# 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?
• 1
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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 ...
• 145
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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 ...
• 103
1 vote
38 views

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 ...
• 365
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• 365
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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}{...
• 365
33 views

### 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 ...
• 365
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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 ...
• 365
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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 ...
• 365
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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? ...
• 365
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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 ...
• 365
1 vote
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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 ...
• 11
1 vote