# Questions tagged [mathematical-biology]

For questions that lie between the intersection of significant mathematical problems and fundamental questions in biology.

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### How to "linearize" a term of the form $\frac{\partial}{\partial x} \left( m \frac{\partial c}{\partial x} \right)$ in a nonlinear PDE?

I am currently studying the following nonlinear PDE model for cells migrating under the influence of diffusion and chemotaxis: \begin{align} \hspace{2cm} \frac{\partial m}{\partial t} & = \...
• 908
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### Calculating pitch and roll from XYZ accelerometer data collected from a wildlife collar

I work with wildlife collars (lions, elephants) which also collect XYZ accelerometer data. From this, I can visualize pitch and roll of the animals in the collar manufacturers web application, but ...
25 views

### Genomic and sum of geometric random variables

In their paper The Maximum of independent Geometric Random Variables as the Time for Genomic Evolutionthe authors noted that if to consider the genomic word of L letters, than the measure of the time ...
• 438
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### Problem in performing sensitivity analysis in prey-predator model

I tried to create a general prey predator model to simulate sensitivity analysis using PRCC and Latin hypercube sampling. But I can a bar plots which are empty. What is wrong in my approach? The code: ...
• 183
18 views

### Texts on coalescent theory/probability methods for DNA evolution

I am starting a PhD on mitochondrial evolution modelling with a focus on probabilistic methods and coalescent theory. For this purpose, I am looking for advanced textbooks on probability methods for ...
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1 vote
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### Nondimensionalization of given equation

I have the following equation, which is a logistic system with a death term, $$\frac{dN}{dt}=rN(1-N/k)-p(N),$$ where $p(N)=\frac{BN^2}{A^2+N^2},$ for unknown constans $A,B$. I want to ...
96 views

### A combinatorial model for multi-sexual reproduction

I was thinking about the following question: why do most creatures on earth reproduce asexually or bisexually, but not trisexually? Looking on the internet, I read an interesting perspective https://...
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### How to slightly modify my ODE system in order to capture bump in the data?

I have the following two sets of data, which show the dependencies of two quantities, namely, $S$ and $B$, on time ($0$ h, $3$ h, $6$ h, $9$ h, $15$ h, $18$ h, $21$ h, and $24$ h): ...
17 views

### How to measure local density of A's in a sequence of A's and B's?

Let me preface this by stating that I am not a mathmagician. I have a DNA sequencing problem, but it boils down to a math problem. But I don't have the math skills to adequately describe the issue, ...
122 views

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### Analytical solution of quadratic recurrence equation with limited capacity

Consider the famous equation associated to the logistic map: $$x_{n+1}=r x_n\left(1-x_n\right),\quad r>1$$ It is well known that there is no closed formula for $x_n$ as a function of $n$. However, ...
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### Book recommendation about Modeling on Mathematical Biology

I would like to ask if you have a good book to suggest about Mathematical Models for the Dynamics of DNA and Proteins.
67 views

### How to approximate $1-\frac{1}{2\lambda}(\lambda+\mu+\beta-\sqrt{(\lambda+\mu+\beta)^2-4\lambda\mu})$?

Problem: I'm trying to verify a claim in this paper where the expression $$P^\infty_1=1-\frac{1}{2\lambda}(\lambda+\mu+\beta-\sqrt{(\lambda+\mu+\beta)^2-4\lambda\mu})$$ is approximated under three ...
61 views

### How do I interpret a low Jaccard similarity and a statistically significant Chi-Squared Value?

There are two genes I am interested in. They both have many samples in which they have no expression. So I decided to see if there is a relationship between when they are expressed. I was looking for ...
1 vote
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### Manual calculation of the interaction p-value using effect estimates and 95% CIs of two (or more) subgroups.

I was wondering if there was a way to calculate the interaction p-value by hand using estimates from a published article that does not report the interaction p-value. For instance, if the hazard ratio ...
126 views

### Recovery Time for Logistic model equation with harvesting

We are given a logistic growth model with constant harvesting as: $\frac{dN}{dt} = rN(1-\frac{N}{K})-Y_0$ We are asked to show that the recovery time for harvesting a yield $Y_0$, $T_R(Y_0)$, ...
18 views

### Understanding the Role of Matrices in Capturing Disease Dynamics on Networks

I am currently reading an article related to Network epidemic, Markov chain and the relationship with automorphism graph, I'am confusing onp age 483: Here the link to the article What are the ...
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1 vote
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### persistence of SEIR epidemic model

We have the following stochastic SEIR model $dS=\Lambda - \beta SI - \mu S - \sigma SI dB(t)$ $dE=\beta SI - (\lambda +\mu) E+\sigma SI dB(t)$ $dI=\lambda E-(\gamma +\alpha +\mu) I$ $dR=\gamma I-\mu R$...
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• 385
1 vote