0, len(stepsDelayed)): a = Patient(viruses, 1000) myPatients.append(a) # run an initial 150 steps prior to guttagonal for i in range(0, 150): for j in myPatients: j.update() for j in myPatients: j.addPrescription('guttagonal') # apply grimpex at delays defined in stepsDelayed counter = 0 for i in range(0, max(stepsDelayed)+150): if counter in stepsDelayed: myPatients[stepsDelayed.index(counter)].addPrescription('grimpex') for j in myPatients: j.update() counter += 1 # one final result for each patient each trial statsStep = [] for z in myPatients: statsStep.append(z.getTotalPop()) print statsStep virusPops.append(statsStep) # for hist to work, list should convert to numpy.array() virusPops = numpy.array(virusPops) stepsDelayed = [str(i) for i in stepsDelayed] # convert ints in list to strs pylab.hist(virusPops, 8, histtype='bar', color=['blue', 'red', 'green', 'purple'], label=stepsDelayed) pylab.xlabel('Virus cells remaining') pylab.ylabel('Patients') pylab.title('Outcomes for delayed treatment w/ 2 drugs') pylab.legend() # labels won't appear without it pylab.show() #simulationTwoDrugsDelayedTreatment([0,75,150,300], 10) # # PROBLEM 5 # def simulationTwoDrugsVirusPopulations(): """ Run simulations and plot graphs examining the relationship between administration of multiple drugs and patient outcome. Plots of total and drug-resistant viruses vs. time are made for a simulation with a 300 time step delay between administering the 2 drugs and a simulations for which drugs are administered simultaneously. """ #TODO # go with stacked graphs # scatter plot for multiple trials # draw a best fit line # groupA 150, guttagonal, 300, grimpex, 150 # groupB 150, guttagonal + grimpex, 150 a = ResistantVirus(0.1, 0.05, {'guttagonal':False, 'grimpex':False}, 0.005) viruses = [a]*100 patientsA = [] patientsB = [] groupA = [] groupB = [] for i in range(0,100): patientsA.append(Patient(viruses, 1000)) patientsB.append(Patient(viruses, 1000)) for i in range(0,150): statsA = [] statsB = [] for j in patientsA: statsA.append(j.update()) for j in patientsB: statsB.append(j.update()) if i % 5 == 0: groupA.append(statsA) groupB.append(statsB) # prescribe guttagonal for j in patientsA: j.addPrescription('guttagonal') for k in patientsB: k.addPrescription('guttagonal') k.addPrescription('grimpex') for i in range(0,300): stats = [] for j in patientsA: stats.append(j.update()) if i % 5 == 0: groupA.append(stats) # prescribe grimpex for m in patientsA: m.addPrescription('grimpex') for i in range(0,150): statsA = [] statsB = [] for j in patientsA: statsA.append(j.update()) for j in patientsB: statsB.append(j.update()) if i % 5 == 0: groupA.append(statsA) groupB.append(statsB) # no virus left in simultaneous group # 25 patients had > 0 (e.g. 1-2) virus count remaining in delayed group print 100 - groupA[-1].count(0) print 100 - groupB[-1].count(0) # averaged line axisA = [sum(i)/len(i) for i in groupA] pylab.subplot(2, 1, 1) pylab.xlim([20,60]) pylab.ylabel("Virus count") pylab.title('Two stage prescriptions') pylab.plot(groupA, 'bo') pylab.plot(axisA, 'r', linewidth=4) # stacked graphs axisB = [sum(i)/len(i) for i in groupB] pylab.subplot(2, 1, 2) pylab.xlim([20,60]) pylab.title('Simultaneous prescriptions') pylab.xlabel("Time") pylab.plot(groupB, 'go') pylab.plot(axisB, 'r', linewidth=4) pylab.show() ''' cannot tell a difference between one drug and two so printed the final numbers at line 501 ''' #simulationTwoDrugsVirusPopulations() |