Questions tagged [biology]

For questions regarding mathematical concepts with applications to Biology.

Filter by
Sorted by
Tagged with
0 votes
0 answers
21 views

Fixed points and stability of 2 differential equations

I need help checking this answer please Question: $\frac{ds}{dt} = -R_0su = f(s,u)$ $\frac{ds}{dt} = R_0su -(S_0 + 1)u= g(s,u) $ Constraint:$s+u=1$ Answer: $FP_1 = (1,0)$ $R_0su -(S_0 + 1)u =0$ $R_0(...
user avatar
1 vote
2 answers
56 views

How is this ODE created?

So what I got was this but it doesn't match the answer sheet so not sure what went wrong
user avatar
0 votes
1 answer
62 views

The French Newbie and the Lotka-Voltera Crazy Idea

I am back to talk with you and to have criticisms on ideas crossing my mind! I am currently working on a disease that is striking french vineyards really hard. I am currently using a model that is ...
user avatar
  • 11
1 vote
1 answer
60 views

Bacteria and logarithms problem. [duplicate]

You are taking a biology class and you are growing a colony of bacteria starting with 5 bacteria. Suppose the colony of bacteria is grow exponentially and can be modeled using the following function: ...
user avatar
1 vote
0 answers
26 views

Solving chromosome mapping problem using linear algebra?

In biology, we were given a problem in which we had to use "distances" (recombination frequency) between genes in order to create a genetic map of how genes are located relative to each ...
user avatar
  • 11
0 votes
0 answers
34 views

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 + ...
user avatar
0 votes
0 answers
30 views

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 ...
user avatar
  • 183
2 votes
0 answers
51 views

Converting one form of the Gompertz equation into another

Consider the Gompertz equation that models the dynamics of the population of a single-species $$\frac{dN}{dt}=r_0e^{-\alpha t}N$$ and convert it to the following form $$\frac{dN}{dt}=\alpha N\ln\left(\...
user avatar
0 votes
0 answers
64 views

Comparing solutions of logistic equation and Gompertz equation

Considering the Gompertz equation, $\frac{dN}{dt}=r_oe^{-\alpha t}N$, and the logistic growth equation, $\frac{dN}{dt}=rN(1-\frac{N}{k})$. How is the carrying capacity from Gompertz equation differ ...
user avatar
1 vote
1 answer
52 views

Question in population dynamics using exponential growth rate equation

Given population doubles in 20 minutes, what is intrinsic growth rate r? Attempt: Given population doubles, using exponential growth rate we have $\frac{dN}{dt}=2N$ so $N(t)=N_0e^{2t}$ therefore r=2, ...
user avatar
0 votes
0 answers
27 views

Can I still use deltadeltaCt with a p-value of 0.2?

I have the following dataset: ...
user avatar
4 votes
2 answers
117 views

Comparison of bird diet at two different nests

I have a list with the different prey types and quantities that birds at Nest $1$ gave to their fledglings. I also have the same information for another nest of the same bird species. Suppose I have <...
user avatar
1 vote
0 answers
34 views

On the initial conditions for bacterial population growth

I want to prepare an example of a differential equation for bacetrial growth. We have $\frac{dy}{dt}=ry(t)$ Multiplying by dt and moving y(t) over to the other side we get $\frac{1}{y(t)}dy=rdt$, ...
user avatar
0 votes
1 answer
63 views

How do you call this system?

Is there a specific name for a dynamical system that depends on the relative indexation $i\pm k$ for some $k$? For example, consider the following dynamical system defined on a ring of cells by $$ \...
user avatar
  • 3,676
0 votes
0 answers
6 views

Interaction between two viscoelastic elements

Consider two cortices formed from two different kinds of viscoelastic filaments 1 and 2. Cortex 1 is inside cortex 2. Both cortices are said to have resistance to bending and extension. So both can we ...
user avatar
4 votes
1 answer
55 views

Turing's Symmetries

In Alan Turing's classic paper on the Chemical Basis of Morphogenesis, the following bilateral and left-right symmetries are defined as follows: Might be an misunderstanding of English from my side, ...
user avatar
  • 3,676
0 votes
0 answers
16 views

Epidemics: number of infections during an infinitesimal time is Poisson distributed?

Here is an extract of the Nature Review on "Mathematical models of infectious disease transmission" [1] : If $I(u)$ is a function that describes the number of individuals who are newly ...
user avatar
  • 21
1 vote
0 answers
21 views

Can I use the number of particles rather than concentration in biological differential equations?

