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

Modified SIR for VectorBorne Diseases
Gay Wei En Colin 4i310
Chua Zhi Ming 4i307
Jacob Savos AOS
Katherine Kamis AOS
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.
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
• 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.
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
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/aedesaegypti__785698.jpg
Aedes albopictus – the most invasive mosquito in the world
Retrieved from
http://www.comune.torino.it/ucstampa/2005/aedesalbopictus.jpg
Literature Review - Ticks
• Ticks have a two-year life cycle
• Ticks acquire a vector-borne disease by feeding on an infected host
• Once infected, ticks transmit the disease by feeding on an
uninfected host
Lone Star Tick
Deer Tick
Literature Review - SIR
• Susceptible
• Infected
• Recovered
Literature Review - SIR
• 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.
SIR - Equations
• S’(t)=-k∙S(t)∙I(t)
• I’(t)=-S’(t)-R'(t)
• R’(t)=c∙I(t)
• k – Transmittal constant
• c – Recovery rate
Research Questions
• Are we able to predict the spread of a disease using the SIR
Model?
• What kind of situations are the basic SIR Model unable to take
into account?
• How can the basic SIR Model be modified to handle real life
situations effectively?
• Is there a pattern in the spread of vector-borne diseases?
Fields of Mathematics 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.
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
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
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, 08938512/98/$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%2bbUzLdEL%2fmJu3ZDKA
RR3p5Nl92FNtJidBD5aoxNkn9rR%2fqal0IQplImz2J6bJxLTsOxaRS3Xl53fcQushF2hTzrn1PirzKnZhujU%2f
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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.
Any questions?