Question

1. (a) Use first order differential equations and diagrams to explain the following terms. (i) Exponential growth (4 Marks) (ii) Exponential decay (4 Marks] (iii) Logistic growth (4 Marks) (6) The graph below represents solution trajectories for the Susceptible, Infected, and Recovered individuals for the basic and well-known SIR epidemic mathematical model. Describe the behavior of the solution trajectories for S(t) and R(t) in terms of exponential growth, logistic growth, or exponential decay. Why does the infection curve I(6) peaked and then decay to zero?. In the context of the recent COVID-19 pandemic, what control measures should be taken so that, the infected cases could exhibit the behavior of I(t) in the plot below? (6 Marks] R(t) s(t) I(t) t Figure 1: SIR model evolving as a function of time

Answer 1

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Logarithmic greneth *. 314) → Exponential decay R(it) --- As s(t)> Rit), so I lt) increases till the intersection point of st) & Rlit) After that K(A) (recovered individuals) than susceptible ones So, infected people becomes less & as sto & Ret) loustait, I '(t) decays too becomes darger be CS Scanned with CamScanner

given flot for For I (t) to exhibit the same as COULD 19, human race have to produce/ discover a vaccine as soon as possible & provide it to all indusduals. Till that in the due time; everyone should maintain social distancing the reduce susceptibles Sej live need to decrease s(t) & increase klit) by maintains & advancing medication facilities vespectively, social distancing CS Scanned with CamScanner

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