For questions regarding mathematical concepts with applications to Biology.

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11 views

Turing criteria for Sel'kvo glycolysis model

I have the Sel'kov reaction diffusion model for glycolysis as follows: \begin{eqnarray} u_t=D_uu_{xx}-u+av+u^2v\\ v_t=D_vv_{xx}+b-av-u^2v \end{eqnarray} How can I obtain the values for $D_u$ and ...
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1answer
34 views

What does three bars and “def” mean in a partial derivate problem?

I'm reading the book "Mathematical Models in Biology" by Leah Edelstein-Keshet and in page 70 the following explanation appears. Here, F(x,y) is a function with P = F(X0 + Y0) and the idea is to ...
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24 views

Quasistationary distribution for the Moran model.

The Moran model is a model for genetic drift. Basically, it is a finite Markov chain (more precise: a birth-death chain) with state space $S:=\{0,...,N\}$ and the following transition probabilites: ...
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1answer
53 views

Calculating biological growth of doubling cells

For some kinds of experiments, biologists use isolated cells grown in culture. Cells differ significantly in their cell doubling times (one cell dividing into two cells). Plant cells ...
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0answers
55 views

Probability for a random k-mer to repeat at least $n$ times in a random $S$ characters long string

What is the probability for a random $k$ characters long string to be repeated $n$ times or more in a random $S$ characters long string, both made of a 4-symbols uniformely distributed alphabet? So ...
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1answer
51 views

How to reduce the chemical reaction system $A+B \rightleftharpoons^{k_+}_{k_-} C$ with transfer using the quasi steady state assumption

Suppose we have the reaction $$A+B \rightleftharpoons^{k_+}_{k_-} C$$ within some reaction $\Omega\subset\mathbb{R}^3$, we assume this region to be well mixed and we denote the concentration of $A$ as ...
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2answers
51 views

Theoretical justification of exponential growth differential equation

Consider a number of $x_0$ reproducing individuals and ignore death and limiting environmental factors. I've heard that the growth of such a population (of bacteria, insects, humans, etc...) can be ...
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1answer
42 views

Mathematical Epidemiology Reference Request

I'm looking for a good Textbook for learning Mathematical Epidemiology. Something that I could read through and use as a future reference book. Thanks for the advice!
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4answers
104 views

Relationship between Mathematics and Genetics [closed]

I was wondering how can we mathematically define the biological nature around us. How can we mathematically define a real plant or a tree, growing from being a 1 cell to a full grown plant with ...
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2answers
32 views

Population dynamics modelled by a wave function (Mathematical Biology)

The size of an insect population $N(x,t)$ is governed by the partial differential equation: $\frac {\partial N}{\partial t}=p(N) + \frac {\partial^2 N}{\partial x^2}$ for some function $p(N)$ . For ...
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1answer
35 views

Does this nonlinear differential equation have a closed form solution?

I have a differential equation inspired by a population dynamics problem and I'm don't know how to solve it. I wonder if anyone here can tell me if a closed form solution exists and how to find it. ...
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1answer
69 views

An algorithmic method to simplify the mathematical modeling of a reaction network using conservation laws

Consider the reaction scheme. where $S$ is the substrate, $E$ is the enzyme, $P$ is the product, $C_1$ and $C_2$ are enzyme substrate complexes. Let $[S] = s$, $[E] = e$, $[C_1] = c_1$, $[C_2] = ...
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1answer
70 views

An easy reference for genetic algorithm

My field is Coding Theory and my background is Algebraic, there are many applications of Genetic Algorithm in Coding Theory, I would to know the easiest and the most elementary and introductory note ...
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1answer
102 views

Applications of Biology in Mathematics

I know that mathematics has applications in Biology, and in fact in everywhere, I am curious to know is it happened that a Biological concept comes to help math? I don't mean Biological names be ...
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44 views

How can I solve this ordinary differential equation? What are the Initial/Boundary Conditions used?

I am having trouble following the solution to this problem, I can understand how to obtain the general solution but cannot figure out the conditions used to obtain the particular solution with the ...
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1answer
65 views

Genetic probability problem(autosomal dominant,x-linked recessive)

Hemophilia is an X-linked recessive trait in humans. Huntington’s Disease is inherited with an autosomal dominant allele. a. Mr. Y is unaffected by either condition. He marries Ms. X, who is ...
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0answers
47 views

In the Glycolysys Sel'kov model, what are the meaning of “a” and “b” values?

