# Questions tagged [epidemics-modeling]

The epidemics-modeling tag has no usage guidance.

23
questions

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### 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 $b$...

0
votes

0
answers

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### Epidemic risk models on graphs with fuzzy edges

I am reading the paper mentioned above, but I have some questions because I have some confusions.
image
Questions
What is the motivation behind transforming the original formula in the network model?
...

4
votes

1
answer

162
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 ...

3
votes

1
answer

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### 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(...

2
votes

1
answer

193
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### 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 ...

1
vote

1
answer

225
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### 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 ...

3
votes

0
answers

91
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### Epidemics: distribution of interarrival times

In models of disease transmission, after an individual is getting infected, he can generate a number of secondary infections. The number of secondary infections depends on the infectiousness of the ...

23
votes

4
answers

936
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### 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 ...

1
vote

0
answers

120
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### 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

242
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### 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 -...

4
votes

2
answers

242
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### Approximated solutions of SEIR models

Numerical solutions of the SEIR equations (describing the spreading of an epidemic disease) – or variations thereof –
$\dot{S} = - N$
$\dot{E} = + N - E/\lambda$
$\dot{I} = + E/\lambda - I/\delta$
...

2
votes

0
answers

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### 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 ...

2
votes

1
answer

226
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### 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}
\...

90
votes

5
answers

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### 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

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### 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 ...

1
vote

1
answer

336
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### 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 ...

2
votes

1
answer

274
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### 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 ...

5
votes

0
answers

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### 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 ...

12
votes

6
answers

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### 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 ...

13
votes

8
answers

3k
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### 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

250
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### 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 ...

6
votes

1
answer

165
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### 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 ...