Learn English – Which one is correct? “I am suffering from fever since yesterday” or “I am suffering from fever from yesterday”

Past tense denotes the completed state as of now. So it is not possible to use "since" as it implies uncompleted period (as of now).

Your textbook is oversimplifying things at best or just plain wrong at worst. To understand which to use in a negative sentence, you need to understand the difference between them in a positive sentence.

Present Perfect: She has sung at many opera houses.

The point here is that the action I'm speaking of is completed. At some unspecified point in the past, the woman I'm speaking of traveled to various opera houses and sang at all of them. Though she may no longer be singing, or no longer singing at multiple venues, this statement doesn't rule out those possibilities. Either fact is simply not relevant to my statement, I'm only talking about the performances she's previously given. Even though the actions I'm referring to are in the past, it is different from using the past tense in that regard.

Past: She sang at many opera houses.

This sentence has a similar meaning to the one above, but with some added implications. The singer may no longer be singing at opera houses (preferring other venues), may not be singing at all, or may even be dead. Regardless, that part of her life is behind her.

Present Perfect Continuous: She has been singing at many opera houses.

Again, the meaning is similar to the first example I gave, but the implications are the opposite of the example above. Just as the name implies, present perfect continuous indicates that the activity is continuous, starting at some point in the past (either specified or unspecified) and continuing up until now. In my example, she has been moving between opera houses and giving performances, and is still in the process of touring around.

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So now let me actually answer your question about negative sentences. In short, the differences in the meanings conveyed are the same.

Present Perfect: She has not sung at many opera houses.

Again, this is referring to an action that is complete and the future of her singing career is not the focus of discussion. This would be suitable in a statement such as: "She has not sung at many opera houses, but I always buy tickets when she does." My actions (buying tickets) are in the present tense. Using the future tense would not be natural here, since I am not making any comment on what she may or may not be doing in the future.

(Actually, you could use the future tense for buying, which would give a slightly different implied meaning to the first half of the sentence but I'm employing a little simplification of my own to avoid getting overly confusing. The future tense of 'buy' would only be wrong paired with the past tense example below.)

For the sake of completion, here's the negative example in past tense:

Past: She did not sing at many opera houses.

Again, her singing career (at least in opera houses) is over. In "She did not sing at many opera houses, but I always bought tickets when she did" my actions are unsurprisingly in the past tense as well, since I'm referring to a time grounded in the past.

Present Perfect Continuous: She has not been singing at many opera houses.

The number of performances she has been giving of late has been fairly low, and that is still the case.

"She has not been singing at many opera houses, but I always buy tickets when she does." "She has not been singing at many opera houses, but I will always buy tickets when she does."

My actions don't sound awkward in either the present tense or the future tense, since this a situation being continued. That allows you to speak of it in the present or project it into the future without sounding bizarre.

[You could also say that you have been buying tickets to either the present perfect or present perfect continuous examples, but that didn't sound like it would help to highlight the differences between them.]