Let's imagine today is Thursday. Which should I say:
I haven't eaten anything since this Monday/since Monday.
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When you use the present perfect tense, there are usually two options, (1) use "for" to indicate a duration (period) and (2) use "since" to indicate the starting point of the period.
The determiner this is used with periods of time related to the present. You can use "this" in the sentence to indicate the last (past) Monday. But using "this" is not absolutely required because it would be easily understood from the context that you are referring to the past Monday as you are using the present perfect tense.
I haven't eaten anything since Monday (this week). - you may add 'this week' if the person you are talking to does not know the context. But if the context is so obvious, '...since Monday.' would suffice.
PS: I don't think an average person would survive easily without eating anything for almost two weeks anyway.