Here are some graphs from reputable government sources which differ from those that are commonly used by anti-vaccine skeptics. In some of them you will notice clear depictions of mortality rates or the number of cases of common diseases that existed at various points in time. 

In all of them, you will see that large portions of various diseases were indeed dramatically reduced with the advent of improved health and sanitation measures but, were virtually eradicated after the use of vaccines became widely available. Remember also that death rates can be very low while the number of cases remains very high. Therefore, such graphs may indicate large drops in either mortality rates or in the numbers of cases, both of which are not uniformly impacted by the other.

This first one is a CDC composite graph showing the crude death rate for infectious diseases between 1900 and 1996. It clearly shows the benefits of better health practice, including  adding chlorine to water, the use of penicillin, the Salk Vaccine, and finally, the introduction of MMR vaccines used to combat infectious illnesses. After the passage of the vaccination Assistance Act. As you can see, improved sanitation and better health practices alone did not tell the entire story. 

In the graphs below, you can see how official charts show the true impact of vaccines on various infectious diseases.

 
https://www.cdc.gov/mmwr/preview/mmwrhtml/figures/m829a1f1.gif
 

 
https://medium.com/@visualvaccines/graphic-proof-that-vaccines-work-with-sources-61c199429c8c
 
 What should also be noted is the fact that, on the following graphs, particularly the graphs depicting measles morbidity rates (the number of cases)  and/or on graphs depicting large numbers of measles mortality rates (deaths) — the data will normally fluctuate wildly (as they may do on a lie detector) revealing that the person being tested is lying. But, in cases of the measles, long smooth changes on graphs, are not truly representative of how the measles progress. Note the many zigzags along the horizontal axis of the measles graph (above) which depicts how the number of measles cases normally vacillates over long periods of time. So, any graphs of the measles which depict long unvacillating or smooth changes should not be believed.

As you can plainly see above, when the inactivated measles vaccines was introduced in the early 1960s there were a bit less than 500,000 reported cases —which then plunged far lower by the mid to late-60s, and by 1991 virtually disappeared. However, we are currently dealing with another large measles outbreak, likely due to parents who have refused to have their children vaccinated. 
 
 

 
 

 
Polio death rates were indeed very high in 1915 and then took a dramatic drop, which could have been due to better health practices.

 But when the number of polio (cases) is examined, nearly 40 per 100,000/pop. existed in 1951. And, then, in only about six years, the number of polio cases shrunk dramatically after the inactivated polio vaccine was first used. It then decreased to almost nothing only 3 years after the oral polio vaccine was introduced in about 1961.

One of my cousins contracted polio in the 1950s and we heard he might have to have his leg amputated. But after receiving the polio vaccine, he recovered from the illness and walks today with only a slight limp — a prime example of how various aspects of any harmful illness need to be virtually eradicated, since death is by far not the only negative outcome possible.

 Modern-day parents don’t share the history that older people like me lived through, so it is easier for them to believe that their children are being made worse, or even killed in large numbers, by common vaccines — which is completely false!!
 

 
The same for diphtheria and pertussis  cases, both of which dropped dramatically after vaccines were available to completely overcome them.
 
 
A similar dramatic drop in chickenpox cases began around 1993 when health care standards were also equal to those of today (meaning that better health care alone) was not behind the drop in reported cases!
 

And, (you can see in the chart above) that chickenpox mortality rates also decreased rapidly, at a time when the quality of healthcare and sanitations was equal to that of today!

 
You can also see (beginning with the first graph), that the use of various vaccines has dramatically reduced the harm and frequency of these dangerous diseases. And while many tragic outcomes were indeed lessened due to improved health care measures, the use of modern vaccines obviously did the rest!