Different mathematical models have been used to predict the fraction of a population that will be infected by a disease under different conditions, one such model is called the Kermack-McKendrick model. This model gives the following equation when solved under certain conditions: ρe−qA =1−A where A is the fraction of the population ultimately affected, q is a measure of disease transmissibility, and ρ is a measure of the fraction of the population that is initially susceptible to infection. How does the outbreak size, A change with an increase in transmissibility q, mathematically this is symbolised by the derivative dA /dq ? 1 Solve the above problem through the following steps: (a) Equation 2 can’t be solved for A and fortunately we don’t have to solve this equation explicitly in order to find dA . What method of differentiation can we use to solve for dA .[1] dq dq (b) Apply this method of differentiation to equation 2, keeping in mind that A is a function of q, that is A (q) and solve for dA/dQ ? . (c) State in English what you understand by the term dA/dq ?
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Different mathematical models have been used to predict the fraction of a population that will be infected by a disease under different conditions, one such model is called the Kermack-McKendrick model. This model gives the following equation when solved under certain conditions:
ρe−qA =1−A
where A is the fraction of the population ultimately affected, q is a measure of disease transmissibility, and ρ is a measure of the fraction of the population that is initially susceptible to infection. How does the outbreak size, A change with an increase in transmissibility q, mathematically this is symbolised by the derivative dA /dq ?
1 Solve the above problem through the following steps:
(a) Equation 2 can’t be solved for A and fortunately we don’t have to solve this equation explicitly in order to find dA . What method of differentiation can we use to solve for dA .[1] dq dq
(b) Apply this method of differentiation to equation 2, keeping in mind that A is a function of q, that is A (q) and solve for dA/dQ ? .
(c) State in English what you understand by the term dA/dq ?
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 3 images
