Download Modified SIR for Vector-Borne Diseases - AOS-HCI-2011

Content Page
1.
Introduction
8. Methodology
2.
Aims and Objectives
9. Timeline
3.
Rationale
10. Assumptions
4.
Literature Review
11. Obstacles Faced
5.
Research Questions
12. Model
6. Data Collection –
Population
7.
Data Analysis –
Population
13. Data Collection – Climate
14. Data Analysis – Climate
15. Bibliography
Introduction
 A vector-borne disease is transmitted by a
pathogenic microorganism from an infected host to
another organism
 HCI will be creating a model using Dengue Fever
 AOS will be creating a model using a tick-borne
disease
Aims and Objectives
 To create a universal modified SIR model for vectorborne diseases to make predictions of the spread of
diseases.
Rationale
 The SIR Model currently used is extremely simplistic
 Only considers three compartments, namely
Susceptible, Infected and Recovered
 Two directions of change, namely from Susceptible
to Infected or from Infected to Recovered
Susceptible
Infected
Recovered
Rationale
 Since most vector-borne diseases do not work in
such a way, this project aims to modify this SIR
model so that it can encompass much more
factors that the original SIR model
 Birth and death rates
 Movement from Recovered to Susceptible
 Make it more applicable to real life, thus
increasing its usability in accurately predicting the
spread of such vector-borne diseases.
Literature Review:
SIR Model
 Neuwirth, E., & Arganbright, D. (2004). The active
modeler: mathematical modeling with Microsoft
Excel. Belmont, CA: Thomson/Brooks/Cole.
 Introduces basic modeling techniques such as dynamic
modeling and graphing
 Rates of change are shown to have relations between
the three compartments: S(t), I(t) and R(t) in the
subtopic simple epidemics.
 Calculus can be used to help us solve the research
questions mentioned.
Literature Review:
Dengue Fever
 A very old disease that reemerged in the past 20
years
 Transmitted via mosquito bites
 In 2009, there were a total of 4452 cases of dengue
fever in Singapore, of which there were 8 deaths
Literature Review:
Aedes Mosquitoes
 Aedes mosquitoes refers to the entire genus of
mosquito – over 700 different species
 Multiple species able to transmit dengue fever
 Have characteristic black and white stripe markings
on body and legs
Aedes aegypti – Main vector of dengue
fever in Singapore
Retrieved from
http://www.telepinar.icrt.cu/ving/images/
stories/aedes-aegypti__785698.jpg
Aedes albopictus – the most invasive
mosquito in the world
Retrieved from
http://www.comune.torino.it/ucstampa/20
05/aedes-albopictus.jpg
Methodology
 Begin with a simple SIR model
 Develop variables needed to modify the model
 Attempt to modify the model to incorporate all
vector-borne diseases
Birth Death Net Migration
Death
Hosts
Susceptible
Infected
Vectors
Infected
Susceptible
Climate
Climate
Differentiation
 Used to determine the rate of change of a
function
 Infection and recovery obtained via
differentiation based on data acquired
 e.g. With the weekly number of cases of the
disease, we are able to find the best fit
graph, the function of which we can then
differentiate to determine the infection rate
in the form of a function.
How can the
basic SIR Model
be modified to
handle birth,
death and
migration rate
effectively?
How can the basic
SIR Model be
modified to handle
climate changes,
with regards to
precipitation and
temperature
changes?
Research
Questions
Is there a pattern
in the spread of
dengue fever in
relation to birth,
death and
migration rates,
and precipitation
and temperature
changes?
Timeline
AOS
HCI
Finalize literature review
Evaluate and ensure research is valid
Nov-Jan
Acquire data from external
scientists
Set parameters to our model based on characteristics of disease
Jan-Apr
Analyze data & identify vital information required
Collate our data & sort it for proper formation of model
Formulate model based on ticks
Formulate model based on
May-Aug
using Excel
mosquitoes using Excel
Finalize model & compare models
Aug
AOS goes to Singapore
Preparation for Finals Presentation
Data Collection –
Number of Weekly Cases
 Extracted from:
 Weekly Infectious Disease Bulletin
 Published by the Ministry of Health, Singapore.
