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COSC2002/2902 Computational Modelling
创建日期：2024-05-29 17:33:14
标签： COSC2002
Computational Modelling

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COSC2002/2902 Computational Modelling

Assignment — due Friday May 26th, 11:59pm
The assignment consists of two questions. It is worth 10% of your total assessment for this Unit of
Study. You will be marked on the correctness and quality of the code, as well as your written responses
to the questions.
You should submit your assignment as a jupyter notebook through the Canvas submission portal.
Written responses to assignment questions should also be included in the jupyter notebook, using
the ‘markdown’ option for a cell (so that your whole notebook can still be run without error). Check
that your notebook runs before submission. If you have incomplete code (i.e. stopping your notebook
running) you should comment this out, and provide some discussion around the code.
You are welcome to work in pairs. If submitting as a pair please both submit the notebook (with
both your SIDs in the file name), so that Canvas records a submission for both members of the pair. If
you submit this assignment with another student, you certify that you have both made a fair contribu-
tion to it, and are happy to both receive the same mark.
Assignments that have simply been copied will not be accepted. Copying the work of another
person without acknowledgement is plagiarism and contrary to University policies. By uploading your
submission to Canvas, you are certifying that you have read and understood the University Academic
Dishonesty and Plagiarism in Coursework Policy.

COSC2002/2902 Assignment
Question 1: Population models(10 marks)
Given the impact it has had on all our lives it seems we should have a go at modelling the spread
of a virus through the community. We will also use this model as a basis for an exploration of two
interacting populations (e.g. rabbits and sheep), seen earlier in the course in the ordinary differential
equation context.
Let’s approach the virus problem in this way. Begin with a 2-dimensional grid of squares (the
“world”). A number of healthy people are randomly distributed throughout the world, as well as one
infected person. Each day, each person either stays still or moves one square up, down, right, or left.
If an infected person spends a day on the same square as a healthy person, the healthy person becomes
infected.
Parameters
The simulation should be initialized with four parameters: the size of the 2-dimensional world people
inhabit (sidelength, default 40 squares per side), the maximum time to run the simulation for
(maxtime, default 1000 days), the number of people (npeople, default 100), and the number of
initially infected people (ninfected, default 1).
People
Each person will be associated with a number of pieces of information: (i) their x coordinate (an
integer between 0 and the size of the world-1), (ii) their y coordinate (same), and (iii) their status
(healthy or infected).
Boundary conditions
If people move outside the world (x, y < 0 or x, y > sidelength-1), they come through the other
side of the world (i.e. we shall assume we have periodic boundary conditions). So, a person who
moves to x = −1 will instead move to x =sidelength-1.
Questions
(1.1) Starting with the defaults specified above, what is the average length of time until the last person
gets infected? Provide also an estimate of the uncertainty in your value.
(1.2) Averaging over many runs: Plot the number of infected people as a function of time.
(1.3) If you halve the size of the world (i.e., set sidelength=20), how does this change the time it
takes until the last person is infected? Briefly discuss the real-world implications of this result.
(1.4) This model could also describe the interaction of two populations (e.g. rabbits and sheep). In
this case, when two individuals meet there are a number of different options. When they are the
same ‘species’ then there is a probability that a third (i.e. new) individual will appear at the same
