Consider the discrete-time SEIR epidemic model Sn+1 - S, + A - 8 - uS. S.In S„In En+1 - E, + B (u+ k)E, In+i I, + kE, - (7+4)n R+1 - R, +In - pR. where S, En, Is and R, denote the proportion of susceptible, latently infected, infective and removed individual at time n respectively and A is the birth rate, u the per capita natural death rate, 3 the contact rate, k is the rate at which a latently infected individual becomes infectious and y is the per capita recovery rate. (a) Sketch the disease progression diagram for this model. (b) Show that the population is not constant and determine the population equilibrium. (c) Determine the disease free equilibrium and the endemic equilibrium for this model.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider the discrete-time SEIR epidemic model
Sn+1
S, + A - 82ndn – uS.
S„In
En + B-
- (u + k)E,
En+1
= In + kEn – (y+ 4)In
R, + yIn - µR,
In+1
Rn+1
where Sn, En, Is and R, denote the proportion of susceptible, latently infected, infective and removed individual
at time n respectively and A is the birth rate, u the per capita natural death rate, 3 the contact rate, k is the
rate at which a latently infected individual becomes infectious and y is the per capita recovery rate.
(a) Sketch the disease progression diagram for this model.
(b) Show that the population is not constant and determine the population equilibrium.
(c) Determine the disease free equilibrium and the endemic equilibrium for this model.
Transcribed Image Text:Consider the discrete-time SEIR epidemic model Sn+1 S, + A - 82ndn – uS. S„In En + B- - (u + k)E, En+1 = In + kEn – (y+ 4)In R, + yIn - µR, In+1 Rn+1 where Sn, En, Is and R, denote the proportion of susceptible, latently infected, infective and removed individual at time n respectively and A is the birth rate, u the per capita natural death rate, 3 the contact rate, k is the rate at which a latently infected individual becomes infectious and y is the per capita recovery rate. (a) Sketch the disease progression diagram for this model. (b) Show that the population is not constant and determine the population equilibrium. (c) Determine the disease free equilibrium and the endemic equilibrium for this model.
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