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Modified SIR models to Forecast Epidemics: Modeling Gonorrhea in Erie County

Biological Background for Gonorrhea. Gonorrhea is a sexually transmitted disease and is the second most common disease in the United States.It is estimated that 700,000 persons in the United States get new Gonorrheal infections each year

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Modified SIR models to Forecast Epidemics: Modeling Gonorrhea in Erie County

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    1. Modified SIR models to Forecast Epidemics: Modeling Gonorrhea in Erie County

    3. Goals of Modeling a Disease Although medical advances have reduced the consequences of infectious disease, preventing infections in the first place is preferable to treating them. Once a model has been formulated that captures the main features of the progression and transmission of a particular disease, it can be used to predict the effects of different strategies for disease eradication or control. Infectious disease modeling, though often inexact, has enormous potential to help improve human lives.

    4. Erie County Data The Erie County Center for Disease Surveillance, has provided the number of cases of Gonorrhea reported between 2001 and 2006. The data is organized in two ways: Yearly (6 data points) with Age and Sex distribution Monthly (72 data points) only given number of cases

    5. Yearly Erie County Data

    6. Yearly Erie County Data

    7. Monthly Erie County Data

    8. Monthly Erie County Data

    9. SIR and SIS Models An SIR model consists of three group Susceptible: Those who may contract the disease Infected: Those infected Recovered: Those with natural immunity or those that have died. An SIS model consists of two group Susceptible: Those who may contract the disease Infected: Those infected

    10. Important Parameters a is the transmission coefficient, which determines the rate ate which the disease travels from one population to another. ? is the recovery rate: (I persons)/(days required to recover) R0 is the basic reproduction number. (Number of new cases arising from one infective) x (Average duration of infection) If R0 > 1 then ?I > 0 and an epidemic occurs

    11. SIR and SIS Models SIR Model: SIS Model:

    12. Basic SIS model for Gonorrhea

    13. Basic SIS model for Gonorrhea

    14. Basic SIS model for Gonorrhea

    15. Basic SIS model for Gonorrhea

    16. Basic SIS model for Gonorrhea

    17. Assumptions for our Erie County Model

    18. Population in Erie County

    19. Our SIS Model for Gonorrhea

    20. Closer Look of our SIS Model

    21. Closer Look of our SIS Model

    22. Findings There is a non zero equilibrium solution for our model We believe that the data we were provided is on the tail end of an equilibrium solution, with small perturbations The transmission rate needs to be extremely small to get similar infected populations

    23. Challenges Assumptions must be made, and this of course can lead to error What is the transmission rate for a given disease How long is the recovery period Further difficulty is encountered when little data is available on a particular subject i.e. our model does not consider homosexual relations, as we have no data specific to the infected persons sexual habits Collecting the data yourself could be a solution Multiple variables make graphing data very difficult or impossible We made the assumption that we have a constant population to reduce the number of equations. This made it possible to write Mathematica code to run the model vs. time. Increasing the number of groups increases the accuracy and usefulness of a model but it typically makes the model more difficult.

    24. Conclusions Modeling is an effective way to determine dynamics of a population. Creating a model to analysis a population lets you see how transmission/removal rates affect the susceptible class. Personally collecting data to formulate a model can be beneficial to a specific disease. Further analysis on our model should tell us the specific transmission rates for all eight groups. We can do this by starting off with the known removal rates and the equilibrium equations, and then work backwards to find Ro and alpha. Hopefully we will eventually be able to forecast future outbreak, by monitoring the transmission rates and comparing it to a critical threshold value.

    25. References Erie County Department of Health Sexually Transmitted Disease Resource Site for Disease Control (CDC) Mathematical Models in Biology, An Introduction Elizabeth Allman & John Rhodes

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