For questions regarding mathematical concepts with applications to Biology.

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1answer
35 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
31 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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0answers
19 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
35 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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0answers
25 views

Stable Stage distribution with asymptotic behavior

Given a population model given by $$X_{t+1}=\begin{pmatrix}1& 2\\3 & 0\\\end{pmatrix}, X(0) = \begin{pmatrix} 4 \\ 1 \\\end{pmatrix}$$ find the asymptotic behavior and find the stable stage ...
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0answers
32 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
37 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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0answers
22 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
66 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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1answer
55 views

Consider a species of animal which only breeds during the spring. Suppose that all adults die before the next…

Consider a species of animal which only breeds during the spring. Suppose that all adults die before the next breeding season. However, assume that every female produces (on average) $R$ female ...
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2answers
41 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
18 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
51 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
40 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
69 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
61 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
31 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
34 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
48 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
106 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
32 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
12 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
44 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} ...
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1answer
64 views

Hopf bifurcation and limit cycles

$$dV/dt=10(V-\frac{V^3}{3}-R+I_{input})$$ $$dR/dt=0.8(-R+1.25V+1.5)$$ Use $I_{input}$ as the relative parameter to prove that there these equations undergo 2 hopf bifurcations and indicate whether ...
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1answer
65 views

How to connect the deterministic and probabilistic descriptions of the SIR model

I am a 17 year old student and I was reading up on epidemic modelling for a math project, specifically the SIR model and I came across this: "This" refers to the assumptions to which the Markov Chain ...
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1answer
49 views

sum of exponential series in population growth model

I am a biology student who has recently started studying population dynamics. I've recently found a model of population growth where the number of organisms at an age class (N) is calculated by: ...
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1answer
65 views

The variance of Lincoln-Peterson estimator

Capture-recapture is a method commonly used in ecology to estimate an animal population's size. Let $N$ = Number of animals in the population; $K$ = Number of animals marked on the first visit; $n$ ...
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1answer
40 views

Is there an introductory book on Genetic Sequencing Theory for mathematicians?

I am interested in Genetic Sequencing Theory (see the wikipedia link over here), and I was wondering whether there is some introduction to this field for someone with a mathematics background and ...
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1answer
56 views

physical meaning of heat equation

consider the heat equation $u_t=a(t)u_{xx}+f(x,t)$, $0<x<L$, $0<t<T$ subject to the initial condition $u(x,0)=g(x)$ and boundary conditions $u(1,t)=0,$ $u_x(0,t)+hu(0,t)=0$ where ...
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2answers
29 views

Patlak equation

For solute flux across microvessel wall, these two equations are supposed to be equivalent: $$ \begin{align} J_s &= J_v(1-\sigma_f)\frac{C_i - C_Le^{\mathrm{Pe}}}{1 - e^{\mathrm{Pe}}} \\ J_s ...
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0answers
172 views

Topology of biological compartments

In the field of cell biology, there is a general sub-field concerned with the topology of organelle membranes, and a key focus remains on how these dynamic membranes deform and interact with cellular ...
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0answers
81 views

Implementing formula correctly in matlab for neuroscience: total soma membrane potential?

Please help me to understand: am I correctly implementing a total soma membrane potential (TSMP) equation in Matlab? Due to being a new member I need to use this list link to refer to the links ...
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1answer
121 views

Start studying mathematical biology from basics

I am really passionate about theoretical and quantitative biology and I would like to build my future career around this topic. I've just got my bachelor's degree in biology (ecology) but scince ...
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0answers
63 views

For starting the studies in Mathematical-Biology

I will take an undergraduate course in Mathematical Biologylearn themes like: population dynamics; the emergence of patterns of Philotaxia; Turing´s bifurcation; Genetics; Chaos; Neural networks; ...
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2answers
147 views

Biology: How to find the probability of randomly generating multiple, sequentially identical sets

If I randomly generate a substring (example "ATGCAGC") with equal probability (1/X where X=4) for each digit with length (L) digits: What is the formula for finding the probability (P) of randomly ...
2
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1answer
97 views

What paradigm of automated theorem proving is appropriate for Principia Mathematica-style formalization?

I am in possession of a book, which, inspired by Russell's Principia Mathematica (PM) and logical positivism, attempts to formalize a specific domain by determining axioms and deducing theorems from ...
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1answer
23 views

Reaction-Diffusion question

Can somebody help me with this question,I don't have a clue really. Q: I The spread of an impulse from one end of a one-dimensional nerve fibre is modelled by the partial differential equation ...
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1answer
79 views

Biology Discrete Population model

I'm stuck on a particular part of a long question, so I will post the entire question and tell you guys where I'm stuck. Q: The size of a locust population in each year is given in terms of the ...
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0answers
25 views

Which cut-off for collapsing this tree?

I have a Newick tree that is built by comparing similarity (euclidean distance) of Position Weight Matrices (PWMs or PSSMs) of DNA regulatory motifs that are ~5-9 bp long sequences. An interactive ...
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1answer
1k views

Gompertz growth model problem

The growth of tumor cells is characterized with Gompertz model. $N'=-aNln(bN),$ where N(t) is proportional to the number of cells in the tumor, while a and b denote positive parameters. ...
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0answers
45 views

Which in graph theory book do you recommend for a Biologist?

I need a book in Graph Theory for my Thesis project in Biology (6 months from now). I have reasonable mathematical knowledge. The book must be strict but not as complicated as an advanced book. The ...
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0answers
58 views

Relationship between Reproductive Ratio and Jacobian in Population Model

In class we defined the Reproductive Ratio, $R_0$ of a population modelled by SIR, SEIR,... as the average number of secondary infections caused by an average infected individual in an average ...
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2answers
73 views

mathematical biology1

Consider the infectious disease model defined by \begin{equation} \frac{dS_3}{dt}= -\rho I_3S_3+\gamma I_3+\mu-\mu S_3\tag 1 \end{equation} \begin{equation} \frac{dI_3}{dt}=\rho I_3S_3-\gamma ...
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1answer
37 views

Why is chemotaxis considered an emergent behavior?

this is an applied math question. I could have posted this under a biological stackexchange, but the idea of emergent behavior or emergent properties of a system seems more appropriate to an applied ...
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0answers
39 views

Quantitatively comparing event trains of different lengths for Poissonness

I have a parameterized, effectively black box process that generates a series of events (simulated action potentials). Different parameter values often lead to different numbers of events. How can I ...
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2answers
139 views

Computing $\langle\sin(\gamma_i)\rangle= \int_{(S^2)^N} \sin(\gamma_i)p(\Theta)dS$

I'm trying to evaluate the following integral, which I know must be zero, $$\langle\sin(\gamma_i)\rangle= \int_{(S^2)^N} \sin(\gamma_i)p(\Gamma)dS$$ Where, $$\langle ...
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0answers
42 views

Normalizing multiple different features from unknown distributions

I'm doing some "exploratory" data analysis over a large set of classes/proteins, with a few hundred different features (I.E. Continuous variables) extracted from the data. The features are calculated ...
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1answer
138 views

Mathematical Biology and modelling

Consider the two species competition model given by $$ \frac{da}{dt }= \frac {λ_1 a} {a+K_1} - r_{ab}\cdot ab - da, \ \ \ \ \ \ \ \ \ \ (1)$$ $$\frac{db}{dt }= λ_2 b (1-\frac{b}{K_2}) - ...
2
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1answer
46 views

Trouble finding equilibrium points

I'm working on a nonlinear predator prey model and am struggling finding my equilibrium points. I've done this three times and gotten three different answers. I'd appreciate if someone could check ...