The paper studies the dynamics of a full delay-logistic population model incorporated with a proportionate harvesting function. The study discusses the stability of the model in comparison with the well-known Hutchinson logistic growth equation with harvesting function using the rate of harvesting as a bifurcation parameter to determine sustainable harvesting rate even at a bigger time delay of
τ
=
3.00
. In all cases, the Hutchinson equation with harvesting was forced to converge to equilibrium using an additional and a different time delay parameter, a deficiency previous researchers have failed to address when the Hutchinson model is used for this purpose. The population fluctuations are catered for with this model making the estimated maximum sustainable growth and harvest reflect realities as this model drastically reduces time-delay associated oscillations compared to the well-known Hutchinson delayed logistic models. The numerical simulations were be done using the MatLab Software.
In this paper, a deterministic mathematical model for the transmission and control of malaria is formulated. The main innovation in the model is that, in addition to the natural death rate of the vector (mosquito), a proportion of the prevention efforts also contributes to a reduction of the mosquito population. The motivation for the model is that in a closed environment, an optimal combination of the percentage of susceptible people needed to implement the preventative strategies
α
and the percentage of infected people needed to seek treatment can reduce both the number of infected humans and infected mosquito populations and eventually eliminate the disease from the community. Prevention effort
α
was found to be the most sensitive parameter in the reduction of
ℛ
0
. Hence, numerical simulations were performed using different values of
α
to determine an optimal value of
α
that reduces the incidence rate fastest. It was discovered that an optimal combination that reduces the incidence rate fastest comes from about
40
%
of adherence to the preventive strategies coupled with about
40
%
of infected humans seeking clinical treatment, as this will reduce the infected human and vector populations considerably.
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