I am modelling Ebola, and I have assumed that the transmission rate decays exponentially with intervention measures, but I would like to make other assumptions with respect to the transmission rate, but I don't find anything. Can someone suggest the some functions to model the transmission rate of Ebola in the context of SEIR model?
In simpe way ; logistic function (see calculus by Stewart, 1998 and new edition available in e-book) perhaps fits to your data. The you combine with prey-predator model for both ( choose which one is prey, which one is predator)
Your choice of functions to represent time or population dependence of transmission rate should be based on what you observe or what can be deduced on biological or public health theoretical grounds. For example you could try linear or quadratic time dependence to represent public health response, or even dependence ot transmission on population affected or susceptible to reflect coping capacity of public health response,immunity etc..
I would second Hanna's suggestion: a logistic function would be another good choice, especially if you want to model intervention/change of behaviour at a specific time. Also, you can try a bunch of other functional forms and see which ones give a better fit to your data (if you aim to fit your model to data).
You may not be able to find a simple function that fits the data, as there would have been many interventions as well as improved public knowledge leading to avoidance behaviours. You need to analyse the real data and see if there are any patterns that emerge. You might need multiple functions that operate at different time points in different countries.
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