Data Analysis –
Number of Weekly Cases
 Calculation of Transmittal Constant (k) and Contact
Probability (CP)
Data Collection Population
 We collected annual data for:




Population
Birth
Death
Net Migration
Data Analysis - Population
 The population of the subsequent years were
predicted based on the data extracted.
 The change in population were predicted based on
the annual births, deaths and net migration.
 The data collected were plotted on a graph and the
best fit line was found.
 Using the equation of the best fit line, we are able to
predict the number of births, deaths and net
migration for the subsequent years.
Assumptions
 All individuals have equal chance of contracting the
disease.
 The government does not implement or change
policies which affect migration rates.
 All variables have a trend that the model is able to
predict.
Obstacles Faced
There were weird
changes in the birth,
death, migration and
population data
between 2003-2004.
We only used the data
from 2004 to 2009.
Demographic data could
only be obtained on an
annual basis
Population forecasts
were only done on an
annual basis and divided
proportionately over
52/53 weeks per year
Data Collection - Climate
 Precipitation and Temperature
 Obtained on a daily basis – allowed for weekly
periods to be found
 Extracted from the US National Oceanic and
Atmospheric Administration (NOAA) supported
database
 All data as recorded at the Singapore Changi Airport
weather station
Data Analysis – Climate
 Extension
 Connect the statistics obtained with number of
new cases
 Based on climate predictions, predict resulting
fluctuations in the number of new cases
Bibliography
Academy of Science. Academy of Science Mathematics BC Calculus Text.
Breish, N., & Thorne, B. (n.d.). Lyme disease and the deer tick in maryland.
Maryland: The University of Maryland.
Duane J. Gubler(1998, July). Clinical Microbiology Reviews, p. 480-496, Vol. 11,
No. 3, 0893-8512/98/$00.00+0. Dengue and Dengue Hemorrhagic Fever.
Retrieved November 3, 2010 from
http://cmr.asm.org/cgi/content/full/11/3/480?view=long&pmid=9665979
Neuwirth, E., & Arganbright, D. (2004). The active modeler: mathematical
modeling with Microsoft Excel. Belmont, CA: Thomson/Brooks/Cole
Ministry of Health: FAQs. (n.d.). Dengue. Retrieved November 3, 2010, from
http://www.pqms.moh.gov.sg/apps/fcd_faqmain.aspx?qst=2fN7e274RAp%2
bbUzLdEL%2fmJu3ZDKARR3p5Nl92FNtJidBD5aoxNkn9rR%2fqal0IQplImz2J6bJ
xLTsOxaRS3Xl53fcQushF2hTzrn1PirzKnZhujU%2f343A5TwKDLTU0ml2TfH7cKB
%2fJRT7PPvlAlopeq%2f%2be2n%2bmrW%2bZ%2fJts8OXGBjRP3hd0qhSL4
Bibliography
Ong, A., Sandar, M., Chen, M. l., & Sin, L. Y. (2007). Fatal dengue hemorrhagic
fever in adults during a dengue epidemic in Singapore. International Journal
of Infectious Diseases, 11, 263-267.
Stafford III, K. (2001). Ticks. New Haven: The Connecticut Agricultural Experiment
Station.
Wei, H., Li, X., & Martcheva, M. (2008). An epidemic model of a vector-borne
disease with direct transmission and time delay. Journal of Mathematical
Analysis and Applications, 342, 895-908.
Dobson, A. (2004). Population Dynamics of Pathogens with Multiple Host
Species. The American Naturalist, 164, 564-578.
Hii, Y. L., Rocklov, J., Ng, N., Tang, C. S., Pang, F. Y., & Sauerborn, R. (2009).
Climate variability and increase in intensity and magnitude of dengue
incidence in Singapore. Glob Health Action, 2. Retrieved April 23, 2011,
from http://www.globalhealthaction.net/index.php/gha/article/view/2036/
2590
Climate Data Online. (n.d.).NNDC Climate Data Online. Retrieved April 23, 2011,
from http://www7.ncdc.noaa.gov/CDO/cdoselect.cmd?datasetabbv=GSOD
&countryabbv=&georegionabbv=
Thank You
Any Questions?