question concerning Covid infection data reported by the media I tried searching stackexchange for existing posts about this, but I could not find them. Please redirect me if appropriate.
My question is very simple, and perhaps partly related to the observations made by several users in this post.
Let me explain the origin of my doubt, in two points.

*

*I am assuming that the most important population parameter for public health measures related Covid is the prevalence, i.e. the percentage of infected people in a given place.
The higher the number of infected people you are likely find in a group of $N$ interacting people, the higher the risk that the infection is transmitted.
This would explain why people who are known to be infected are subjected to quarantine in many countries, and why meetings in large groups are discouraged or even forbidden.


*as far as I can tell - and it seems confirmed by the post I linked above - you cannot estimate with any accuracy the prevalence of infections in a population if you take a biased sample.
So here is why I find media reports so far very puzzling: they always talk about absolute numbers of confirmed cases of infection, rather than prevalence, and always without any attempt to correct for bias, although the average number of tests per day has increased enormously since March, and the groups of people being tested are carefully selected by the authorities, thus highly biased.
A friend of mine, who knows a doctor working in a Covid ward, told me that he had exactly the same reaction to these data continuously being propagated by the media.
How can you possibly consider a sentence like 'an extra 100 cases of infection were recorded in the last 24 hours' to mean the same thing, regardless of whether it is based on 10000 tests run on a fairly random population, or instead on 100000 tests run on people coming back from high risk countries?
To be even more explicit and concrete, if I wanted to know how 'risky' it is to be in an enclosed situation with 100 people (picked randomly) from the population of a city or town, I would have to estimate how many of these 100 people are likely to be infected - and for this I need the prevalence.
How are the figures given by the media of any relevance to this, considering that they are based on absolute numbers obtained from a biased population?
There are some websites (sometimes even official government ones) where the number of infections, e.g. per 100000 people, is reported, often subdivided by geographical or administrative criteria. Do you think this is the 'real' prevalence, or is it still based on the biased evidence we seem to have? Do you know of any source of more reliable figures that could be consulted?
I can only hope that the public health protection measures being enforced by various governments are based on real science and on correct data analysis, because frankly the impression one gets from the media is one of confusion, misrepresentation of reality, miscommunication, quite suspiciously as if the actual goal was to create fear, panic and uncertainty and leave people bamboozled into submission to anything that the governments will decide next, regardless of the facts.
I am following the news from a few different European countries, and I can tell you, one day infections were 'up', the next 'down', then 'up' again, for weeks and weeks... Of course! Oscillations are expected, given the way they do tests. Don't you think that continuously switching between 'good' and 'bad' news is like providing no information at all, but just stupid chaos, in the eyes of the non-expert?
And in practice, given that the authorities test 'high risk' people and quarantine them if they are found to be positive, even if one had the 'real' prevalence, the number of infected people one is likely to meet in a given group is probably lower than the one that could be estimated from it.
So I am even less confident that any of what we are being fed by the media has any link to what is really relevant for the control of this infection.
Sorry, maybe I am not making sense, and in that case I would be glad if someone set the record straight and corrected me.
Otherwise, it would be interesting to know where we are going with all this, and why science isn't more prominently contributing at least to the correct representation of the facts.
 A: The prevalence is indeed an important number. The exponential growth in cases that we saw in many countries without protective measures/lockdowns illustrates exactly why prevalance is important and that your point (1) is indeed correct. It suggests a mechanism of spread that can be approximately described by each infected person (on average) infecting a number $R_0$ of other people. All the measures most governments are taking are about reducing that number (if you get it <1, the number of new case should eventually start declining).
The prevalence and the number of newly positively identified (usually through testing) cases is indeed not the same thing. Even if tests have no false positive, not everyone who is infected gets tested, so the number of positive tests is almost certainly an underestimate of the number of newly infected people. Secondly, prevalence is not just about how many are newly infected, but also how many people are still infected after being previously infected.
While positive tests are thus only one useful measure, we at least know the direction of the bias of the estimate they provide: the true number of cases is very, very likely to be higher. There are various other indicators that can tell us some things about the extent to which this is the case. These include the proportion of tests that are done that return positive (if this number rises without the policy for who gets tested changing, then the more cases are likely being missed), antibody tests on a large number of randomly selected individuals of a population (there is some controversy as to whether some of these were misinterpreted/mis-analyzed, but in principle doing such studies should be useful), the number of hospitalizations and/or ICU admissions (again difficult, if the admission policy changes), and the number of deaths attributed to COVID-19 or from any cause (although with a lag-time from infection to death to the numbers becoming public, which makes this difficult to use).
So, I would not call it "biased evidence", but rather a lower bound (or underestimate).
