Hello Shervin Mossadeghi

Differential equations help to model and understand biological systems that change over time.

For instance, the biochemical reactions that occur in biological systems.

Biochemical reactions are often described by the law of mass action, which states that the rate of a reaction is proportional to the product of the concentrations of the reactants. This leads to differential equations that describe how the concentration of reactants and products changes over time.

For example, a reaction like A + B -> C can be modeled using differential equations:

d[A]/dt = -k[A][B] (rate of decrease of A)

d[B]/dt = -k[A][B] (rate of decrease of B)

d[C]/dt = k[A][B] (rate of increase of C)

where [A], [B], and [C] are concentrations, and k is the reaction rate constant.

It will help to describe how the concentrations of reactants and products change over time in a dynamic system.

So, differential equations are crucial in biology because they provide a mathematical framework to model and understand dynamic processes in biological systems, allowing for the prediction of future states and the analysis of how systems respond to changes.

Best,

According to www.cambridge.org and biologystackexchange.com, differential equations are essential in biology because they provide a rigorous mathematical framework to describe how biological systems change over time. At their core, differential equations relate a quantity to its rate of change, enabling researchers to model dynamic processes—whether that’s the spread of a disease, the growth of a population, or the kinetics of a chemical reaction.

Below are several key applications:

The beauty of using differential equations in biology is their ability to reduce complex, interdependent processes into more tractable models. With advancements in numerical methods and computing power, these equations can often be solved (or approximated) to simulate a wide variety of biological phenomena—from the micro-scale of cellular reactions to the macro-scale of ecosystem interactions.

Differential equations can be used in biology to model dynamic processes—situations where quantities change over time or space. These equations help describe the rate of change of biological variables and predict future behavior of biological systems.

These equation are used in biology to mathematically describe changes in systems over time or space, helping researchers analyze and predict complex biological behavior.