Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [mathematical-biology]

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

An excerpt by Frank Hoppensteadt in Scholarpedia: Mathematical biology is a highly interdisciplinary area that defies classification into the usual categories of mathematical research, although it has involved all areas of mathematics (real and complex analysis, integral and differential systems, metamathematics, algebra, geometry, number theory, topology, probability and statistics, as well as computer sciences). The area lies at the intersection of significant mathematical problems and fundamental questions in biology. The value of mathematics in biology comes partly from applications of statistics and calculus to quantifying life science phenomena, but more importantly from the sophisticated point of view it can bring to complicated real life systems by organizing information and identifying and studying emergent structures. Mathematical scientists, and many more from physics, chemistry, engineering, and medicine have developed and used mathematical methods in biology investigations. It is difficult to grasp the broad influence mathematics has had in biology.

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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://www.zhihu.com/question/303528094 that attempts to…
abacaba
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Traveling-wave solution for McKendrick age-structure model with finite lifespan

The model was described many times before, so I keep the details concise. We have $$ \frac{\partial}{\partial t} \rho(t,a) + \frac{\partial}{\partial a} \rho(t,a) = -\delta(a) \rho(t,a) $$ where $\rho$ is population (number) density and $\delta$ is…
Durden
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Can protein folding be used to solve SAT problems?

Given a sequence of amino acids, the protein folding problem is to find a geometric structure of the amino acids that minimizes energy. Given that this problem is NP-Hard, one should be able to do the following: Convert an instance of an arbitrary…
Kai Arakawa
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Some good books for ODE and Dynamical system.

I am trying to shift my research area from Pure math to math bio for various reasons. So whatever time I invested in my algebra is not of much use plus I have to make the basics of ODE and the Dynamical system strong. I was reading Teschl's book on…
Ri-Li
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How do you calculate how long until a drug reaches its steady state?

I encountered a mathematically intriguing conundrum, in that it's related to medicine but is centered around mathematics. Suppose drug A has a half-life in the body of 30 hours. The patient takes 40mg once per day. How long is it then until the…
askquestions4
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Mathematical Models Describing Monkey Warfare?

Are there mathematical models that describe warfare tactics between competing clans of monkeys, perhaps similar to the predator-prey dynamics modeled by the Lotka–Volterra equations? I am particularly interested in the formation of opposing lines…
rehband
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Stability and Asymptotical behavior of a nonlinear system

A simple mathematical model to describe how the HIV/AIDS virus infects healthy cells is given by the following equations: $$ \begin{align} \frac{dT}{dt} &= s - dT - \beta Tv \\ \frac{dT^*}{dt} &= \beta Tv - \mu T^* \\ \frac{dv}{dt} &= kT^* -…
N00BMaster
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Help Finding a Traveling Wave Solution

I am looking for traveling wave solutions of \begin{align} \frac{\partial U}{\partial t} &= AU\left(1-\frac{U}{K}\right)-BUV+D_{1}\nabla^{2}U \\ \frac{\partial V}{\partial t} &= CUV-DV+D_{2}\nabla^{2}V \end{align} Where $A,B,C,D,K,D_{1}$,and $D_{2}$…
Iesha Patterson
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Dependence of travelling wave speed in Fisher-KPP on asymptotic initial conditions

I'm currently reading J.D. Murray's Mathematical Biology I, Chapter 13.2 discussing travelling wave solutions to the Fisher-KPP equation, and in particular their dependence on initial conditions $u(x, 0)$ as $x \to \infty$. We say that $u(x,t)$ is a…
Ike
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How can I prove that Lotka-Volterra has periodic solutions for IVP problems?

I have read that Lotka-Volterra equations have periodic solutions. I would like to find a proof of this fact, but I haven't found one that is satisfactory. We can compute to find the solution that satisfies the equation $$\log(x_1(t)) +…
user628623
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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): Sdata = {{0, 9.74},{3, 4.92},{6, 8.29},{9, 5.54},{15, 2.08},{18,…
user1256672
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Epidemiology SEI disease model

I have the following model for simple endemic with susceptible (S), exposed (E), and infective (I), $$\frac{dS}{dt}=-\beta SI,$$ $$\frac{dE}{dt}=\beta SI-\delta E,$$ $$\frac{dI}{dt}=\delta E.$$ I have already found the steady states I think which…
user00134857693
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Where to learn about whether a travelling wave solution to the reaction diffusion equation is a pushed or pulled wave?

I'm trying to understand pushed and pulled waves as seen in many biology articles such as: Gene Surfing in Expanding Populations by Hallatschek Spatial gene drives and pushed genetic waves by Tanaka et al Evolution transforms pushed waves into…
Yous
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For the given delay-differential equation, $x'(t)=x(t-T)e^{3-x(t-T)}-x(t)$, how do you find stability for given equilibria?

The delay differential equation given by, $x'(t)=x(t-T)e^{3-x(t-T)}-x(t)$, how to find stability conditions? So here's my attempt: to find equilibria we have, $x^*e^{3-x^*}-x^*=0$ which leads us to $x^*_1=0$ and $x^*_2=3$. Linearizing I get,…
user5896534
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Is there a name for a discrete distribution on -1, 0 and 1?

I am working on a probability theory question related to coalescent theory in population genetics, and the following distribution occurred in my derivation. For three values $a, b, c$, each between 0 and 1, let $$ X = \begin{cases}1 \text{ with…
Egor Lappo
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