Use this for questions on the spread of disease through a population resulting in an epidemic or epidemics. These questions often encompass the study of differential equations, stochastic processes, markov chains, and machine learning.
Questions tagged [epidemiology]
20 questions
3
votes
1 answer
Stability and Asymptotical behavior of a nonlinear system
A simple mathematical model to describe how the HIV/AIDS virus infects healthy cells is given by the following equations:
$$
\begin{align}
\frac{dT}{dt} &= s - dT - \beta Tv \\
\frac{dT^*}{dt} &= \beta Tv - \mu T^* \\
\frac{dv}{dt} &= kT^* -…
N00BMaster
- 721
3
votes
2 answers
Stability of the SIR epidemic model — Jacobian is singular
The SIR epidemic model presents three differential equations for three time-dependent variables — $S(t)$, $I(t)$, $R(t)$.
\begin{aligned}
\frac{dS}{dt} &= -\beta SI\\
\frac{dI}{dt} &= \beta SI - \gamma I\\
\frac{dR}{dt} &= \gamma…
3
votes
1 answer
Proof for positivity of solutions of an ODE system
I have an ODE system that takes a mathematical model describing the dynamics between HCV and the immune system. My question is about the proof that the solution of the ODE system is positive if the initial conditions are all positive. I tried this…
Anas TABET
- 31
2
votes
1 answer
Numerical computation of the basic reproduction number (R0) for reaction-diffusion-advection epidemiological models
I am working on a "reaction-advection-diffusion" type epidemiological model using a system of partial differential equations (PDEs). From this PDE model, I would like to numerically compute the basic reproduction number (R0) to represent its…
Nell
- 63
2
votes
1 answer
Epidemiology SEI disease model
I have the following model for simple endemic with susceptible (S), exposed (E), and infective (I),
$$\frac{dS}{dt}=-\beta SI,$$ $$\frac{dE}{dt}=\beta SI-\delta E,$$ $$\frac{dI}{dt}=\delta E.$$
I have already found the steady states I think which…
1
vote
3 answers
Potential Applications of Simpson's Paradox
Simpson's paradox arises in statistics, when a trend in independent groups becomes different when they are combined. For instance, baseball player A might have a better average than player B in two successive seasons, but Player B could have a…
user1346804
1
vote
0 answers
What is the distribution of order in ordered sets of poisson processes
I have a question from epidemiology that I'm struggling 1) to write down mathematically and 2) determine if it has a closed form solution.
First here's the epidemiological question. Say I have $C$ children. They are all independently infected by a…
Nick Savill
- 11
1
vote
0 answers
Approximate solutions to a system of differential equations
This system of differential equations corresponds to a compartmental model in epidemiology called SIRD:
\begin{aligned}&{\frac {dS}{dt}}=-{\frac {\beta IS}{N}}\\[6pt]&{\frac {dI}{dt}}={\frac {\beta IS}{N}}-\gamma I-\mu I\\[6pt]&{\frac…
user1385231
1
vote
1 answer
For an epidemic model, I got a negative 'basic reproduction number' obtained by next-generation matrix method. How this can be corrected?
I have a system of 6 ODE representing infected subpopulations of a model of epidemic
$$
\begin{cases}
\dfrac{de}{dt} =\dfrac{dy_2}{dt} = \phi y_1(y_4+y_5)-p_2 y_2\\
\dfrac{dq^*}{dt} =\dfrac{dy_3}{dt} = \mu y_2 -P_3 y_3\\
\dfrac{ di_s}{dt}…
HRAUNMAKASH
- 11
1
vote
0 answers
Why does an admissible control need to be measurable?
I am reviewing some literature on controlling SIR models. I have come across the following article
Khalid Hattaf, Noura Yousfi, Optimal control of a delayed HIV infection model with immune response using an efficient numerical method, ISRN…
CHOSM
- 164
1
vote
1 answer
Solution of $R(t)$ in SIR model
Consider the SIR model,
$$
\begin{align}
\frac{dS}{dt}&= -rSI \tag 1\\
\frac{dI}{dt}&= rSI-\gamma I\tag 2\\
\frac{dR}{dt}&= \gamma I\tag 3
\end{align}
$$
from $(1)$ and $(3)$ we get, $\frac{dS}{S}+\frac{dR}{\rho}=0$ and the solution $S(R)=S_0…
WhyMeasureTheory
- 895
0
votes
2 answers
Where does the e come from in the SIR model?
I am learning infectious disease modeling, and I have come across something in my textbook that has me stumped. They take the equation:
$$\frac{dS}{dR} = -R_0S $$
Then, they say "upon integrating with respect to R, we obtain:
$S(t) =…
0
votes
0 answers
Ross' Model - Classification of equilibrium point $(0,0)$ given that $pqa^2d=\alpha\mu$
Considering
\begin{equation}
\begin{cases}
\dot{m}=pa(1-m)h-\mu m \\
\dot{h}=qad(1-h)m-\alpha h
\end{cases}
\end{equation}
where $m$ is the proportion of infected mosquitoes and $h$ is the proportion of infected humans and $d$ represents the density…
J P
- 1,152
0
votes
0 answers
Calculating exact probability distributions in binomial trials with varying runs of success (diseased, D) and failures (healthy, H).
I haul this problem over from Pielou, 1965 (The spread of disease in patchily-infected forest stands. Forest Science, 11(1):18–26).
Diseased plants in a plant population are often found to be patchily dispersed, patches of diseased plants being…
dd_rookie
- 103
0
votes
0 answers
Estimating parameters in a system of ODE's from data.
I'm trying to model the COVID-19 pandemic in Madrid during the first wave, to model the data I'm using the SIR model. The SIR model stands for suceptible, infected and recovered. It is a compartmental model meaning that it puts each person in one of…
