The transition of E to I depends on S susceptibility. So it depends on the disease but also on herd immunity of the population, possible genetic factors and so on.

So it depends on the modelling technique - you take differential equations - how you implement the transition probability from S being E to I. Susceptibility may not be equally distributed in a population - differences due to age! I also may be split up according to severity of the disease manifestation. In some diseases there is an interval where someone is infected can spread the infectious agent but does not show signs of the disease. They show up some days later - that's important if you want to model separation of sick people as intervention. Also there are cases which get infected don't show signs of illness and are infectious. also it is possible that after being infected and sick persons are no longer susceptible - so an epidemic stops as the susceptible population decreases and the probability E targets someone with S+ decreases accordingly.

I recommend - describe the pattern of the natural course of the disease first.

Degree of susceptibility, time from E to I, probability going from S to I given E, way of transmission (sexually transmitted, food, blood, airborne, contact....), time being infectious , time being sick - severity of sickness (so probability to show up as incidence in monitoring systems), consequence of being I - getting sick, loosing S, being infectious. Their may be some other aspects in special diseases.  

So a lot depends on your choice of disease - if you go to hepatitis look up Uwe Siebert's work.

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Dear Sir,

Thank you for your precious response,

Actually, disease is viral and vector borne (Aedes sp.). Every new born is Susceptible and there is no upper limit of age. So, I am not considering age factor. In my compartmental model, I am assuming S as susceptibles which will be ~N at t(0). Then, Exposed and then Infected. At the end there will be a recovery stage.

Similarly, I am assuming the compartmental model structure for mosquitoes, S(m) E(m) I(m). In this, I am assuming an infected mosquito is never recovered. In this way, I have like 7 compartments. Now, I am thinking to fit my data to Infectious (I) humans, because data from epidemic is based on appearance of symptoms. 

I would like to get a suggestion from you, in the case of humans, I know how much human population (proportion) is in which compartment. But in the case of mosquitoes, how can I justify, for no initial condition data is available for mosquitoes. Should I guestimate it?

Your response is very precious, I am downloading all of the studies above, they might also shed some light on my issues.

Regards

Mazhar

Happy the answer was helpful

Looks like you address haemorrhagic fever like Dengue or Yellow fever (rift valley or chikunginya are other examples). I am a MD in Europe and as a GP no expert in this field. But I took a look at this two diseases and saw that for yellow fever there are 3 types of infection cycles described - a urban, a jungle and a savannah one.After infection there is lifelong immunity. Incubation time is 3-6 days - its not stated if persons can transmit the virus in this timespan (to mosquitos).

In Dengue you have an incubation time of 3-14 days. At the end of the disease there is permanent immunity only for the actual serotype - S for other serotypes remains. For Dengue there is also the possibility that the virus is transmitted vertically inside the mosquito population and there are also different transmission cycles described.

May be different for other viruses. -  So there is not "one" answer to your question.

Taking data from an outbreak means - maybe - a time of an urban transmission cycle. So the real starting point is First case minus incubation time. At this point the transmission cycles and therefore the characteristics of the mosquitos switch. In the incubation time the number of infected mosquitos - exposed and infected humans increase. During the outbreak = after verifying the diagnosis - the probability for exposure and infection should decline due to sanitary measures. How long lives a female mosquito? Taking this time you loose risk of exposure - in the urban transmission scenario. Taking the real life data and calculating back  when did you need how much S(m)/I(m) to generate the outbreak given a risk of E you get figures for risk and the start scenario _ switching transmission - fitting your concrete data. But then you have to check the literature if this is plausible....

Maybe with few individuals affected (on the human side) agent based modelling or discrete event simulation techniques would fit better?

Is it possible to apply some inverse problem in Statistics to identify the value of parameters used in your model? e.g., genetic algorithm, differential evolution, and etc. So, the incidence can be any form.