Sensitivity equations for a size-structured population model

Abstract

Abstract. In this paper we consider the classical Sinko-Streifer size-structured population model and derive sensitivity partial differential equations for the sensitivities of solutions with respect to initial conditions, growth rate, mortality rate and fecundity rate. Sample numerical results to illustrate the use of these equations are also presented. [3,4,29,32] have focused on establishing well-posedness and stability analysis of models, formulating schemes for numerical solutions, and parameter estimation of individual rates. However, to the best of our knowledge, thus far there is no literature on sensitivity equations and the related analysis for size-structured population models. Sensitivity analysis of dynamical systems has drawn the attention of numerous researchers [1,6,9,10,11,13,14,15,16,17,20,24,25,27,28,35,38,40] for many years because the resulting sensitivity functions can be used in many areas such as optimization and design [16,26,27,34,38], computation of standard errors [9,10,19,21,36], and information theory [12] related quantities (e.g., the Fisher information matrix) as well as control theory, parameter estimation and inverse problems [5,8,9,10,11,40,41]. One of our motivations for investigating sensitivity for size-structured population models derives from our efforts reported in [7], where a shrimp biomass production system and a

Analysis of the Sensitivity of Algorithms for Assessing the Harmful Information Indicators in the Interests of Cyber-Physical Security

“…But these approaches are complex for mathematical specification and time consuming to implement. In Reference [15], the sensitivity equations for structured models of the processes assessed are presented. However, structuring principles may not be applicable for the models of harmful information detection.…”

“…Analysis of relevant works [1][2][3][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] shows that the direct application of the results obtained in most of these works is impossible for the task of a reliable assessment of indicators of harmful information. The reason is that the actual analysis of the features of harmful information in the CPS digital network content occurs under conditions of a priori uncertainty.…”

“…At the same time, the variable ∆η r in Equation (13) has the physical meaning of the deviation from the "ideal" of the values of a particular indicator of harmful information. The symbol ∆φ(k + 1, k, u) in Equations (15), (17) and (18) characterizes the deviation of the elements of the probability matrix of the transition of any particular indicator of harmful information from state to state. The type → Θ(k) variables referred to in Equations (9)-(15), (19)- (21) have the physical meaning of auxiliary indicators, traditional for Kalman's filtering but in our case these are the indicators of the transition of any particular indicator of harmful information from state to state.…”

Sensitivity analysis for a nonlinear size-structured population model

“…Such equations are useful for computing variances of estimated model parameters from observation data (e.g., see [2,6,15]). Our direct motivation comes from the paper [8], wherein sensitivity partial differential equations were derived for the following linear size-structured population model:…”

Extinction and uniform strong persistence of a size-structured population model

“…Later, stability 832 KENG DENG AND YIXIANG WU of the steady state solution of nonlinear models has been studied in [6,8,9]. Very recently, sensitivity analysis for linear and nonlinear versions of model (1.1) has been conducted in [2] and [7], respectively.…”