In the Sel'kov model of glycolysis which I put on next $u'=-u+av+u^2v\\ v'=b-av-u^2v$ which have a limit cycle and have all sense because it is a glycolytic cycle. What are the ...
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0answers
27 views

How to determine the probability of seeing a time based event?

I am trying to figure out what the probability of capturing a time based event is. This is the situation. I'm observing a video of clusters of proteins in a cell with proteins tagged green and red ...
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2answers
34 views

Approximation of a negative exponential model?

I am trying to get an approximation of this model, it is a negative exponential model introduced by Olson in 1963 "Energy storage and the balance of producers and decomposers in ecological systems". ...
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0answers
25 views

How to make sense of this contour graph?

Recently, I have been studying the paper "Estimating the basic reproductive ratio for the Ebola outbreak in Liberia and Sierra Leone", published in Infectious Diseases of Poverty. I came across the ...
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0answers
48 views

How to model compartment chemical concentration with permeation through a membrane

Suppose we have one chemical species $V$ and two compartments in which $V$ can be, $A$ and $B$, with volumes $\Omega_A$ and $\Omega_B$ respectively, where $\Omega_A < \Omega_B$. Compartments $A$ ...
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1answer
35 views

How to write a covariance

Could somebody kindly explain how you can express something as a covariance? A paper I am reading contains this term: $$\sum_in_i(p_i-p)(b_a+\sum_t\sum_jr^t\frac {n_j} {n_i}b_c)$$ The author then ...
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1answer
40 views

Probability distribution of the number of heterozygous sites

We'll consider a stretch of DNA on a chromosome and we'll be looking at specific sites that are at certain distances on from the others. The distance between any two sites is express in centiMorgan ...
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51 views

testing significant difference on species richness

I measured the species richness (number species) in three different sites. Now, I want to test whether there is significant difference between each site in terms of species richness. The species ...
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38 views

A good book about quantitative analysis of movement in theoretical ecology?

Does anyone know a good book to start studying animal patterns of movement? I am interested in exploring different approaches, in particular models in stochastic settings. I have been checking ...
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0answers
37 views

Coalescent theory - Why are coalescent times independent?

I am reading from this book and I want to make sure I understand what is going on. What I get from the book Consider a population of $N$ individuals. The population size ($N$) is constant. select ...
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1answer
45 views

Equilibrium and Stability of Nonlinear Interactions

Examine the nonlinear model: $$\triangle x_t = rx_t(1-\frac{x_t}{K})-sx_ty_t$$ $$\triangle y_t = -dy_t+\epsilon x_ty_t$$ Find the equilibrium and their stability. Here all the parameters are ...
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0answers
81 views

How to define boundary conditions for a sphere to run reaction-diffusion equations on its surface?

I'm in a Biology lab, and we managed to simulate reaction-diffusion equations on a torus using periodic boundary conditions for a 2D matrix. We want to try doing the same on a sphere, but I'm a ...
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1answer
139 views

Conditions for Deriving $R_0$ for SIR Model Using Survival Function Method

I'm taking a look at the SIR model given by the system of differential equations \begin{align} \frac{dS}{dt} & = - \beta S I \\ \frac{dI}{dt} & = \beta S I - \gamma I \\ \frac{dR}{dt}& ...
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2answers
204 views

Finding Eigenvalues and Eigenvectors for Leslie Matrix

A Leslie Matrix is given by $$L =\begin{pmatrix}0 & (3/2)a^2 & (3/2)a^3\\1/2 & 0 & 0\\ 0 & 1/3 & 0\end{pmatrix}\cdot$$ Find the Eigenvalues and determine the dominant ...
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1answer
55 views

How to test if data follows a distribution?

Have been given some data and the question says to determine if the data follows any distribution. It says to compare the observed data vs expected graphically and to test further. The distributions ...
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1answer
46 views

Number of combinations in a string with n states

I have a problem in biology involving amino acids (think of them as a string of characters) that I want to formalise. Let assume we have a amino acid sequence of length 4, typical examples may be: ...
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47 views

Biological modelling math question?

