Modeling the Spread of an Epidemic

By developing a computer model of the spread of an infectious disease, the student develops an understanding of the role of the infection rate and the removal rate on the spread of the disease. The Threshold Theorem of Epidemiology claims that the extent of spread of an epidemic can be predicted if three values are known: initial number of susceptible people (S(0)), the infection rate (K), and the removal rate (by quarantine or cure) (Q). The extent of the spread of the epidemic is indicated by the percentage of susceptible who become infected.

Diseases that are easily transmitted spread quickly unless measures are taken to quarantine or cure infected people quickly. The three epidemic models below can each be used to experiment with various factors to see the impact on the populations. Vensim or STELLA software is needed to run the models. Right-click on the model link to download the model. Simple Epidemic Model - Vensim Simple Epidemic Model - STELLA Assumes the infected people never leave the system | | Infectious(t) = Infectious(t - dt) + (sick_per_day) * dt    INIT Infectious = 1 Susceptible(t) = Susceptible(t - dt) + (- sick_per_day) * dt    INIT Susceptible = 999 sick_per_day = Infectious*Susceptible*infection_rate infection_rate = . 0015 | | 1 globalization ofhealthcare pros and cons.

 

 The simple epidemic model may be used to explore the impact of the infection rate variable on the healthy and infected populations. Change the infection rate and record the change in the output of the model. How does the shape of the s-shaped growth curve change? At what time does the model stabilize? Infection RateStabilization TimeShape of Curve2. Exponential growth usually occurs when the rate of change is proportional to the amount present. Steady-state occurs when the system reaches equilibrium.

Why does this model yield an s-shaped curve? 3. This model could be used to represent the spread of a highly contagious disease in a population living in close By developing a computer model of the spread of an infectious disease, the student develops an understanding of the role of the infection rate and the removal rate on the spread of the disease. The Threshold Theorem of Epidemiology claims that the extent of spread of an epidemic can be predicted if three values are known: initial number of susceptible people (S(0)), the infection rate (K), and the removal rate (by quarantine or cure) (Q).

The extent of the spread of the epidemic is indicated by the percentage of susceptible who become infected. Diseases that are easily transmitted spread quickly unless measures are taken to quarantine or cure infected people quickly. The three epidemic models below can each be used to experiment with various factors to see the impact on the populations. Vensim or STELLA software is needed to run the models. Right-click on the model link to download the model. Simple Epidemic Model - Vensim Simple Epidemic Model - STELLA

Assumes the infected people never leave the system | | Infectious(t) = Infectious(t - dt) + (sick_per_day) * dt    INIT Infectious = 1 Susceptible(t) = Susceptible(t - dt) + (- sick_per_day) * dt    INIT Susceptible = 999 sick_per_day = Infectious*Susceptible*infection_rate infection_rate = . 0015 | | 1. The simple epidemic model may be used to explore the impact of the infection rate variable on the healthy and infected populations. Change the infection rate and record the change in the output of the model. How does the shape of the s-shaped growth curve change? At what time does the model stabilize?

Infection RateStabilization TimeShape of Curve2. Exponential growth usually occurs when the rate of change is proportional to the amount present. Steady-state occurs when the system reaches equilibrium. Why does this model yield an s-shaped curve? 3. This model could be used to represent the spread of a highly contagious disease in a population living in close Quarantined = 0 Susceptible(t) = Susceptible(t - dt) + (- sick_per_day) * dt    INIT Susceptible = 999 quarantined_per_day = Infectious*quarantine_rate sick_per_day = Infectious*Susceptible*infection_rate infection_rate = . 0015 quarantine_rate = .

 

8 | | | 5. According to the Threshold Theorem of Epidemiology, the ratio of the quarantine rate to the infection rate determines whether an illness turns into an epidemic. Use the model above to find the ratio that will result in approximately 50% of the population getting the disease. 6. Design an epidemic model which incorporates any of the features below into the Third Epidemic Model. a) Introduce births and natural deaths into the population b) Introduce a vaccination program to prevent susceptible people from getting sick. How many must be vaccinated to reach steady state in the model?

7. Set up a STELLA model of the transmission of aids in the United States by identifying various segments of the population and their probability of engaging in behavior that puts them in danger of becoming infected. Stocks * Children Healthy, HIV Positive, Aids, Dead * Women Low Risk, Drug Abusing, Heterosexual, HIV Positive, Aids, Dead * Men Low Risk, Drug Abusing, Heterosexual, Bisexual, Gay, HIV Positive Heterosexuals, HIV Positive Bisexuals, HIV Positive Gays, Aids, DeadDetermine the flows to connect the stocks and do research to determine the appropriate values to use. |