For questions regarding mathematical concepts with applications to Biology.

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1answer
13 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
43 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
33 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
13 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
36 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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8 views

Biostatistics book

Do you know a book in biostatistics that fits very well to these topics: Analysis of counts: estimating probabilities, re-expression probabilities as ratios, odds, logits, probits, etc., comparing ...
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0answers
16 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
32 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
25 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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71 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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46 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
75 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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49 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
90 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 ...
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1answer
66 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
19 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
65 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
19 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
448 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
37 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
44 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
70 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
35 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
38 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
137 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
34 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
114 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}) - ...
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1answer
35 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 ...
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1answer
17 views

Time-Scale Decomposition: The slow variable only has a single unstable steady state?

I'm completing a time-scale decomposition of a set of equations. The original set of two equations is $$ S'= 3k_1S^3E_T + (3k_{-1}-3k_1S^3)E_1 $$ $$ E_1'=-k_1S^3E_T+(k_{-1}+k_2+k_1S^3)E_1 $$ I was ...
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1answer
23 views

How to interpret this summation equation

I'm a computational biologist trying to interpret this equation correctly. $$CI(x)= 1- \frac{2}{(N(N-1))} \sum_i^N\sum_j^N [ S(x_i,x_j) / \sqrt{S(x_i,x_i)S(x_j,x_j)}\ ] $$ i=1 ; j=i+1 I'm confused ...
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1answer
27 views

Indirect Way of Standarizing Sample means: Is this possible?

I'm an undergrad working on a biochemistry experiment where I take a bunch of fish fin samples (each of which is composed of n individual cut fins) and run the samples through a mass spec. It is ...
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1answer
42 views

Equilibrium analysis of a Holling Type II differential Equation

I'm working on a problem which I am to determine what value of parameter $a$ will make a population become extinct. However, I am struggling in getting to the equilibrium points, which is necessary. ...
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1answer
62 views

Understanding a derivative in a biology article

From this biology article (5th page, right column) They have... $$1-P_t ≈ 1-(1+s)P_{t+1}+\frac{p_{t+1}^2}{2}$$ and they conclude that... $$\frac{dP}{dt} ≈ -sP + \frac{P^2}{2}$$ I don't really ...
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30 views

What fundamental assumption is taken here?

In biology, the following is often used for collecting data from a population: if we have data from $n$ people, over $m$ years, then we have $nm$ years of data for one person (to simplify). To give a ...
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1answer
99 views

Fitting Vogel's formula for phyllotaxis to an actual plant.

A simple model for the arrangement of florets in a sunflower was given by Vogel: $r = c\sqrt{n}$ $\theta = 137.508 n$ Where $r$ and $\theta$ are polar coordinates, $c$ is some constant and $n$ is ...
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0answers
44 views

Formula for residence time/turnover rate with unsteady state

I'm not sure this is the correct place to ask my question... but maybe someone could still help me. I'm looking for a way to calculate the residence time/turnover rate. I have the production and ...
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2answers
354 views

Biology: Wright-Fisher model of genetic drift

In evolutionary biology (in population genetics to be more accurate) exists the concept of genetic drift. It describes how an allele (gene variant) (that has no advantage or disadvantage in terms of ...
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2answers
308 views

Any application of vector spaces in Biology or Biotechnology?

I would like to know any application of vector spaces in Biology or Bitechnology, if you got an example i would be very glad to know it. But basically just what tool or what operations of vector ...
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1answer
29 views

Expectation and variance of occurrences of patterns in a random text

I'm not sure how to complete the following problem from the book An Introduction to Bioinformatics Algorithms: Problem 9.1 Derive the expectation and the variance of the number of occurrences ...
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1answer
89 views

Square brackets in derivatives

I have two equations that (attempt to) describe biological systems. (1) vgen = d[s]/dt (2) vdec = -d[s]/dt When (1) = (2) then we have homeostasis When (1) > (2) then we have growth When (1) ...
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4answers
54 views

Can a sampling based method estimate how many species exist?

I've got in to a bit of a debate online and I'm hoping some people here can help clear it up. The position I'm arguing against is "It's impossible even come up with a ballpark estimate for how many ...
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0answers
87 views

Case study in population biology. Sequences and series, find general solution.

Think about a population of individuals which all have two set of chromosomes (as human do). There is one gene that codes for a helping behaviour. This gene has two alleles (an allele is a variant of ...
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0answers
74 views

Are Navier-Stokes equations used in molecular biology research?

I am wondering whether Navier-Stokes equations have been used in some molecular biology research papers in the past. A quick Google search revealed that such papers exist but I want to know if there ...
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1answer
91 views

How to learn biomathematics?

I'm currently an undergraduate math student and researching on the internet I discover that exists an area called "biomathematics". Looks so interesting. They use the graph theory and topology to ...
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4answers
521 views

PDEs in biology

I am student who mostly heard lectures on partial differential equations and homogenization. But I really like the idea of working in biology or with biologists - but (with my lack of overview) it ...
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1answer
220 views

steady states and stability mathematical biology

could anyone help on how to do this please? find the steady states of $$F(N)=\frac{rN}{1+N}.$$ do you differentiate and set it equal to zero and find $N$? many thanks in advance.
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Caclulating limits of Hassell Model to show under/over compensation

For this question, you will need the following definition: For a discrete time model of intraspecific competition $N_{t+1} = F(N_t)$, if the limit $F_{\infty} = \lim_{N \to \infty} F(N)$ exists, ...
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82 views

van der pol and liapunov

i have attempted this question and done as much as i possibly could, any help regarding this question would be very helpful and appreciated. a) show that the second-order differential equation for ...
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2answers
507 views

steady states and stability

im just checking to see if im doing this right? $$\frac{du}{d\tau}=u(1-u)-h $$ show this equations has 2 steady states and check their linear stability. this is what i have done: $u=0$ and ...
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1answer
120 views

Find the value of a function with definite integrals

I am trying to understand a paper of Maynard Smith (1974), that connects biology with game theory. I don't want to overwhelm you with useless stuff, but I have this definite integrals: ...