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Predicting Further Values in a Set of Data


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Good day to everyone reading this. Thanks for your time.
I've got this question here (more like an research assignment) which requires me to predict further values in a given set of values.
I've attached a picture for a better understanding.
The data is the cases of influenza in a country over the years.
There's values missing in from May onwards.
We have to use the previous set of data, come up with a "Prediction model" and use that to predict the values until end of 2019.
The thing is, our teacher is very incompetent, and only told us to use "polynomials from the graphs we make in excel" and use that...
Anyone got any clues/hints on how i could come up with this prediction model? Please ask if you need any of the graphs. 
P.S. I used the polynomial of 6 for the graphing.
The graphing is done monthly, (Jan - December for a year)


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