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Figure 5 Size of the recovered class over time.
Additionally there is flow from the recovered class into the class of susceptibles at a rate (alpha_{3}R), due to loss of infection-acquired immunity.
The recovered z admits the constant natural death rate d, does not have permanent immunity, hence there is a constant transfer rate δ from the recovered class back to the susceptible class.
After the maternal antibodies disappear from the body, the infant moves to the susceptible class S. Infants who do not have any passive immunity, because their mothers were never infected, also enter the class S of susceptible individuals; next the susceptible enters the I class while they are infectious and then move to the recovered class R upon temporary recovery.
where b is the birth rate of the population, d is the natural death rate of the population, k is the proportionality constant, μ is the rate at which infected individuals become temporarily immune, γ is the rate at which the recovered class revert to the infective class, α is the saturated parameter, and b, d, k, α, γ, μ, h are positive parameters.
Since recovered class R does not have any effect on the dynamics of S, V, E and I class, we shall investigate the following system: textstylebegin{cases} frac{dS}{dt} =A-delta_{0}S-f(S,I +eta V-mu S, frac{dE}{dt} =f(S,I - delta_{0}+delta_{1})E, frac{dI}{dt} =delta_{1}E-(delta_{0}+delta_{2}+delta_{3})I-g(I), frac{dV}{dt} =mu S,I - delta_{eta)V.
Similar(47)
In model (2), (S(n)), (E(n)), (I(n)), and (R(n)) denote the numbers of susceptible, exposed, infectious, and recovered classes at nth generation, respectively, Λ is the recruitment rate of the susceptible, (mu_{i}) ((i=1,2,3,4)) are the death rates of susceptible, exposed, infectious, and recovered individuals, respectively.
Thus, we include four recovered classes which correspond to each infected class.
It is assumed that the same proportion of the resulting susceptible and recovered classes from the first wave are vaccinated.
The resulting susceptible and recovered classes will be used as the initial population for the second wave model.
The reason for this is that these parameters are estimated based on oscillations in data collected on the recovered classes R1– R10, and these oscillations are sensitive to the waning rate: a slow rate of waning will cause individuals to stay in the R-classes longer and will dampen the oscillations.
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