CHAPTER ONE
INTRODUCTION
1.1 General Overview
In this research
work we shall demonstrate how mathematical model can be use to describe the
growth of microbial organism(s) and how it can be used to predict such growth
in the future with the view of preventing it. This is very pertinent especially
when the growth is of negative economic gain. A mathematical model for
microbial growth is a necessary component in the efficient assessment of food
contamination, shelf-life and risk assessment in supply chain.
When food is
chilled, it is meant to stand a taste of time before decay. But the durability
of this (the shelf-life of the food) is a function of many environmental
factors such as the storage temperature, pressure, the amount of
micro-organisms in that environment etc
(Gordon, 2010). This research is geared toward taken into consideration
one of these variables (temperature) to predict the growth of the
micro-organism under variable temperature and how the shelf- life of chicken can
be affected.
Pseudomonas
species is one of the micro-organisms that cause spoilage in chilled foods.
Sequel to the economic implications of the growth in freeze chicken then, the
need for the prediction.
Mathematical
modeling is one of the few available instruments for predicting possible growth
of pseudomonas species and the effects of such on the shelf-life of frozen
chicken. Our model(s) will consist of differential equation(s) which is
normally analytically solved to predict the growth of pseudomonas species on
chicken and how this reduces the shelf-life.
1.2 Research Overview
Growth is one of
the phenomena that characterize living things. The term growth is used to
indicate both increase in size (of individual organisms) and increase in
numbers (of populations). Traditionally, growth of individuals and population
growth belong to different provinces of biology but modelers rarely respect
this demarcation lines. The growth of micro-organisms especially those of
negative economic importance call for concern from every rational human being
in the society. The increase in the number of cells (unicellular microbial
organisms) will lead to increase (aggravation) in their physiological actions
that will tend to affect people in the society either positively or negatively.
The growth may leads to outbreak of diseases and reduction in shelf-life of
food when acting on them.
This reduction
in shelf-life means economic danger as when the food cannot stand a taste of
time. It means that the owner cannot make the best out of it, thus, maximum utility cannot be achieved.
Pseudomonas
species are motile, rod shaped aerobe gram-negative bacteria. They are found
everywhere, in soil, water, plants and animals. In most cases, it is not
pathogenic and in fact can be beneficial. For example, pseudomonas putida is
used as bio-scrubber to aid in the bio-degradation of diverse organic compounds
in polluted air and waste water.
However,
pseudomonas aeruginosa is an infamous opportunistic human pathogen most
commonly affecting immuno-compromised patients. Along with pseudomonas
mattophilia, it accounts for the majority infections and spoilage. Pathogenic
pseudomonas are found throughout the body most commonly, urinary tract,
respiratory tract, blood and wounds.
They can remain
viable for long period of time in many different habitats and under very
adverse conditions. Pseudomonas are wide spread, found in water, saline
solution, utensils and even in cosmetics, pharmaceuticals, and disinfectants
,and many natural and manufactured foods (Kenneth,2009). Psychrotrophic (cold tolerant) pseudomonas
are significant food spoilage problem in refrigerated meat, shell-fish, chicken
and dairy products.
The growth of
pseudomonas can be inhibited by a considerably very low temperature thus, the
importance of storing manufactured foods under such temperature. Thus, storing
chicken under these temperature zones, we can be able to predict the quantity
of the microbial growth and the effects on the shelf-life of chicken.
In this
research, we shall be concerned with the quantitative aspect of predicting the
growth of pseudomonas and interpreting the effects of the given quantity at
particular time on chicken shelf-life. Basically the modeling process in this
research will involve:
i.
Taking real world problem.
ii.
Formulate a mathematical model(s) for the real
life situation.
iii.
Interpret/solve the model(s) and
iv.
Returning it back to real life for
analysis.
From
above, the expectation of this work is to know how the organisms grow and how
the growths affect the shelf-life with the view of knowing the best temperature
to store chicken products.
In the past,
predictive microbiology can be used to determine and predicts the shelf-life of
perishable foods under commercial distribution conditions based on microbial
growth kinetics.
A
combination of microbial kinetics with engineering accumulation approach can be
used to predict the final microbial level in a food or the loss of shelf-life
for any known time-temperature sequence if there is no history effect or the
history effect is negligible.
Specifically,
the case study of this research will be chicken killed and prepared for
preservation under variable temperature. And, our model shall try to estimate
the increase in the concentration of pseudomonas species as the time changes
under the temperature condition. The model will be simple ordinary differential
equation(s).
In
all cases, microbial growth under variable environmental conditions is
described by first order kinetic that is by a single or by a system of ordinary
differential equations of first order (poschet etal 2005).
One
of the most important environmental parameters, from the food safety and
quality point of view is temperature. Considering the temperature changes along
the supply change, the use of dynamic models which are able to take into
account the influence of temperature variation and other factors on microbial
growth is essential for prediction of products shelf life when considering
decay causing microorganisms and for risk assessment, when considering food
borne pathogens.
1.3 Aims and Objectives
The aim shall be
specifically concerned with how to use simple growth model to estimate the
increase in the concentration of pseudomonas in chilled chickens and how this
change affects the shelf life. We shall formulate the growth model in terms of
ordinary differential equation.
This work will
equally try to look the two basic growth models-Geometric growth model and
logistic growth model, and why the earlier can hardly be used to estimate the
concentration in the population.
1.4 Scope and Limitations:
Our
scope shall be limited to single simple differential growth models. Equally our
temperature of investigation will range from normal room temperature to
freezing temperature. And since we are not going to collect data for investigation,
our model will be based on the assumptions mentioned in (3.4)
1.5 Definition
of basic Terms
(a) Growth:
Growth
may be refers to an increase in size or numbers of living organisms over time
(Haughton, 2005).
(b) Bacterial
Growth:
Bacterial
growth is the division of one piece of bacterium into two daughter cells in a
process called binary fission (Paul and Peter, 1992).
(c) Binary
Fission:
This
can be defined as the method of asexual reproduction that involves the
splitting of a parent cell into two approximately equal parts. (Paul and
Peter,1992).
(d) Shelf
Life:
Shelf
life is the length of time a product may be stored without becoming unsuitable
for use or consumption (Gordon, 2010).
(e) Temperature:
This
can be defines as the degree of hotness or coldness of a body or environment
(Gordon, 2010).
(f) Food
Temperature Danger Zone:
The
temperature range in which food borne bacteria can grow is known as the danger
zone (Gordon, 2010).
(g) Doubling
Time:
This
is the period of time required for the microorganism to double in number
(Neeraj and Sharma, 2007).
(h) Specific
Growth Rate (ยต):
This
can be define as the increase in cell mass per unit time (Friedrick, 2010)
(i) Relative
Rate of Spoilage (RRS):
RRS
at a temperature 
has been defined as the shelf at 00C
divide by the shelf life at (Gordon, 2010).
has been defined as the shelf at 00C
divide by the shelf life at (Gordon, 2010).
(j) Model:
Model
can be defined as a simplified representation of a certain aspects of a real system
(Edwards, 2001).
(k) Mathematical
Model:
This
can be define d as a model created using mathematical concepts such as
functions and equations (Edwards, 2001).
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