please show full steps Assume that the population of individuals is constant and it is N. Assume that this population issubdivided into susceptible (S), infective (I) and removed/recovered (R) classes. Assume that the rate oftransmission of disease is given by a, the rate of recovery is given by ß and the rate of loss of immunity isgiven by y.a) Draw the diagram of this epidemicb) Write the system of differential equations corresponding to this epidemicc) Find the steady states of this epidemic, i.e the states for which the derivatives areequal to zero

Answered: Assume that the population of…

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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Assume that the population of individuals is constant and it is N. Assume that this population is
subdivided into susceptible (S), infective (I) and removed/recovered (R) classes. Assume that the rate of
transmission of disease is given by a, the rate of recovery is given by ß and the rate of loss of immunity is
given by y.
a) Draw the diagram of this epidemic
b) Write the system of differential equations corresponding to this epidemic
c) Find the steady states of this epidemic, i.e the states for which the derivatives are
equal to zero

Expert Solution

Step 1

$G i v e n, a s s u m e t h a t t h e p o p u l a t i o n o f i n d i v i d u a l s i s c o n s \tan t a n d i t i s N . A s s u m e t h a t t h i s p o p u l a t i o n i s s u b d i v i d e d i n t o s u s c e p t i b l e (S), i n f e c t i v e (I) a n d r e m o v e d / r e c o v e r e d (R) c l a s s e s . A s s u m e t h a t t h e r a t e o f t r a n s m m i s s i o n o f d i s e a s e i s g i v e n b y α, t h e r a t e o f r e c o v e r y i s g i v e b b y β a n d t h e r a t e o f l o s s o f i m m u n i t y i s g i v e n b y γ .$