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Therefore, the birth rate function of mosquitoes is taken as (r_{m}N_{m} t-tau )e^{-d_{j} t-tau{-alpha N_{m}(t)}), where the meanings of the parameters can be found in Table 1.
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The expression (px_{2}(t)/(q+x_{2}^{n}(t))) is a birth rates function of the susceptible pest population.
Birth rate or input function is dependent on age or dependent on time in these models cited therein.
In fact, birth rate or input function is dependent not only on age and time but also on the total population.
The model follows the basic form of models produced by Anderson & May 19811) except that the host population is assumed to be dioecious and its birth rate is a function of the number of females.
We assume the birth rate is a periodic function with respect to time and the death rate is a time-independent function.
The birth rate is a decrease function until the population attend certain level such as Logistic growth rate.
We assumed the birth rate is a periodic function with respect to time and the death rate is only age dependent.
Under the assumption that the birth rate is a time-periodic function and the death rate is a time-independent function, we obtain an exact upper and lower bound for the number of newborns and the total population.
A birth-and-death model was developed to account for the age distribution of the human miRNAs in the same way Lu et al. used [ 24], which incorporates a constant birth rate v and a survivorship function P t).
In this paper, we discuss the dynamical behaviors of a single-species discrete model with the Ricker function as the birth rate and only the mature population reproducing.
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