# Questions tagged [mathematical-biology]

Mathematical biology is an interdisciplinary science that uses mathematical methods to study problems arising from biology, the science studying living organisms and ecosystems.

Mathematical biology is an interdisciplinary science that uses mathematical methods to study problems arising from biology, the science studying living organisms and ecosystems.

33
questions

3
votes

1
answer

111
views

Can I express the expected value of
\begin{equation}
\langle \tau\rangle_\text{total}=\int_0^\infty \tau \psi_\text{inf}(\tau)\Psi_\text{rec}(\tau)\mathrm{d}\tau
\end{equation}
in terms of the moment(...

1
vote

1
answer

52
views

I am currently working on my undergraduate thesis, and my adviser suggested that I look into a Polyhedral Active Set Algorithm (PASA) for my paper. I have been trying to find resources/materials on it ...

2
votes

0
answers

54
views

I am studying some stochastic process (a voter model for example) on a finite size lattice of 1 dimension and of size $N_t$. However $N_t$ grows at rate $\lambda$ and can be represented as follows:
\...

19
votes

4
answers

2k
views

In calculus we learn about many applications of real exponentials like $e^x$ for bacteria growth, radioactive decay, compound interest, etc. These are very simple and direct applications. My question ...

6
votes

1
answer

195
views

A very simple stochastic growth model on a lattice is the Richardson's model (Actually originally defined by Murray Eden in the 60s).
Each point of the lattice can be either occupied or vacant, once ...

3
votes

0
answers

87
views

In models of disease transmission, after an individual is getting infected, he can generate a number of secondary infections. The number of secondary infections depends on the infectiousness of the ...

8
votes

3
answers

600
views

Context Working with some biological datasets it was puzzling to see the patterns like Figure 2 (right) below. The first feeling was, that it corresponds to some biological effects like correlations ...

3
votes

1
answer

109
views

This problem is motivated by the problem of reconstructing a genome from the family of its short subwords.
Given a word $w$ and a positive integer $k$, let $M_k(w)$ be the family of all subwords of ...

0
votes

0
answers

164
views

I need to prove that set $D$(A picture for Set $D$) given by
$$D=\{(x,y):0\leq x\leq L_0,~0\leq y\leq X_0,~0\leq x+y \leq R_0\}\subseteq \mathbb{R}_+^2$$ of the system:
$$\dot{x}=k_1(R_0-x-y)(L_0-x)-...

6
votes

1
answer

218
views

I've learned some classical results on the peak and the attack rate of an idealized epidemic which evolves according to a SIR model
$\dot{s} = -\beta\cdot i \cdot s$
$\dot{i} = +\beta\cdot i \cdot s -...

3
votes

1
answer

1k
views

I have a biological system that exhibits a feedback type of behavior. The diagram is a schematic of the system of ODEs. In this system, the total amount of $x_1, x_2, x_3$ is conserved; however, there ...

64
votes

3
answers

5k
views

The Navier-Stokes equations are as follows,
$$\dot{u}+(u\cdot \nabla ) u +\nu \nabla^2 u =\nabla p$$
where $u$ is the velocity field, $\nu$ is the viscosity, and $p$ is the pressure.
Some elementary ...

4
votes

2
answers

226
views

Numerical solutions of the SEIR equations (describing the spreading of an epidemic disease) – or variations thereof –
$\dot{S} = - N$
$\dot{E} = + N - E/\lambda$
$\dot{I} = + E/\lambda - I/\delta$
...

0
votes

0
answers

79
views

Disclaimer: this is an open-ended, imprecise question, asking for speculation in a topic that I know relatively little about (random matrix theory and principal component analysis). I originally asked ...

12
votes

6
answers

1k
views

What are suggestions for reducing the transmission rate of the current epidemics?
In summary, my best one so far is (once we are down to the stay home rule) to discretize time, i.e., to introduce the ...

13
votes

6
answers

3k
views

Remark: All the answers so far have been very insightful and on point but after receiving public and private feedback from other mathematicians on the MathOverflow I decided to clarify a few notions ...

0
votes

1
answer

147
views

From a delay system, I obtain the following as part of a characteristic equation:
$$f(\lambda) = \lambda - a + be^{-c\lambda},$$
where $a, b,$ and $c$ are positive number and $a<b, ac<1$. My ...

5
votes

0
answers

458
views

The set-theoretic version of the Salmon Conjecture (that is, finding the equations that cut out the fourth secant variety of the Segre embedding of $\mathbb P^3 \times \mathbb P^3 \times \mathbb P^3$ ...

4
votes

1
answer

608
views

Motivation:
During a discussion with neuroscientists the question arose as to whether the human brain may emulate any Turing machine. If we assume that animal brains may be modelled as deterministic ...

6
votes

1
answer

373
views

Within the context of mathematical biology, a sphere packing problem occurred to me. I must note that unlike the typical sphere packing problems, the variant I consider involves minimising the average ...

30
votes

7
answers

5k
views

What are some examples of successful mathematical attempts in clinical setting, specifically at the patient-disease-drug level?
To clarify, by patient-disease-drug level, I mean the mathematical work ...

17
votes

4
answers

1k
views

This was originally a question posted here on MathSE. But I'll ask again here to see if I can get some different answers.
I'm looking for current areas of research which apply techniques from ...

3
votes

0
answers

73
views

I have the following simple dynamical system:
\begin{align}
x_1' &= a - f(x_2)x_1\\
x_2' &= bx_1 - cx_2,
\end{align}
where all parameters and initial conditions are positive. $f(x_2)$ is a ...

7
votes

1
answer

373
views

I am studying a biological system (HIV) and arrived at this simplified dynamical system:
\begin{align}
x_1' &= a_1 + a_2x_2 - a_1x_2 - a_4x_1 - a_5\frac{1+a_6x_3}{1+a_7x_3}x_1\\
x_2' &= a_5\...

9
votes

1
answer

938
views

In an interview (I link the Google translation), Voevodsky talks about how, in the late 2000s, he worked on the problem of "restoring the history of populations according to their modern genetic ...

2
votes

1
answer

51
views

I would like to know what is the purpose of using the term $P\over (k+P)$ in the following. I found it when reading the article found here but it was commonly used in few other related articles .
Is ...

1
vote

0
answers

293
views

My question is pure mathematics when restricted to the cellular automata theory.
John von Neumann got the grasp of and defined life. Many years later biologists supported von Neumann's definition of ...

27
votes

4
answers

3k
views

Let me start by acknowledging the existence of this thread: Mathematics and cancer research
It is well-known that mathematical modeling and computational biology are effective tools in cancer research....

10
votes

2
answers

5k
views

Are there applications of algebraic geometry/commutative algebra to biology/pharmacology?
It might be that some Gröbner basis technique is used somewhere? I know there are some applications to ...

10
votes

3
answers

2k
views

What are the applications of knot theory to biology/pharmacology?
I guess there should be some, since proteins are quite long and some of their properties are probably related to whether they are ...

26
votes

7
answers

7k
views

Are there applications of group theory — broadly, say, representation theory, Lie algebras, $q$-groups, etc — to mathematical biology?
In particular, I am interested in applications to pharmacology — ...

27
votes

16
answers

7k
views

What are applications of mathematics in cancer research?
Unfortunately, I heard quite little about applications of mathematics, but I heard something about applications of physics, and let me put this ...

36
votes

16
answers

9k
views

I've heard that there's a relatively new field of science called mathematical biology.
It will certainly apply well known and less known mathematical techniques to the understanding of some biological ...