attached below. I need a fully detailed write up for questions 2, 3, and 4.

attached below. I need a fully detailed write up for questions 2, 3, and 4.


Microsoft Word - SIS Epidemic Models Final (1).docx SIS Epidemic Models Modelling diseases allow for public health teams to work out the impact of real-world diseases. One such model is the SIS epidemic model. The SIS model describes that people are Initially susceptible to disease →Infected by the disease →Susceptible to disease again People are infected at a rate of a People become susceptible again at a rate b Some assumptions about the mode of transmission • Infections depends on contact between susceptible and Infected • Recovery is at a constant rate (a), proportional to the number of infected (I). • The total population (N) is constant. The disease doesn’t kill people. A mathematical description of this model of all this formation can be derived to form the following differential equation. ?? ?? = (? − ??)?, ???ℎ? = ?? − ? This can be simplified to the following ?? (? − ??)? = ?? Reproduction Rates Epidemiologists when talking about infectious diseases, use a constant called The Basic Reproduction number R0. R0 is the average number of people an infectious person will infect assuming the rest of the population is susceptible. We can define the R0 in terms of our recovery rate and the infection rate b. In real world epidemiology it is easier to work out R0, then work out the recovery rate and then work out the infection rate. We can do this by defining ?! = ????????????? ???????????? = ? ? We can determine the recovery rate very simply as ? = 1 ?????????????????????? We can then work backward and work out a value Question One (16 marks) By integrating both sides, using partial fractions and finding the constant of integration show that the number of infected people at any time is ?(?) = (?? − ?)?!?(#$%&)( (?? − ?) + ??![?(#$%&)( − 1] , ???ℎ?(0) = ?! Question Two (2 marks) By using the definition of the SIS model explain why at any time the number of people susceptible at any time is ?(?) = ? − (?? − ?)?!?(#$%&)( (?? − ?) + ??![?(#$%&)( − 1] Question Three (12 marks) Research three world diseases, with references state their values of R0, N, a and b. For each of the three diseases plot I and S on the same graph. To plot your graphs, you can limit your population by a scale factor and assume an initial infected population of 1. Question Four (10 marks) Using your diseases in question three, write a report that contains the following • A description of how the parameters of R0,N,a and B impact the difference between the Susceptible and the Infected over time. • A comparison of the infectivity of the three diseases and the impacts on their populations • Outlines how any assumptions in the SIS model we have used may not truly replicate some diseases. Give real life examples where these assumptions do not hold. • Any other interesting and relevant information regarding the modelling of your disease Your report must be at least one page, be well formatted and contain all references in APA formatting.