you would want to make a strategy that goes to both sides of the problem. there are not enough children being born/surviving birth and a lot of death.
the biggest thing one could do to raise birth rates is by encouraging an overall approval of children in the country as a blessing not a burden by the state. also keeping hospitals well armed for childbirth. therefore having all the medical tools and medication possible, sanitation practices, due diligence in nurses and doctors looking for any possible signs of birth complications or early health problems in mom and baby.
On the other hand, death will come no matter what . however good eating practices, general knowledge of good health by the general population, and no hesitation by a state's citizenry to go to the local doctor is very important. that's another point making health physicians and nurses available and known to the general public.
hope that helps
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Even though the Death Rate is high, the population can increase. This is possible if the Birth Rate and/or Immigration rate is higher than the death rate.