I am trying to write a biological model that models protein interaction. I am having an issue with one aspect. Lets say protein A and protein B interact with eachother to form complex AB. Now every A ...
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1answer
57 views

How do find the general solution to this system of differential equations?

$$ \begin{align} \frac{dI_n}{dt} &= 2(1-p) I_n - I_n + 2(1-p) I_v \\ \frac{dI_v}{dt} &= 2p I_v - 3 I_v + 2p I_n \end{align} $$ I tried to find the eigenvalues and the eigenvectors for this ...
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38 views

Discrete Population Model Crashing

Consider the discrete population model $$U_{t+1} = au_t^2/(b^2+u_t^2)$$ Where $a >0$ If $a^2 > 4b^2$ show that the population may be driven to extinction if it becomes less than a critical ...
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0answers
77 views

PDE reaction diffusion equilibrium solutions reaction diffusion cauchy (R-D-C)

where H1 is: f is lipschitz continuous on any closed bounded interval and H2 is: f(0)=0 I am unsure on how to start this question to show that f satisfies H1, and how to show that R-D-C cauchy has ...
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2answers
68 views

What is math branch that studies general populations.

A population is a summation of all the organisms of the same group or species, which live in a particular geographical area, and have the capability of interbreeding so i would like to understand the ...
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0answers
25 views

Question about the cell cycle

A diploid cell in G1 has 6 chromosomes. How many chromosomes and how many chromatids are present in each of the following stages? Here is what I am guessing G1: 6 chromosomes ; 6 chromatids G2: 6 ...
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1answer
56 views

Keeping an exponentially decaying system steady.

To give a bit of background: I am trying to figure out what amount of substance X to continuously add over a time interval in order to keep it constant in a system where substance X has the half-life ...
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0answers
45 views

How do I interpret this density function

I'm currently freshing up on math for my computational biology seminar. Now I have a question concerning the following density function that is used to calculate the signaling time in a signaling ...
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1answer
106 views

Opportunities for Mathematicians to Work in Biological/Disease Areas

Yesterday, I was reading some of the question Can I Use My Powers for Good? and it got me thinking. It's quite an old question (3 years), so I don't want to resurrect it and also my own question's ...
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1answer
82 views

Differential Equation with biology!

I am working on a growth model for bacteria as a function of a nutrient, and I am stuck. So the differential equation I am supposed to be solving is $\frac{dN}{\ DT} = k(C_0 -\alpha N(T)) N$ The ...
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1answer
48 views

Calculate migration probability matrix from distances matrix

Imagine the world-wide human populations as a series of interconnecting populations. The distances between any two populations is given by the following kind of matrix $$ \begin{matrix} ...
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1answer
44 views

Fish Eggs, Calculus, and Optimization

The survival of a fish egg through its critical period is a function of its mass, $x$. The larger the egg, the more nutrients are present and the more likely it is to hatch successfully. This ...
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5answers
2k views

Can mathematics get from other sciences what it got from physics?

Throughout history, physics has been an unparalleled source of '' inspiration'' for discovering/inventing mathematical ideas, which is due to its ability to describe the physical world. But can this ...
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1answer
86 views

Neural networks and mathematical modelling

Could you point out some reference books [accessible to an undergrad math student] that deal with the mathematical modelling aspect of neural networks?
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1answer
137 views

How can I model the number of insects in a house?

I really don't know if this question applies here or if it makes sense, but I'm curious as to whether these ideas are commonly used. Imagine you are in a room, this room has holes, where bugs may ...
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1answer
41 views

Sigmoidal function

Can someone explain what a sigmoidal function is? I have "$S(x)$ is a sigmoidal function with $S'(x)\ge0$ and $\lim_{x\rightarrow-\infty}S(x)=0$ but I really don't understand what $S(x)$ is I found ...
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1answer
14 views

serial dilution

If $0.01$ is $10$ to the negative 2nd power then what is $0.2$? I am having trouble making all the test tubes a number that can be added together. Test tube A is $.01 = 10$ to the negative 2nd ...
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1answer
76 views

How to find the basic reproductive number of a discrete SIS epidemic model

I have been following a textbook called Mathematical Models in Population Biology and Epidemiology. The SIS model is given by the system \begin{aligned} S_{n+1} &= \Lambda + S_n e^{-\mu} ...