Hovav Talpaz

Epidemiological and economic models for spread and control of citrus tristeza virus disease

Citrus tristeza virus (CTV) causes a most destructive citrus disease in many parts of the world, and indications of natural spread were found in Israel in 1970. The strategy for controlling the disease in Israel is based on the eradication of virus-infected trees, detected by test plants or immunological methods. Mathematical models for CTV infection and spread were developed and used to assess the cost-effectiveness of the eradication policy. It was concluded that the discovery-eradication program is economically justified and superior to allowing the disease to progress unchecked.

On the spatial distribution of citrus tristeza virus disease

The spatial spread of citrus tristeza virus (CTV) disease was studied using data from two infected groves. Statistical analysis indicated a spatial grouping of infected trees. A gamma distribution was fitted to the empirical distribution of the distances between nearest infected neighbors. The findings suggest that, after locating a newly infected tree, additional inspections to detect CTV should be carried out mainly on trees within 14 m of that tree.

Economic Optimization of a Growth Trajectory for Broilers

A dynamic model was constructed to select the economically optimal growth trajectory of broilers and compute the feeding schedule designed to satisfy the nutritional requirements along this trajectory. Alterations in the normal growth rates are possible by utilization of the phenomenon of compensatory growth which follows a period of feed restriction. The optimal trajectory is solved for by a reduced-gradient nonlinear programming algorithm. The model calculates the daily optimal growth rates along with the corresponding requirements of total protein, amino acids, and energy in obtaining the optimal diets. A substantial increase in profits can be achieved by following this methodology.

A mathematical model for the description of chymosin action on casein micelles

A mathematical model for chymosin action on casein micelles is presented in a two-stage equation which results in a single curve demonstrating the lag time from enzyme addition to the end of coagulum firming. The model uses the Michaelis–Menten enzyme kinetics equation for the first reaction followed by an n th order reaction for the casein micelles agglomeration stage. The computer output using these equations shows that lag time is elongated as enzyme concentration is lowered. Regression analysis of time of gelation against l/ E 0 shows good correlation. Viscosity of the milk drops at the beginning of the κ-casein hydrolysis and increases thereafter, when the coagulum is being formed.

Modeling of the dynamics of accelerated growth following feed restriction in chicks

Abstract A model for normal growth and accelerated growth resulting from an early-age feed restriction in chickens, has been constructed. The model describes normal growth by a Gompertz equation, whereas compensatory growth is the product of three terms: a time derivative of the Gompertz equation; a compensation factor which is a function of the severity of feed restriction and a time-dependent exponential term. The model was fitted to experimental results obtained in male and female broiler chicks, with the aid of an iterative algorithm, based on numerical integration of the time-function, in two steps.

On testing homogeneity of t normal means against ordered alternatives in r groups

Given k=rt normal populations with a common but unknown variance consisting of t treatments applied to r different groups of units, and supposing that in each group the means are monoto-nically non-decreasing (or non-increasing), then the likelihood ratio test of homogeneity of the means in each group against the simple order alternative is considered. Critical values are provided when one observation is drawn from each of the k populations.

Parameter estimation in differential equations, using random time transformations

Differential equations with measurements subject to errors are usually handled by Least Squares methods or by Likelihood methods based on diffusion-type stochastic modifications of the differential equation. We study the performance of likelihood methods based on substituting a Gaussian random time transformation as argument in the solution of the original deterministic differential equation. This method may be applied to the simultaneous estimation of parameters describing a number of differential equations, based on data with dependent measurement errors. The model is fitted to disease progress curves derived from a real data set consisting of disease assessments of melon plants infected by Zucchini Yellow Mosaic Virus (ZYMV).

Parameter estimation for ligand binding systems kinetics applied to 1,25-dihydroxycholecalciferol

A mathematical analysis of the kinetics of the hormone-receptor interaction was applied to the 1,25-dihydroxycholecalciferol-intestinal receptor system. The exact analytical solution and the numerical integration of the kinetic equation were installed in a Statistical Analysis System (SAS) computer program to estimate the rate constants of the reaction. Estimates of the parameters obtained by these two methods are similar, demonstrating that the numerical integration can be combined with the nonlinear regression procedure for least-squares parameter fitting using a simple SAS program. This enables estimation of kinetics rate constants when the kinetic equation cannot be solved analytically. The ratio of the rate constants (ka/kd) found by the nonlinear procedure is close to the independently determined equilibrium (Scatchard) constant in the nonlinear analysis.

Abstracts of papers presented at the F.E. Nitzany Workshop on Epidemiology and Diagnosis of Plant Viruses

ON E P I D E M I O L O G Y A N D D I A G N O S I S O F P L A N T V I R U S E S

A model for the spread and control of citrus tristeza virus disease

Citrus Tristeza Virus (CTV) causes a most destructive citrus disease in many parts of the world. The strategy for controlling the disease in Israel is based on the eradication of virus-infected trees, detected by an immunological method. A model for the spread and control of CTV is described. The disease spread depends on an infection rate parameter and on a detection coefficient. Both parameters vary with time. Simulation of the model under different conditions assists us to make decisions regarding the control of CTV disease.