The measles pathogenesis function used to model the development of the disease is given by the following equation: f (t) = −t(t − 21)(t + 1) (2) where t is measured in days and f (t) represents the number of infected cells per milliliter [mL] of plasma. What is the peak infection time for the measles virus? Solve the above problem through the following steps: (a) Expand equation 2 fully. [1] (b) Calculate the first derivative f′ (t), of the equation found in part (a). [1] (c) Find the intervals of increase or decrease of f′ (t) and state why the negative solution should be ignored? (Hint: the quadratic formula will be used). [5] (d) Find the maximum value of the function f′ (t) and state in english what this value describes?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Measles is a highly contagious infection of the respiratory system and is caused by a virus. Despite the fact that more than 80% of the world’s population is vaccinated for it, measles remains the fifth leading cause of death worldwide. In general, the term pathogenesis refers to the way a disease originates and develops over time. In the case of measles, the virus enters through the respiratory tract and replicates there before spreading into the bloodstream and then the skin.
Figure 1: Shown is a transmission electron micrograph of a measles virus.
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The measles pathogenesis function used to model the development of the disease is given by the following equation: f (t) = −t(t − 21)(t + 1) (2)
where t is measured in days and f (t) represents the number of infected cells per milliliter [mL] of plasma. What is the peak infection time for the measles virus? Solve the above problem through the following steps:
(a) Expand equation 2 fully. [1] (b) Calculate the first derivative f′ (t), of the equation found in part (a). [1] (c) Find the intervals of increase or decrease of f′ (t) and state why the negative solution should be ignored? (Hint: the quadratic formula will be used). [5] (d) Find the maximum value of the function f′ (t) and state in english what this value describes?
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