Mathematical Models in Biology

Mathematics and Biology are separate disciplines, but more often than not, you’ll find a number of mathematical theories in biology, mainly used in explaining theories, justifying hypotheses and performing experiments to solve many scientific problems.

Typically, mathematical theories are used in answering such biology-related questions as, “how quickly can a disease spread within a particular area?”, or “what percentage of a national population needs to be vaccinated, at an early age, against a particular disease (say polio) for it to be eradicated or for the occurrence to be drastically reduced?” or “how effective is a drug is healing or managing a disease?” Students are taught how to evaluate certain hypotheses and interpret theoretical predictions scientifically using mathematical models introduced earlier into the field for these specified purposes.

Generally, in all sciences, mathematical models are often found in different aspects to explain different models and theories. And essentially, their complexities could broadly range from simple procedures, such as that of the population models, to fairly complex ones, such as computational modelings adopted to make scientific predictions in solving the numerous scientific problems of today, especially in the field of biology.

So, why do we have mathematics in biology? Is it because they’re both fun and interesting subjects or because they need to be combined to explain some things about life? In this article, we’ll be answering this question and, at the same time, examining some of these mathematical models and how high their effectiveness is in investigating and solving many problems posed in interpretation and analysis of different biological theories and hypotheses.

To support the rapidly growing body of knowledge in biology, there’s the need to find quantitative means of justifying the analyses and interpretations of data and discoveries about living things, their co-existence and, importantly, their habitation. The scientists then introduced some formal and verbal models into the field of biology to explain occurrences ad events as they occur. Some models that were introduced are:

1. The Population Growth

This model is a simple mathematical model. Population growth is a statistics-based model, and, as the name implies, it is used in determining percentage and population range. This model is best used in explaining processes and evaluating the dynamics and nature of certain occurrences to provide a detailed understanding of how numbers can change over a period of time. Such things as population size, age distribution are examined in understanding how living things interact with their environment, one another as well as with other similar and/or different species.

Population models are especially useful when an organism is in danger of extinction. They are used to track the population and strength of species and also present different scientific processes and techniques in which the endangerment can be solved.

In the end, this model provides both a quantitative and qualitative analysis of the problem posed. There are some equations used under this study; the logistic growth, species-area relationship, etc.

2. ODE-Based Modeling

ODE-Based Modelling is a formal based model. This method is specially used to represent the relations between different biological molecules that present the time-changing effects of different processes. In evaluating the different biological hypotheses, there are 3 different categories of ODE-based methods, namely;

● Hill-function

● Law of mass action, and

● Michaelis-Menten Kinetics

The method one decides to use fully depends on the problem or the scientific data available.

All the methods are quite essential in evaluating networks on a small-scale level. They are used in explaining the comprehensive approaches that can be adopted for complex mechanisms of serious diseases on intercellular and intracellular levels.

This model is also used in the evaluation of different healing strategies that can be used in effectively managing less common types of disease, the prostate tumor growth. The model offers different approaches that can be adopted in tackling the disease in a patient.

3. Agent-Based Model of Biological Systems (AMB)

This model falls under the computational models, and it is used for the simulation of interactions and activities of individual agents. It does this to evaluate the effects they have as a whole process. This model is often not adopted in study tumor growth, drug efficacy especially, and angiogenesis in cancer environments.

The AMB is used to simulate organs, tissues, and the microenvironment to understand the real situation of things. The variability of models is also examined to analyze performance and results in progress.

There are more biological models, each of which presents complex processes in examining problems and evaluating biological hypotheses. Analysis of large data must be done to get verified information and solutions on a multiscale level.