Interpolation solution in generalized stochastic exponential population growth model

Some aspects in population growth rate

“…Consider the following simple population growth model 1) where N(t) is the number of population individuals at time t and r(t) is the growth rate at time t, which is an accurate and nonrandom given function. The solution of it is obtained as follows [1] …”

“…Population growth models are central in modern ecological theory. A good, thorough reference is the text by [1,2].…”

An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics

“…Moreover the study of stochastic or random functional equations can be very useful in application, due to the fact that they arise in many situations. For example, stochastic integral equations arise in a wide range of problems such as the stochastic formulation of problems in reactor dynamics [1][2][3], the study of the growth of biological populations [4], the theory of automatic systems resulting in delay-differential equations [5], and in many other problems occurring in the general areas of biology, physics and engineering. Also, nowadays, there is an increasing demand to investigate the behavior of even more sophisticated dynamical systems in physical, medical, engineering and financial applications [6][7][8][9][10][11][12][13].…”

“…Also, nowadays, there is an increasing demand to investigate the behavior of even more sophisticated dynamical systems in physical, medical, engineering and financial applications [6][7][8][9][10][11][12][13]. These systems often depend on a noise source, like a Gaussian white noise, governed by certain probability laws, so that modeling such phenomena naturally involves the use of various stochastic differential equations (SDEs) [4,[14][15][16][17][18][19][20], or in more complicated cases, stochastic Volterra integral equations and stochastic integro-differential equations [21][22][23][24][25][28][29][30]. In most cases it is difficult to solve such problems explicitly.…”

Confidence interval for number of population in dynamical stochastic exponential population growth models

“…In paper [3], the stochastic and generalized stochastic exponential population growth models are introduced. So, in the present paper, We construct a confidence interval for number of population obtained in [3]. …”