You will not have issues in 99% of the cases. However you cannot be sure since this depends on the source AND target country AND on recent events of infections. If there was a recent infection, they might ask you some questions and/or do a temperature check in most of the cases.
There are 2 main reasons for the questions on immigration forms that relate to health issues.
- Trying to determine if they should check you before they allow you into the country
- Trying to find you or back-trace infection sources later in case they find out that an infected person arrived on your flight.
In 99% of the cases, No 2 will apply.
Some of the forms ask you how you feel (cough, fever), where you sit in the airplane, where you have been in the last 1-2 weeks, and where you will stay in the arriving country, contact information and so on.
For example: lot of Asian countries, where trading in live poultry is common, had their share of bird flu occurrences over the last 7 years. During an alert, they ramped up the screening and sometimes also the contents of those cards quite a lot. They started routine temperature checks in airports where passengers arrive. Sometimes they would give you a second card to fill out depending on the latest issues, asking for more specific items, such as if you handled raw poultry meat or touched animals.
The attempt to track you down is needed when there is a confirmed case of someone being infected with a contagious disease without having been in a dangerous area. The Airline will then conclude that the infection has happened in the Airplane and will try to find all people that have been sitting in the vicinity of the victim to check if they have also been affected and on top of that, with the question where the person has been before, determine who was the source of the infection. With such information they for example they tracked back a sick person with bird flu and subsequently quarantined a complete hotel in Hong Kong 2-3 years ago and locked down all customers (including a prostitute with her customer).
What does not exist to my knowledge however is that anywhere they would either generally bar you or examine you in 100% of the cases just because you come from a certain place - with the exception of automated temperature checks through IR cameras.
This is also recognizable if you simply observe the flights from and to places. There are for example dozens of flights from Africa to Australia. However they do not examine 100% of the arriving passengers on arrival and of course also do not block them from entering.