Modified SIR for Vector-Borne Diseases

1. Modified SIR for Vector-Borne Diseases Group 9-019 Gay Wei En Colin 4i310 Chua Zhi Ming 4i307 Katherine Kamis AOS Jacob Savos AOS

2. Aims & Objectives • To create a universal modified SIR model for vector-borne diseases to make predictions of the spread of these diseases.

3. Motivation Academy of Science Hwa Chong Institution • In 2005, there was an epidemic of Dengue in Singapore. • Since then the number of cases has been at an increased level. • The number of cases of Lyme disease has been increasing in Loudoun County, Virginia, an area previously devoid of Lyme disease. A model will help to predict if the current trend will continue.

4. Motivation Academy of Science Hwa Chong Institution

5. Simple SIR • The SIR model is used to predict outbreaks of diseases. • Considers 3 compartments: • Susceptible • Infected • Recovered • Two directions of change, namely from Susceptible to Infected or from Infected to Recovered

6. Simple SIR • S’(t) = -k * S(t) * I(t) • I’(t) = -S’(t) – R’(t) • R’(t) = c * I(t) • k – Transmittal constant • c – Recovery rate

7. Euler’s Method • Tangent line – slope at a certain point • Tangent lines are estimates of the rates of change • Rates of change can be used to estimate actual points • S(t + h) = S(t) + S’(t)*h

8. Vector-Borne Disease Model Net Migration Net Migration Birth Death Death Hosts (N) Susceptible Infected Vectors (V) Infected Susceptible Death Death Birth

9. Z. QiuEquations (2008) • S – Susceptible host population • I – Infected host population • T – Susceptible vector population • X – Infected vector population • B – Birth rate of hosts • µ – Death rate of hosts • N – Total Host population • b – Contact rate • β – Disease transmission probability (vectors to host) • γ – Recovery Rate • m – Migration Rate Rate of Change of Susceptible Hosts Rate of Change of Infected Hosts

10. Z. QiuEquations (2008) • S – Susceptible host population • I – Infected host population • T – Susceptible vector population • X – Infected vector population • N – Total Host population • b – Contact rate • V – Total Vector population • B’ – Birth rate of vectors • ε– Death rate of vectors • M – Maximum number of vectors per host • α – Disease transmission probability Rate of Change of Susceptible Vectors Rate of Change of Infected Vectors

11. Assumptions • A person recovers from Dengue after 2 weeks • 5% of the mosquito population is infected with dengue fever • Birth, death, and migration rates stay the same after 2004 • Vector birth and death rates stay constant

12. Data Collection • Dengue Fever Statistics • Singapore Human Population Statistics • Singapore Climate Data • Temperature • Precipitation

13. Dengue Fever Statistics

14. Human Population Statistics http://www.indexmundi.com/

15. Climate Data

16. Data Analysis - Climate • Spearman’s Rank Correlation Coefficient • Used to determine to what extent temperature and precipitation are correlated to the number of cases of dengue fever.

17. Spearman’s Rank Correlation Coefficient

18. Data Analysis - Climate

19. Data Analysis - Climate • Using the 14 week lag and the statistics for weekly cases, we can determine when to extract our transmittal constant.

22. Data Analysis - Seasonality • Tick populations are affected by different seasons in the United States • Summer & Winter: • Birth rate is lower • Death rate is higher • Spring & Fall: • Birth rate is higher • Death rate is lower

23. Dengue Fever Data

24. Dengue Fever Data Susceptible Hosts Population Susceptible Vectors Population Infected Vectors Population

25. Dengue Fever Data Susceptible Vectors Population Infected Vectors Population

26. Z. Qiu Model –Estimates from Initial Data

27. Z. Qiu Model –Theoretical Population

28. Lyme Disease

29. Problems & Limitations • Data was not accessible for use in either country • Collection of data for models was difficult • If this data was available we would be able to create models to help predict infected populations and determine: • Health Care Costs • Wellness of the Population • Control Methods

30. Future Work • We have created a model that we can use to predict trends in populations • With field work, the necessary data such as mosquito population count and transmission rates along with other parameters that can be measured in the field can used with the model to predict the spread of Dengue and Lyme disease

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33. Thank You! Any Questions?