Questions tagged [epidemics-modeling]
The epidemics-modeling tag has no usage guidance.
22 questions
0
votes
0
answers
21
views
Compartment models with infinite compartments
Compartment models are used in a number of fields. While studying the literature (and especially E. Allen‘s book on Modeling with Itô Stochastic Differential Equations) I have noticed that all the ...
- 309
0
votes
1
answer
301
views
Poisson Process x SIR model [closed]
Consider the simplest SIR model:
$$S'=-a SI$$
$$I'=a SI - b I$$
$$R'=b I$$
It is known that the waiting time of an infeccious person in the compartment $I$ follows an exponential behavior with rate $b$...
- 123
5
votes
1
answer
213
views
Equation in epidemic SIR model with the influence of vaccinations
I am currently preparing a presentation on different modifications of the SIR model. In my sources about the use of vaccines, I came across the following model for a specific rate at which the ...
- 51
3
votes
1
answer
274
views
Epidemic modelling: expectation of time of infection given the distribution of transmission and recovery
Can I express the expected value of
\begin{equation}
\langle \tau\rangle_\text{total}=\int_0^\infty \tau \psi_\text{inf}(\tau)\Psi_\text{rec}(\tau)\mathrm{d}\tau
\end{equation}
in terms of the moment(...
- 274
2
votes
1
answer
244
views
Literature on reaction diffusion equations
My research area is age structure modelling, basically when applied to reaction diffusion equations. We mainly discuss the existence of travelling wave solutions; I want to work on the stability of ...
- 21
1
vote
1
answer
355
views
Why should we model infectious diseases with fractional differential equations?
With COVID19 becoming a pandemic I saw some researchers trying to model it with fractional differential equations (FDE) instead of ordinary differential equations (ODE). From a technical standpoint I ...
23
votes
4
answers
978
views
What nodes of a graph should be vaccinated first?
Consider a graph, choose some "p: 0<p<1" (probability to infect the neighbor node).
Choose some random number "K" of nodes which are "infected" initially.
So we ...
- 24.8k
1
vote
0
answers
129
views
Next-generation matrix of infectious disease
If the population is classified into $\mathbf{S}$, $\mathbf{E}$, $\mathbf{I}$ and $\mathbf{R}$ compartments such that
\begin{equation}
\label{eq4}
\begin{aligned}
\mathbf{S} &=\dfrac{S_{1}N_{1}+...
6
votes
1
answer
300
views
Time of peak of an SIR epidemic
I've learned some classical results on the peak and the attack rate of an idealized epidemic which evolves according to a SIR model
$\dot{s} = -\beta\cdot i \cdot s$
$\dot{i} = +\beta\cdot i \cdot s -...
- 9,720
4
votes
2
answers
270
views
Approximated solutions of SEIR models
Numerical solutions of the SEIR equations (describing the spreading of an epidemic disease) – or variations thereof –
$\dot{S} = - N$
$\dot{E} = + N - E/\lambda$
$\dot{I} = + E/\lambda - I/\delta$
...
- 9,720
2
votes
0
answers
74
views
SIR model constraint [closed]
During these past months, I've heard a lot about some pandemic modelling techniques, specially the so-called SIR model. Before I begin, I'd like to stress that my interest and question are just a ...
- 3,515
2
votes
1
answer
238
views
Seeking a Lyapunov function for a SIR model with immunity loss
We add the immunity loss to the SIR model and obtain the following autonomous system.
$$
\begin{align}
s' &= -is+\alpha r \\
i' &= i s - \gamma i\\
r' &= \gamma i-\alpha r
\end{align}
\...
- 2,239
95
votes
5
answers
13k
views
Note rejected from arXiv: what to do next?
Short version: A note of mine was rejected by the arXiv moderation (something I didn't even know was possible) on account of being “unrefereeable”. The moderation process provides absolutely no ...
27
votes
1
answer
1k
views
Solving a delay-differential equation related to epidemiology
For some inexplicable reason, I have recently been interested in epidemiology. One of the classical and simplistic models in epidemiology is the SIR model given by the following system of first-order ...
- 32.4k
1
vote
1
answer
403
views
Densest safe disk packing
Inspired by current regulations regarding the minimal distance to be kept among people to prevent spreading of the COVID-19 virus and the maximal number of people in a group that is not subjected to ...
- 13.2k
1
vote
1
answer
280
views
How many persons pass your 1.5 meter neighbourhood during 1 week ? If the distribution is power law what is the exponent?
Consider a graph with vertices being people (in some region), and make an edge if one person pass another closer than say 1.5 meter during say one week.
(Such a graph might be thought a kind of ...
- 24.8k
5
votes
0
answers
513
views
Coronavirus in NYC: What is happening in the near-term? [closed]
Although I am motivated to have some different questions answered (see below), I would like to build or use a model to predict the number of COVID-19 Cases in NYC in the near term (perhaps through the ...
- 75
12
votes
6
answers
1k
views
Suggestions for reducing the transmission rate?
What are suggestions for reducing the transmission rate of the current epidemics?
In summary, my best one so far is (once we are down to the stay home rule) to discretize time, i.e., to introduce the ...
8
votes
4
answers
1k
views
Virus community spread mathematical modeling [closed]
What is the basic math behind the Virus community spread mathematical modeling,and how the time variable;(in these models),interacts with knowledge (data)?.
I am not asking about how the virus is ...
14
votes
8
answers
3k
views
Relevant mathematics to the recent coronavirus outbreak
I would like to ask about (old* and new) reliable mathematical literature relevant to various mathematical aspects of the recent coronavirus outbreak: In particular, standard statistical/mathematical ...
5
votes
1
answer
261
views
Epidemic threshold
Need some help / ideas to proceed. Stuck for a while on this.
In the literature of epidemic theory, it is found that the epidemic threshold is $1/\lambda_{\max}(A)$ where $\lambda_{\max}(A)$ is the ...
- 355
6
votes
1
answer
171
views
Relative vulnerabilities in SIS epidemic model
Consider the SIS model of epidemic spreading. There is a finite graph $G(V,E)$, link infection rates $\lambda_{ij}$ and node recovery rates $\mu_i$. There are a few initial nodes which are infected at ...
- 519