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In
this research work, we have reviewed and studied two disease models: a disease
model with logistic recruitment rate with and without incubation period and a
disease model with linear recruitment rate with and without incubation
period. The existence and stability or
otherwise of the equilibrium states of the models were studied; also numerical
experiments were conducted using a written computer program in MATLAB function
ode45; for which table of parameter values were generated using secondary data
from the works of Dhar and Sharma (2009) and graphs were plotted, giving
pictorial representation of the schemes with the transmission rate from the
infected to the susceptible population ‘b’ as the varying parameter. It was observed
during the study that in replacing the model with logistic recruitment rate
with linear recruitment rate without incubation period, one important critical
point (the disease free) was lost. Numerical experiments using published data
showed that as the transmission rate from infected to susceptible population
increases; the overall population of the infected people for the model with
linear recruitment rate goes slightly higher than that of the model with
logistic recruitment rate. Our numerical results also showed that as the
transmission rate increases, the peak values of the model with logistic
recruitment rate decreases and always less than the peak values of the model
with linear recruitment rate. This study
provides a comparative analysis of the disease models; the study reveals that
the incidence of infection for a disease model with linear recruitment rate is
slightly higher than that of a disease model with logistic recruitment rate.
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