3 IntroductionA vector-borne disease is transmitted by a pathogenic microorganism from an infected host to another organismHCI will be creating a model using Dengue FeverAOS will be creating a model using a tick-borne disease
4 Aims and ObjectivesTo 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 RecoveredTwo directions of change, namely from Susceptible to Infected or from Infected to RecoveredSusceptibleInfectedRecovered
6 RationaleSince 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 modelBirth and death ratesMovement from Recovered to SusceptibleMake 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 graphingRates 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 yearsTransmitted via mosquito bitesIn 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 speciesMultiple species able to transmit dengue feverHave characteristic black and white stripe markings on body and legsAedes albopictus – the most invasive mosquito in the worldRetrieved fromAedes aegypti – Main vector of dengue fever in SingaporeRetrieved from
10 Methodology Begin with a simple SIR model Develop variables needed to modify the modelAttempt to modify the model to incorporate all vector-borne diseasesBirthDeathNet MigrationDeathHostsSusceptibleInfectedVectorsInfectedSusceptibleClimateClimate
11 Differentiation Used to determine the rate of change of a function Infection and recovery obtained via differentiation based on data acquirede.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 QuestionsHow 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?
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:PopulationBirthDeathNet 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 AssumptionsAll 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 FacedThere were weird changes in the birth, death, migration and population data betweenWe only used the data from 2004 to 2009.Demographic data could only be obtained on an annual basisPopulation forecasts were only done on an annual basis and divided proportionately over 52/53 weeks per year
22 Data Collection - Climate Precipitation and TemperatureObtained on a daily basis – allowed for weekly periods to be foundExtracted from the US National Oceanic and Atmospheric Administration (NOAA) supported databaseAll data as recorded at the Singapore Changi Airport weather station
24 Data Analysis – Climate ExtensionConnect the statistics obtained with number of new casesBased on climate predictions, predict resulting fluctuations in the number of new cases
25 BibliographyAcademy 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 fromNeuwirth, E., & Arganbright, D. (2004). The active modeler: mathematical modeling with Microsoft Excel. Belmont, CA: Thomson/Brooks/ColeMinistry of Health: FAQs. (n.d.). Dengue. Retrieved November 3, 2010, from bbUzLdEL%2fmJu3ZDKARR3p5Nl92FNtJidBD5aoxNkn9rR%2fqal0IQplImz2J6bJ xLTsOxaRS3Xl53fcQushF2hTzrn1PirzKnZhujU%2f343A5TwKDLTU0ml2TfH7cKB %2fJRT7PPvlAlopeq%2f%2be2n%2bmrW%2bZ%2fJts8OXGBjRP3hd0qhSL4
26 BibliographyOng, 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=