Mathematical Modeling: Models, Analysis and Applications, Second Edition introduces models of both discrete and continuous systems. This book is aimed at newcomers who desires to learn mathematical modeling, especially students taking a first course in the subject. Beginning with the step-by-step guidance of model formulation, this book equips the reader about modeling with difference equations (discrete models), ODE's, PDE's, delay and stochastic differential equations (continuous models). This book provides interdisciplinary and integrative overview of mathematical modeling, making it a complete textbook for a wide audience. A unique feature of the book is the breadth of coverage of different examples on mathematical modelling, which include population models, economic models, arms race models, combat models, learning model, alcohol dynamics model, carbon dating, drug distribution models, mechanical oscillation models, epidemic models, tumor models, traffic flow models, crime flow models, spatial models, football team performance model, breathing model, two neuron system model, zombie model and model on love affairs. Common themes such as equilibrium points, stability, phase plane analysis, bifurcations, limit cycles, period doubling and chaos run through several chapters and their interpretations in the context of the model have been highlighted. In chapter 3, a section on estimation of system parameters with real life data for model validation has also been discussed. Features Covers discrete, continuous, spatial, delayed and stochastic models. Over 250 illustrations, 300 examples and exercises with complete solutions. Incorporates MATHEMATICA (R) and MATLAB (R), each chapter contains Mathematica and Matlab codes used to display numerical results (available at CRC website). Separate sections for Projects. Several exercise problems can also be used for projects. Presents real life examples of discrete and continuous scenarios. The book is ideal for an introductory course for undergraduate and graduate students, engineers, applied mathematicians and researchers working in various areas of natural and applied sciences.

The presented study was conducted in selected areas of central highlands of Ethiopia to evaluate the hygienic practices being carried out by the small holder dairy farmers of various dairy products including raw milk. The aim of the study was to determine the microbial and chemical properties of milk and asses the marketing situation of milk and milk products. The study was carried out with 173 smallholder dairy farmers, 74, 50 and 49 respondents each from Holetta, Selale and Debre Brhan respectively. The average of total solids, total proteins, fat, carbohydrate and ash percentages of milk were 12.97, 3.52, 4.53, 4.36 and 0.64 respectively. The average total bacteria, coliform and entrobacteria counts of milk samples were 7.6, 3.6 and 3.2 Log CFU/ml respectively; there was no significant difference between the areas. The level of contamination of milk was high and about 88.8% of the pathogens were entrobacteria.The price of whole milk was almost similar in all study areas whereas higher price was observed for butter in Debre Brhan and Ayib in Holetta. Incidence of microbial contamination of milk is a challenge for quality milk production and consumption in the area