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Exercise Consider the following model, with a constant recruitment rate A. This means that a certain fixed number of individuals arrive into the susceptible class per unit time. dS A - BS Bs- us dt dI BS- N dt dR I- µR dt with N(t) = S(t) + I(t) + R(t). (a) Determine the population steady state N*. (b) Show that N(t) → A/u as t → 0o. (c) Find all equilibrium points

Exercise Consider the following model, with a constant recruitment rate A. This means that a certain fixed number of individuals arrive into the susceptible class per unit time. dS A - BS Bs- us dt dI BS- N dt dR I- µR dt with N(t) = S(t) + I(t) + R(t). (a) Determine the population steady state N*. (b) Show that N(t) → A/u as t → 0o. (c) Find all equilibrium points

Advanced Engineering Mathematics
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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Please help with question a, b and c

Consider the following model, with a constant recruitment rate A. This means that a certain fixed number of individuals arrive into the susceptible class per unit time. Exercise dS A - BS dt dI BS- N dt dR I- µR dt with N(t) = S(t) + I(t) + R(t). (a) Determine the population steady state N*. (b) Show that N(t) → A/u as t → o. (c) Find all equilibrium points (d) Find Ro by the usual method (e) find the basic reproduction number, Ro by the next generation matrix method. (f) Make a stability analysis of the DFE point.
Transcribed Image Text:Consider the following model, with a constant recruitment rate A. This means that a certain fixed number of individuals arrive into the susceptible class per unit time. Exercise dS A - BS dt dI BS- N dt dR I- µR dt with N(t) = S(t) + I(t) + R(t). (a) Determine the population steady state N*. (b) Show that N(t) → A/u as t → o. (c) Find all equilibrium points (d) Find Ro by the usual method (e) find the basic reproduction number, Ro by the next generation matrix method. (f) Make a stability analysis of the DFE point.
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