3
votes
1answer
40 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 ...
0
votes
1answer
84 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. ...
2
votes
0answers
33 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 ...
0
votes
2answers
67 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 ...
1
vote
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 ...
0
votes
1answer
86 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}) - ...
2
votes
1answer
28 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 ...
4
votes
2answers
256 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 ...
4
votes
3answers
240 views

Mathematical (or physical) formulation of life

I recently started to have interest in the characteristics of life. Especially, I wonder if there are some kind of mathematical description of the true meaning of life and how it is emerged. Why does ...
1
vote
1answer
308 views

Why does this example of Hardy-Weinberg equilibrium not work?

Background Info Hardy-Weinberg equilibrium is a mathematical model of the frequencies of alleles (i.e., versions of a gene) in a population. The model states that the frequency of the 2 alleles in a ...
3
votes
1answer
159 views

Help with recursion/difference equation manipulation

I'm trying to reproduce the analysis of a simple biological model from an old paper. The model describes the frequency of two organism types in a population as: $p_{t+1} = \frac{p_t ( s + (1 - ...
2
votes
4answers
421 views

Biological processes described by the exponential function

What are biological or biochemical processes that are described (stochastically or deterministically) by exponential function $f(x) = e^{ax}$? Edit: What about examples that are not related to the ...