(This question is not specific to biology, but I was just wondering about a common way that people view differential equations in biology.) Some simple biological differential equations take the form $...
user avatar
0 votes
1 answer
36 views

Finding units for constants in ODE's

$$ \begin{array}{r c l} \frac{dN}{dt} & = & rN\left(1-\frac{N}{K}\right)-\alpha \frac{NP}{\beta P + \gamma N} \\ \frac{dP}{dt} & = & \epsilon \frac{NP}{\beta P + \gamma N} - \delta P \...
user avatar
0 votes
1 answer
86 views

How to solve simple differential equation (biology)

First of all, I am a biologist and I am not really knowledgeable in mathematics. Thus, I apologize if what I am asking is naive or not fully explained. I am trying to solve analytically a differential ...
user avatar
-1 votes
1 answer
74 views

Predator-Prey Model [closed]

Can anyone explain the biological interpretation on the right hand side of these equations please? $$ \begin{array}{r c l} \frac{dN}{dt} & = & rN\left(1-\frac{N}{K}\right)-\alpha \frac{NP}{\...
user avatar
0 votes
0 answers
19 views

What is Iteration Number in modeling?

I am a biologist. Referring to mathematical modeling for biological data in the literature. Could someone explain what is the "Iteration Number" of modeling and the meaning of the up and ...
user avatar
1 vote
0 answers
28 views

Non-trivial, time-independent solution at long times for a separable solution of an age-structured model

I'm taking an introductory course on mathematical modelling in biology and am completely at a loss with this question. We are considering the PDE for a population of cells $n$ with age $a$ over time $...
user avatar
  • 348
0 votes
1 answer
34 views

Simplify the following differential equation by variable scaling

We have: $\frac{dx}{dt}=\frac{a}{x+b}, a>0,b>0$. We make substitutes: $x\to\alpha h, t\to\beta \tau$. Then the differential equation will be: $\frac{\alpha}{\beta}\frac{dx}{dt}=\frac{a}{x+b}$, ...
user avatar
  • 162
0 votes
0 answers
8 views

Calculate necessary sample size to achieve desired power in genome ancestry determination

I currently have an algorithm that takes a genome and returns its % ancestry of 10 ancestries. To do this, the genome is compared to a file of mutations broken down by ancestry. The file might look ...
user avatar
  • 1
1 vote
1 answer
32 views

Probability of having an all-heterogeneous genotype

Find the probability that the genotype of an offspring will be $\mathrm{AaBbCcDdEeFfGgHhIiJj}$ from the cross $\mathrm{AaBbCcDdEeFfGgHhIiJj \times AaBbCcDdEeFfGgHhIiJj}$. Making a Punnett square for ...
user avatar
  • 1,954
0 votes
0 answers
29 views

Logistics model or Malthus model?

Consider the following table: There, n is the discrete time, and the variable Pn is the population size at time n, expressed in thousands. To determine which model it is I tried to write the ...
user avatar
  • 162
0 votes
0 answers
29 views

System of differential equations in economics and areas of interest

More than a question, I'm looking for suggestions of models of system of differential equations applied in economics or maybe in another area of interes. I have a research homework and I have to make ...
user avatar
  • 33
3 votes
1 answer
137 views

Can SIR models explain reduction in COVID case numbers in Florida and Texas, despite lack of restrictions?

This is a question about SIR or SEIR models and understanding the trajectory of the covid infections in Florida and Texas in September 2021. This is a genuinely academic question, and not meant to be ...
user avatar
  • 1,675
0 votes
0 answers
27 views

Hamilton's Rule (Biology) Derivation

In the most recent Primer video about Hamilton's rule, at 16:40 he talks about deriving a version of Hamilton's rule based on the principle that, in order for an altruistic allele to be successful, ...
user avatar
1 vote
0 answers
25 views

Expected Value for distinct substrings of length $k$

Genomes consist of 4 nucleobases (A, C, G, T). If we take genome substrings of length $k$ (called $k$-mers), we have $4^k$ theoretically possible substrings. If we have a genome of length $l$ (meaning ...
user avatar
2 votes
1 answer
68 views

Equivalence of Leaky Integrator and Low-Pass Filter Decision Models

I'm working with a decision making model from the cognitive neuroscience literature (the Urgency Gating Model) and have found two different implementations. My concern is that these two ...
user avatar
  • 129
1 vote
0 answers
50 views

Two-stage catalytic model with variable rate (epidemiology)

In epidemiology, the two-stage catalytic model gives the observed cumulative prevalence $y$ of a disease (often termed seroprevalence, measured with an antibody test) for individuals of age $a$; where ...
user avatar
0 votes
0 answers
19 views

How to derive Slime Mould Equations

As shown in https://en.wikiversity.org/wiki/Slime_Mould_Algorithm, we have the Slime Mould equations for Approach food and Wrap food. I do not know how to derive these equations. Please help me or ...
user avatar
1 vote
0 answers
24 views