I would agree that it is important that the media not over-emphasize day-to-day fluctuations in inherently random outcomes (where I live, I do not think the press has done this, but this can of course vary from country to country or even from one publication/news channel to another), but over severals days or weeks general trends can be sensibly looked at.
And because numbers are to an extent a lower bound (in some places where testing is less than it should be given the high prevalance probably more so than in countries that do thorough testing), it is to some extent important to look at the relative trends rather than the absolute numbers. I.e. even if in a place 50% of cases are missed, if the number of positive tests are with all else being approx. equal going up, then we at least know the number of cases is going up (=$R_0>1$ = unless something is done cases will keep exponentially increasing).
The extent to which prevalence is a cause for concern about further spread depends on a lot of things: Firstly, if the true prevalence keeps risings (as indicated by, say, more positive tests), then clearly infections are still happening and not being stopped (part of it can of course be spread before/without people becoming symptomatic). Secondly, even if everyone who is infected were tested, it matters when they get the results and whether/when they take measures to stop the spread (e.g. with too much of a delay a test may not help much, or if economically people cannot afford to stay home, then a positive test may not help etc.). So, people getting told to self-isolate once a positive test comes back does not necessarily remove concerns.
A: Yes, the use of the term “prevalence” is tricky for viruses during a time when the virus is being actively spread and people are becoming immune.
Epidemiologists describe the measurement and reporting of prevalence in relation to the timeframe of the estimate.
Point prevalence is the proportion of a population that has the condition of interest at a specific point in time—a given day, or week, or month.  Point prevalence is often used to describe the population burden of a condition that might come and go—like depression or pain.
Period prevalence is the proportion of a population that has had the condition at any point during a stated time period of interest.  For chronic diseases, “past 12 months” is commonly used.
Lifetime prevalence is the proportion of a population who, at some point in life, has had the condition.
Here is a publication in which point prevalence (30-day), period prevalence (12 months), and lifetime prevalence of generalized anxiety disorder were estimated.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5594751/
POINT PREVALENCE OF VIRAL INFECTION
For the SARS-CoV-2 virus, a measure of interest in terms of the likelihood of viral spread is the point prevalence of infectious people in a given (small) interval of time—the proportion of people who are infectious today (or in a given week).  This is the number of people who would have a positive RT-PCR test for the virus if everyone had a RT-PCR test on a given day (or in a week) divided by the total number of people in the population.  To be useful, this measure would be specific for a geographic area.
Point prevalence could also be measured by doing RT-PCR tests over a specified (short) period of time on a representative sample of people and dividing the number of people with a positive RT-PCR test by the number in the sampled population.  One study, conducted in Slovenia, did this and the results have been published.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7367804/
The point prevalence measured on an entire population or on a sample is a quantity that changes over time.  It decreases as the proportion of the population that has been infected increases because there are more people who have become immune (assuming these people can’t be re-infected).  And it increases or decreases because of changes in the spread of the virus that occur due to people’s behavior.
For many reasons, the estimate of the point prevalence of SARS-CoV-2 infection that is of greatest interest--what proportion of the population is able to transmit the virus right now--is virtually impossible to measure for an infectious disease that is actively being spread in a population.
The number of people who have a positive RPT-PCR test for the SARS-CoV-2 virus on a given day (or in a given interval) divided by the number of people in the population is a poor measure of point prevalence because not everyone who is able to be infected gets tested in a given interval of time.
PERIOD PREVALENCE OF VIRAL INFECTION
For the SARS-CoV-2 virus, period prevalence—the proportion of the population that has been infected with SARS-CoV-2 in some defined prior period of time—can be estimated by conducting serosurveys.  A serosurvey is a study in which a representative sample of people in the population have their blood drawn and tested to see if they have antibodies to the SARS-CoV-2 virus, indicating that they have been infected in the past.  To accurately estimate period prevalence, response rates in serosurveys need to be high and the antibody tests used must be very good.
The CDC describes detailed plans for conducting serosurveys of the US population to answer a large number of questions about the epidemic.
https://www.cdc.gov/coronavirus/2019-ncov/covid-data/serology-surveillance/index.html
A protocol to conduct a study that would estimate the period prevalence of SARS-CoV-2 infection for the United States has been written and published.
https://pubmed.ncbi.nlm.nih.gov/32791199/
LIFETIME PREVALENCE OF (PAST) VIRAL INFECTION
If no vaccine against SARS-CoV-2 is developed, someday in the distant future, it would be possible to estimate the lifetime prevalence of infection with the SARS-CoV-2 virus by doing a serosurvey of very old people.  If a vaccine is developed, it might not be possible to identify antibodies that form because of “natural” infection and those that develop because of vaccination.
OTHER
Measurement of antibodies in blood samples leftover from tests for other reasons was used to assess the prevalence of past SARS-CoV-2 infection for a “convenience” sample of geographic sites in the United States.  The number of people who were estimated to have been infected (which could be seen as a period prevalence where the period is “start of pandemic” and the cut-off date for the measurement of antibodies).  The publication about this study reported that:
“….six to 24 times more infections were estimated per site with seroprevalence than with coronavirus disease 2019 (COVID-19) case report data…”
https://jamanetwork.com/journals/jamainternalmedicine/fullarticle/2768834
