Questions tagged [mathematical-biology]

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

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Why life expectancy calculate as 1/μ in SIR model?

In the SIR model, when the death rate is μ, life expectancy is calculated as 1/μ. Can anyone explain it intuitively?
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Finding the steady state solutions of a model.

Problem: Find the steady states and check for stability of the model \begin{align*} X_{t+1} &= rX_te^{r(1-X/k)-aY_t} \\ Y_{t+1} &= X_t(1-e^{-aY_t}) \end{align*} Attempt: Calculating ...
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Difficulty understanding some inequalities in S,A,I,R disease modelling

Consider this paper (reading the entire pdf is not required) on disease modelling. There are four real functions of interest, based on constant positive parameters $\mu,\nu,\delta,\beta$ and four ...
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Finding nullclines and linearization about the steady state

Here's my system: $$ \left\{ \begin{aligned} \frac{du}{dt} &= u(1-u^2)-w \\[5pt] \frac{dw}{dt} &= u \end{aligned} \right. $$ I'm coming to the conclusion that the only steady state ...
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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^...
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For the difference equation $x_{n+1}=ax_n\exp(-x_n)$, find values of $a$ that lead to a period-doubling bifurcation and values that lead to extinction

For the difference equation, $x_{n+1}=ax_n\exp(-x_n)$, find values of $a\in(-1,1)\cup(1,e^2)$ that lead to a period-doubling bifurcation, and values that lead to extinction So for $x_{n+1}=ax_n\exp(-...
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For given system of ODE's, in a region $\Omega$ in the $uw$-plane, show it's a trapping region for large R

Need help figuring out what this question wants me to do. No need to do entire problem for me, just need a push in the right direction on how to solve Here's my system: \begin{gather*} \frac{du}{...
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Performing linear stability analysis for nonlinear discrete system by approximating function for large values of the varying bifurcation parameter

Here's my system, \begin{gather*} N_{t+2}=N_t\exp{[r(1-\frac{N_t}{K})]}\frac{1-e^{-aP_t}}{aP_t} \\ P_{t+1}=N_t[1-\frac{1-e^{-aP_t}}{aP_t}] \end{gather*} In the research paper, it states that ...
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How to determine equilibrium points numerically for linear stability analysis of the following Predator-Prey system?

Consider the following system, \begin{gather*} N_{t+2}=N_t\exp[r(1-\frac{N_t}{K})]\frac{1-e^{-aP_t}}{aP_t} \\ P_{t+1}=N_t[1-\frac{1-e^{-aP_t}}{aP_t}] \end{gather*} how should I go about ...
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How to determine $R_0$, the basic reproduction number, for following system?

Consider a population of size $N$ with per capita birth rate $b(N)$ and death rate $d(N)$. Assume that it reaches stable steady state $N^*$ in absence of disease, with $b(N^*)=d(N^*)$. Find $R_0$ when ...
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Where did the r value go for this ODE?

Question: Answer: So I got the same answer except mine has e^rt instead of e^t so can someone explain why the r just disappeared and if my answer is still correct?
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How to determine bifurcation diagram for following system of difference equations?

So given this system, $\begin{gather*}N_{t+2}=N_t\exp[r(1-\frac{N_t}{K})]\frac{1-e^{-aP_t}}{aP_t}\\ P_{t+1}=N_t[1-\frac{1-e^{-aP_t}}{aP_t}]\end{gather*}$, how do I determine the bifurcation diagram? ...
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What Matlab packages are good for producing bifurcation diagrams for predator prey systems?

So some background, this is my predator-prey system: $\begin{gather*}N_{t+2}=N_t\exp[r(1-\frac{N}{K})]\frac{1-e^{-aP}}{aP}\\ P_{t+1}=N_t[1-\frac{1-e^{-aP}}{aP}]\end{gather*}$. I've tried doing it by ...
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French newbie looking for feedbacks on Simulink simulation

I am new on this forum and I hope that I will provide useful answer to mathematics problems that people might have to face in the future. Also, I do want to meet mathematicians from all over the world ...
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I need help to find out an equation about mathematic-biology for a piece of art

I am not a mathematician but I do love mathematic a lot, and many other things that I constantly connect to maths. Alas, I was away from the most beautiful form of poetry for very long in my life, ...
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How to deduce steady state is stable if $\mu\tau _c=\frac{\pi-\cos^{-1}\frac{1}{b}}{(b^2-1)^{1/2}}$ for DDE

A continuous time model with delay equation $\frac{dN}{dt}=-\mu N(t)+\mu N(t-\tau)[1+q\{1-[N(t-\tau)/K]^z\}]$. Deduce equation governing small perturbations $n(t)$ about the positive equilibrium is $\...
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Using Jury Conditions to Show Instability

If I want to force an equilibrium point of a discrete dynamical system to be unstable can I just violate one of the conditions for stability stated in the jury conditions $$|\mbox{Trace} (J)| < 1 + ...
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Plotting nullclines for a set of equations

I'm doing an analysis of a paper, and I want to reproduce a plot in the paper where they have the nullclines of two functions, namely: $$ \begin{align}\frac{dW}{dt}&=\ \beta(1-\rho)W+\delta A - \...
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How to determine boundaries in the $(\delta\tau,\alpha\tau)$ plane after determining equilibrium and linearization of Delay-Differential equation

Problem: Consider the following population model: $\frac{dN}{dt}=\alpha N(t-\tau)e^{-\beta N(t-\tau)}-\delta N(t)$ Determine equilibrium and Linearize about the equilibrium. From Linearization, draw ...
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Calculation of the efficacy rate of a drug

I am participating in a mathematical biology project. I would like to discuss the following problem: Let A be a drug such that $x_{o}$ chemical units of it kills $12\text{%}$ of $y$ cells per day, I ...
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Loss of Fertility Per Unit of Time

Consider a study examining fertility of a mammal. Suppose there is a probability space $(\Omega,F,P)$. Consider a random variable $t:\Omega\rightarrow [0,T]$ for some $T>0$, and suppose it ...
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