Epidemic Results Color of 1st Shared 2nd Shared 3rd Shared 4th Shared Tube After Infected or Not with? with? with? with? Exercise? Infected? Tube # (Tube #) (Tube #) (Tube #) (Tube #) (+or-) (+or-) 1 4 + 14 + 3 + 9 - - 2 18 + 5 + 7 + 17 + + + 3 11 + 10 + 1 - 12 + + + 4 1 - 13 + 12 - 15 + + + 5 12 + 2 + 17 + 13 + + + 6 9 - 7 + 8 + 10 + + + 7 13 + 6 + 2 + 16 + + + 8 10 11 6 18 - - 9 6 15 18 1 - - 10 8 3 15 6 + + 11 3 8 16 14 + + 12 5 + 18 + 4 + 3 + + + 13 7 4 14 5 + + 14 15 1 13 11 + + 15 14 + 9 - 10 + 4 + + + 16 17 11 7 + + 17 10 5 2 + + 18 2 12 9 e + + Collect data by filling in the table. After all data is collected, answer the following questions: 1) Who was patient zero (tube #)? How many students became infected? 2) Are any students not infected? How many? 3) Why would some students not be infected? 4) What kind of viral diseases can be spread this way?
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To determine patient zero, we need to look at the data in the table and identify the tube number of the student who was the first to show signs of infection. Show more…
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Let us suppose that a curable disease spreads in a very large and constant population such as a University Campus. Also, the person who recovers from the disease creates defenses and is no longer susceptible to acquiring it again. At any time, due to the presence of the disease, the population is divided into three different classes of people: Susceptible: People who can get sick. Infected: They have the disease. Recovered: They had the disease and are okay. This is shown in the following figure (total of population): We will call: S (t) = The number of susceptible people to the disease at time t I (t) = The number of infected people at time t R(t) = The number of recovered people recovered at time t Observe that S = S (t), I = I (t), and R = R (t), are functions that depend on time. 1. Explain why the three classes are related by the following system of equations: dS/dt = -0.00001 S I dI/dt = 0.00001 S I - 1/14 I dR/dt = 1/14 I Suppose we start (t = 0) to analyze the spread of the disease when there were 45,400 susceptible, 2,100 infected, and 2,500 recovered. 2. Infer and sketch the 5 graphs of S (t), I (t), and R (t) in the following quadrants. Explain your answers
Sri K.
Let's start our modeling process with R(n). Our assumption for the length of time someone has the flu is 5/3 weeks. Thus, 3/5 or 60% of the infected people will be removed each week: R(n + 1) = R(n) + 0.6I(n) The value 0.6 is called the removal rate per week. It represents the proportion of the infected persons who are removed from infection each week. I(n) will have terms that both increase and decrease its amount over time. It is decreased by the number of people removed each week: 0.6 * I(n). It is increased by the number of susceptible people who come into contact with infected people and catch the disease: aS(n)I(n). We define a as the rate at which the disease is spread, or the transmission coefficient. We realize this is a probabilistic coefficient. We will assume, initially, that this rate is a constant value that can be found from the initial conditions. Let's illustrate as follows: Assume we have a population of 1000 students residing in the dorms. Our nurse found 5 students reporting to the infirmary initially: I(0) = 5 and S(0) = 995. After one week, the total number infected with the flu is 9. We compute a as follows: I(0) = 5, I(1) = I(0) - 0.6 * I(0) + aI(0) * S(0) I(1) = 9 = 5 - 3 + a * 5 * 995 7 = a(4975) a = 0.001407 Lets consider S(n). This number is decreased only by the number that becomes infected. We may use the same rate a as before to obtain the model: S(n + 1) = S(n) - aS(n)I(n) Our coupled model is R(n + 1) = R(n) + 0.6I(n) I(n + 1) = I(n) - 0.6I(n) + 0.001407I(n)S(n) S(n + 1) = S(n) - 0.001407S(n)I(n) (1.11) I(0) = 5, S(0) = 995, R(0) = 0 The SIR model Equation (1.11), can be solved iteratively and viewed graphically. Lets iterate the solution and obtain the graph to observe the behavior to obtain some insights.
10. Given the population: 300 sera are tested for SARS-CoV-2 antibody; 255 of which are from confirmed COVID-19 patients, while the remaining 45 are from healthy individuals. The students produced a rapid antibody testing kit. They subjected their test kits for evaluation, and the test results reveal only 247 IgM/IgG positives out of 255 infected individuals, which produces 8 false negatives. Compute the sensitivity of the test kit. 11. The rapid antibody test kit of the students is subjected to its specificity. 300 sera are tested for SARS-CoV-2 antibody; 255 of which are from healthy individuals and 45 sera from confirmed COVID-19 patients. The test results show 240 IgM/IgG negatives out of 255 negative test results, which produces 15 false positive results. Compute the specificity of the test kit. 12. From your answers in items 10 and 11, compute the test efficiency. 13. From your answers in items 10 and 11, compute the Positive Predictive Value and Negative Predictive Value.
Adi S.
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