Modified SIR for Vector-Borne

Diseases

Gay Wei En Colin 4i310Chua Zhi Ming 4i307

Jacob Savos AOSKatherine Kamis AOS

Content Page

1. Introduction

2. Aims and Objectives

3. Rationale

4. Literature Review

5. Research Questions

6. Data Collection – Population

7. Data Analysis – Population

8. Methodology

9. Timeline

10. Assumptions

11. Obstacles Faced

12. Model

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 vector-borne 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 RecoveredSusceptible Infected Recover

ed

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 albopictus – the most invasive mosquito in the worldRetrieved from http://www.comune.torino.it/ucstampa/2005/aedes-albopictus.jpg

Aedes aegypti – Main vector of dengue fever in SingaporeRetrieved from http://www.telepinar.icrt.cu/ving/images/stories/aedes-aegypti__785698.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

Susceptible

SusceptibleInfected

InfectedHosts

Vectors

Death Death

Climate

Climate

Birth Net Migration

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.

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?

TimelineAOS HCI

Acquire data from external scientists

May-AugFormulate model based on ticks

using Excel Formulate model based on

mosquitoes using Excel

AOS goes to Singapore Finalize model & compare models

Preparation for Finals Presentation Aug

Evaluate and ensure research is validFinalize literature review

Nov-Jan

Set parameters to our model based on characteristics of disease Analyze data & identify vital information required

Collate our data & sort it for proper formation of model Jan-Apr

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%2bbUzLdEL%2fmJu3ZDKARR3p5Nl92FNtJidBD5aoxNkn9rR%2fqal0IQplImz2J6bJxLTsOxaRS3Xl53fcQushF2hTzrn1PirzKnZhujU%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 YouAny Questions?