square. If they are different species then there is a probability that one or both individuals die.
Modify your code so that it is now possible for new individuals to appear in your population.
Starting with the same default grid size, but now 50 individuals in each species, we want to
carry out a population simulation. Take the probability of a new individual appearing, and the
probability of an individual dying when encountering the opposite species, to be the same for
2
COSC2002/2902 Assignment
each species. Plot the population numbers versus time, and specify your chosen probabilities
for the two parameters in the title of your plot (these must be both nonzero).
(1.5) Explore your model for different parameter values, and different values between species. De-
scribe your main findings here. Do they agree with the findings of the ordinary differential
equation model used earlier in the course? Justify your answer and comment on the validity of
the model.
(1.6) COSC2902 ONLY Discuss how this model might be improved.
3
COSC2002/2902 Assignment
Question 2 Network models (10 marks)
Before COVID-19, in Australia we had the bushfires. The bushfires of the 2019/2020 summer devas-
tated the wilderness areas of the east coast of Australia. This event was accompanied by a correspond-
ingly large response on social media, with discussion of the causes trending globally. In this question
we shall use this event as a motivation to explore the spreading of content on a network.
Consider a network of users connected to followers (where a user may follow one of their follow-
ers). This is known as a directed network, as information flows from a user to the user’s followers.
Consider the establishment of the network in the following way. Users in the network join one by
one. When a user joins they initially randomly follow one other user in the network, and are followed
by one other random user (which may be the same user). They also decide to follow one other user
on the network. 
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MATH20602 COMP532 MAS275 COMP5318 COMP4002 FIT5086 MAST20004 FIT3152 FIT5129 CIS2380 CS521 COMP 1005 EECMS CITS5501 ECE 462 ECON 6002 ENG 4051 CSC 648 CMT654 MECHENG 713 PHYS1002 AMME 2000 FP0060 DDES3200 MECHENG 743 BINF90002 FIT2081 ISYS90081 ELECTENG 722 BUS 360 ECOS3010 BUS2810 ETF2100 ENG2048 STAT5002 COMP2017 CEME 2003 MATS3004 COMP9319 PHYS1001 COMP5349 AMME2261 COMP-381 FIT3173 COSC2757 ENG4025 QBUS2820 COMP9414 MATH2021 EOSC118 MFIN6690 PMATH 321 CSE-141L MATH575A COMPSCI5002 COMP1511 management comp2123 FINS3616 COMP 3331 COMS30034 DTSC 71 AcF 702 AcF702 DTSC71 MAT021 ELE8083 ACFI213 EG-127J 127J FIT5163 FIT2001 ELE00113M CMT310 CS 245 ENGL 1101 MTH6115 EE497 CS 325 Math 124A MTH5130 MBA502 MGT 5380 ARCH 1261 F033800 20LLP109 ELE4009 FINANCIAL COMP3331 Computer ECE4179 20T3 COMP9311 COMP9311 UNSW MFIN6210 ACCT 5930 EE590 ENG2029 ECO100 SIT315 ACCT3610 COMP3600 STK2100 FIT2004 COMP30020 ACTL1101 Stat 101B BANA 200 COSC2473 ENGG1400 AI COMP90043 MMF 1914H PHYS 127 CS584 CIVL2010 ECMT2150 CS 333 CP1406 KIT308 Economics 701 ECON3740 ECE 5759 BFC3340 FINC2012 COMP4500 MATH3871 FIT3080 18-819C Economic ECO202Y5Y PHY100 FINC-780 Econ 100B EC602 IE582 EE450 COMP9517 WRDS 150B ECON 570 LECTURE 2 ECA5101 ECE 4420 ADAD9311 FIT3031 CS 544 MF 703 CS 6140 KIT501 ENGSCI 344 CSC171 IE 332 FINM8007 21S2 COSC 1114 FE545 E471 SIT102 CSC108 MAT301 IAE 101 COP3503 STAT2004 EC 303 CS1026 STAT1203 MATH3171 ISOM5160 IFN657 FIT2014 ACCT2102 DSCI550 STATS 330 ELEC421 COMP3670 QBUS6840 MEES:698B MAST30027 MIET1077 Economics IFT 6758 FIT5122 BUSN5101 CptS 111 HRMT5502 Math2018 PP 312 INFS3200 CZ3005 CSSE1001 SENG 2011 MKTG 553Q BUFN 640 COMP507 ETF5952 DATA 311 ECE4043 BANK3011 finance M3H623544 HW1 INFS 7410 AI6103 STAT3888 INFS3208 ACCT7103 ECOS3013 PSYCH 20B F79MA STAT3006 ENGG952 2X MGSC 7000 ECE4132 MSF 526 MATH 3033 CDS 511 EEEE4120 EEET2465 ECA5103 MATH2070 ELEC3104 BU51019 EEE8147 ENGR20003 COSC 1107 ETF3200 FNCE 435 MSFI 435 ISyE6420 GENG4405 HW ETC5523 IE 7315 MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A 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