1. Modified SIR for Vector-Borne Diseases
Gay Wei En Colin 4i310
Chua Zhi Ming 4i307
Jacob Savos AOS
Katherine Kamis AOS

2. Content Page Introduction Aims and Objectives Rationale
Literature Review
Research Questions
Data Collection – Population
Data Analysis – Population
Methodology
Timeline
Assumptions
Obstacles Faced
Model
Data Collection – Climate
Data Analysis – Climate
Bibliography

3. 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

4. Aims and Objectives
To create a universal modified SIR model for vector- borne diseases to make predictions of the spread of diseases.

5. 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

6. 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.

7. 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.

8. 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

9. 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 albopictus – the most invasive mosquito in the world
Retrieved from
Aedes aegypti – Main vector of dengue fever in Singapore
Retrieved from

10. 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

11. 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.

12. Research Questions
How can the basic SIR Model be modified to handle birth, death and migration rate effectively?
Is there a pattern in the spread of dengue fever in relation to birth, death and migration rates, and precipitation and temperature changes?
How can the basic SIR Model be modified to handle climate changes, with regards to precipitation and temperature changes?

13. Timeline

14. Data Collection – Number of Weekly Cases
Extracted from:
Weekly Infectious Disease Bulletin
Published by the Ministry of Health, Singapore.

16. Data Analysis – Number of Weekly Cases
Calculation of Transmittal Constant (k) and Contact Probability (CP)

17. Data Collection - Population
We collected annual data for:
Population
Birth
Death
Net Migration

18. 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.

20. 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.

21. Obstacles Faced
There were weird changes in the birth, death, migration and population data between
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

22. 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

24. 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

25. 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 , Vol. 11, No. 3, /98/$ Dengue and Dengue Hemorrhagic Fever. Retrieved November 3, 2010 from
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 bbUzLdEL%2fmJu3ZDKARR3p5Nl92FNtJidBD5aoxNkn9rR%2fqal0IQplImz2J6bJ xLTsOxaRS3Xl53fcQushF2hTzrn1PirzKnZhujU%2f343A5TwKDLTU0ml2TfH7cKB %2fJRT7PPvlAlopeq%2f%2be2n%2bmrW%2bZ%2fJts8OXGBjRP3hd0qhSL4

26. 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, 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, Dobson, A. (2004). Population Dynamics of Pathogens with Multiple Host Species. The American Naturalist, 164, 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 Climate Data Online. (n.d.).NNDC Climate Data Online. Retrieved April 23, 2011, from &countryabbv=&georegionabbv=

27. Thank You
Any Questions?