I am not an ifectious disease specialist. Logistic growt model is an differential equation solution. There are variations of this model. This model is useful for some anaysis. But what are the advantages and disadvantes of this model for COVID-19 ?
C R Rao did the classic work. Start with this link:
https://www.bing.com/search?q=C+R+RAO+Growth+curve+models+and+their+comparison&qs=n&form=QBRE&sp=-1&pq=c+r+rao+growth+curve+models+and+their+comparison&sc=0-48&sk=&cvid=86A174DB41CF4B628679FDCC14805D99
and follow with this one:
https://www.bing.com/search?q=+Growth+curve+models+and+virus++growth&qs=n&form=QBRE&sp=-1&pq=growth+curve+models+and+virus+growth&sc=1-36&sk=&cvid=FB2FB99737054046AFBEE755E95F8D3C
The general logistic model is
dC(t)/dt= r*C(t)^p*[1-(C(t)/K)^α]
where C(t) is the cumulative number of cases at time t, r is the growth rate at the early stage, and K is the final epidemic size. 𝑝 ∈ [0,1] is a parameter that allows the model to capture different growth profiles including the constant incidence (𝑝 = 0), sub-exponential growth (0 < 𝑝 < 1 ) and exponential growth ( 𝑝 = 1). The exponent α measures the deviation from the symmetric s-shaped dynamics of the simple logistic curve.
For the calibration the 4 parameters r, p, K and α the standard Levenberg–Marquardt algorithm can be used to solve the non-linear least square optimization.
Most current COVID19 data are still at an early stage of the outbreak, i.e. the cumulative number of cases is not yet reaching the inflection point. Therefore, the additional parameter α describing the asymmetry between growth and decay of the incidence curve cannot be accurately obtained with the limited available data. Therefore, the following three simpler models with fewer parameters can be used: - Logistic growing model:
dC(t)/dt= r*C(t)*[1-(C(t)/K)] (1), p=1, α=1
-generalized logistic model
dC(t)/dt= r*C(t)^p*[1-(C(t)/K)] (2) α=1
-generalized growth model
dC(t)/dt= r*C(t)^p (3), K->infinity
The generalized growth model (3) allows for a sub-exponential growth of the outbreak in the early stage (for p < 1), but cannot describe the decay of the incidence rate. It thus serves as a rough upper limit, obtained by assuming that the outbreak continues to grow following the same process as in the past. The generalized Logistic model (2) and Logistic growth model (1) both assume a logistic decay of the growth rate as the total number of confirmed cases increases. Both Logistic type models tend to under-estimate the total size of the infected population at the early stage, so they should provide lower bounds. The generalized Logistic model allows for an early sub-exponential growth and can better describe the possible asymmetry between growth and decay dynamics.
The bottom line:
regardless of the type, all models are usually non-linear and contain a number of empirical parameters. However, the numerical values of these parameters depend on available data; the volume and quality of data continually change, thus making predictions of the future state difficult and conditional on numerical values of the parameters.
For details, see e.g. a preprint "Generalized logistic growth modeling of the COVID-19 outbreak in 29 provinces in China and in the rest of the world" by
Ke Wu, Didier Darcet , Qian Wang and Didier Sornette.
Hi Rafet, here are some resources that you may find helpful.
Hello,
I don't know at the moment : it's too early.
On the other hand, what I can say is that the dimensioning (or the level) of security stocks is really called into question.
The same could be said about the reactivity of the supply chain, and about the legendary logistic agility...
Tomorrow, managers, forced by governments, will probably do better, much better. It will probably cost more... but does life have a real price?
Bye
Take care!
Yes, using the logistics growth model and based on data from people living with the Cavid 19 virus in the last month, we can predict how many people will be infected in the next year.
Hola
Pienso que es una buena opción, el modelo de regresión logística y la teoría del caos
Saludos
Disadvantages include uncertainty of the upper asymptote K, the maximum number of individuals that will be infected, Inflection point when the number is K/2 and the growth rate under limited noisy data. The noise is chiefly contributed by interventions that hinder smooth transmission of the virus. Otherwise, the logistic model is good enough.
Logistic is quite good if you think there will be just one wave (otherwise a subepidemic framework is better), but in any case, even for the one wave case, you need a good guess for the upper asymptote K, otherwise the quality of the forecast h-steps ahead deteriorates considerably.
However, you can use some heuristics if you want to use the model for short-term forecasting. After some experimentation I found you could always get good results by starting to search in the parameter space with a K0 that is twice the current cumulative incidence and then let the optimization of the parameters to explore in between the current cumulative incidence and the total population size.
If you can lay your hands on the inflection point, which happens to be roughly K/2 in a single wave epidemic with no major interruption, then you are approximately good to go. The problem is that interventions keep changing the infection rate. Further, studying case data from countries who are on down side of the curve, e.g. China Italy, France..., There is serious lack of symmetry. So K will be larger than twice the inflection point. But then what else can be done? any better model?
