Consider the SIR model for disease control and prevention measures: immunization and quarantinepSbNSIRdsIPdRFigure 1: Transfer diagram for an SIR Vaccination model.i. Derive the system of differential equations for the model with transfer diagram for S(0)So, I(0) = lo = 0 and R(0) = Ro = 0.ii. Explain the physical meaning of each of the parameters p, b, 2,y, d in each compartmentiii. State the Ro value for this model and explain what it representsiv. Find the disease free equilibrium pointv. Find the Jacobian analyse the stability of the disease free equilibrium pointvi. Find an endemic equilibrium point

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The spread of a contagious disease through a population involves intricate interactions from the level of populations down to the level of individual cells and viruses. However, it is still possible to lean interesting and useful information from relatively simple models. The SIR model of an Epidemic ? Classic model introduced in 1927 ? Simple model that provide interesting and useful information ? Population divided in three groups: S ? Susceptible ? Infected Recovered R S (t) + I(t) + R(t) = 1 dS dt aSI dI dt - aSIBI dR dt = BI
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