Didactic models for tipping dynamics

I would like to know if there are some toy models that describe an ecosystem dynamic (eg. ice-sheet cover, rainforest-savanna cover, permafrost thawing ) in which a critical treshold can be observed, ...
user avatar
  • 859
0 votes
0 answers
45 views

Interpreting replicator dynamic for simplest population model

Suppose the simplest population model where we track the size $y$ of a population: $$\frac{dy}{dt} = ry$$ for a positive constant $r$ and some $y$ such that $y(0) > 0$. For this population model ...
user avatar
1 vote
0 answers
18 views

Using integral within discrete time model

I have a semi-discrete model, tracking the number of insects that emerge from pupae, and I'm struggling a bit with the maths. I have an emergence function, let's say $e(t)\sim N(\mu,\sigma^2)$, ...
user avatar
  • 11
0 votes
0 answers
16 views

Understanding Hill Plot of the Genetic Toggle Switch Model

I am currently conducting research on the genetic toggle switch (Gardner et al., 2000.), as simple genetic circuit featuring two mutually repressing promoters. I am trying to fully understand a plot (...
user avatar
0 votes
0 answers
48 views

Bifurcation Diagrams

Thank you for taking the time to read my question! I need help to understand how backward bifurcation diagrams are plot. I understand what backward bifurcation is, and I can even find necessary and ...
user avatar
0 votes
0 answers
69 views

Solving Laplace's equation with discontinuous Robin boundary conditions

There is a simple model of cells taking nutrients that I figure should have an exact solution, but I am struggling to find it. The root of the problem is the boundary condition. I am solving the ...
user avatar
1 vote
1 answer
62 views

Deriving logistic growth equation from the exponential

I'm following along with this: https://jdyeakel.github.io/teaching/ecology/section9/ and I just want to make sure my derivation is correct since this website seems to use prime notation not for ...
user avatar
0 votes
1 answer
50 views

How to read the surface plots?

I was reading this paper and I could not understand this figure. How do you read these kind of graphs? How to interpret the twists and folds; it's not like heat maps that are intuitive. Any help ...
user avatar
0 votes
1 answer
42 views

Logistic decay in mathematical biology

I am studying a course of Mathematical Biology. I am trying to interp the following ODE: $$ \frac{dR}{dt} = \beta R-\gamma(1+\frac{R}{K})R $$ My attempt: $R$ describes a population in time $t$ $\beta ...
user avatar
  • 183
4 votes
0 answers
97 views

Why viruses such as covid-19 are shaped like a sphere from a mathematical point of view [closed]

I can't find anything online about the relationship between spheres and the envelope of a virus from a purely mathematical point of view, what I need to know is why the outer-layer of viruses is a ...
user avatar
0 votes
1 answer
37 views

Confused about parameters SIRD model

I'm trying to understand the meaning of the parameters of the following model: \begin{align*} \frac{dS}{dt}&=-\alpha I S+b-dS\\[5pt] \frac{dI}{dt}&=\alpha IS-\delta I-\mu I-dI\\[5pt] \frac{dR}{...
user avatar
  • 27
1 vote
0 answers
26 views

Dominant eigenvalue of next-generation matrix

I came across an article that says the $R_0$-number is the dominant eigenvalue of the next generation matrix. So I started research and I think I understand what the next generation matrix is. My ...
user avatar
  • 23
0 votes
1 answer
21 views

Find the next gen frequency of diploid selfing and selection model

So we have the genetic diploid model for the spread of an advantageous gene: genotype $AA$ $Aa$ $aa$ zygote frequency $P$ $Q$ $R$ relative fitness $1+s$ $1$ $1$ Now that this model applies to the ...
user avatar
  • 711
1 vote
0 answers
34 views

Determining an ODE with monotonically increasing solution and multiple steady states

I am trying to understand what kind of ODE or system of ODE would result in a monotonically increasing solution with multiple steady states. For lack of better terminology, a solution that increases ...
user avatar
1 vote
0 answers
79 views

SIS model with vaccination

For the simple SIS model $$ \begin{aligned} \mathsf{S}′ &= \Lambda − \beta \mathsf{SI} − \mu \mathsf{S} + \gamma \mathsf{I} \\ \mathsf{I}′ &= \beta \mathsf{SI} −(\mu+\gamma)\mathsf{I} \...
user avatar
  • 45
1 vote
2 answers
283 views

SIR model (3 differential equations)

The SIR model for epidemics is Susceptible (not yet infected) -> Infected (have disease and are infectious) -> Recovered (recovered from the disease) and is governed by the system of 3 ...
user avatar
  • 9,340

1
2 3 4 5
8