I am modelling the CoronaVirus for my IB maths IA (project). I have explained the principles and assumptions and derived the system of differential equations of the SEIRS Model. However, the R(recovered) compartment does not make much sense for me... and its presence adds difficulty in the calculation. I am considering the SEIS model which is pretty much the same as the SEIRS model apart from having a separate compartment.
The current problem is that it seems to be worthless calculating the R compartment as it is added back to the S(susceptible) compartment anyways, assuming that recovered individuals do not develop immunity and can be infected again immediately.
Also, the system of ordinary differential equations that I got without vital dynamics and in absence of vaccination and isolation is
Can someone confirm this? I couldn't find one online.
Many thanks!!
You mentioned that the $R$ compartment is added back to the $S$ compartment. If the survived Coronavirus patients gain permanent immunity, then this should not happen. On the other hand, if they only gain temporary immunity, then adding $R$ back to $S$ makes sense.
Assume we have the second case where the immunity is only temporary, then whether you want to consider having a $R$ compartment will depend on the time-scale. Since your model does not have vital dynamics (birth/death), this is on a shorter time scale (~months). You will need to find out whether the immunity lasts for months or longer. If the time it takes to lose immunity is much longer than the duration of the outbreak, then you do not even need to add $R$ back to $S$ (this would be similar to if immunity is permanent).
Now, assume that the immunity is lost at a relatively fast rate. Then whether you want to add a $R$ compartment or not is a stylistic choice. If you add it, then it adds a delay between being infected and going back to being susceptible. Whether it matters or not, this depends on the specific cases.
By the way, there are thousands of preprints on this topic right now. You could also search for similar models in the case of Ebola. It may be helpful in your analysis and search for parameters.