Studying the world population since 1650 suggests that demographic transition of a nation involves of 5 stages.These stages constitute the “demographic cycle”.(1) FIRST STAGE (High stationary)It is characterized by both*A high birth rate and*A high death rateTherefore the population remains stationaryIt is seen when the country is economically most weakIndia was in this stage till 1920(2) SECOND STAGE (Early expanding)It begins with the*Declining of death rate while*Birth rate still remains high.As a result a huge increase of population occurs. AinaiThe DR decline is mainly due to improvements in food supply, health care and sanitation)At present many developing countries of Asia and Africa are in this stageThe BRs have actually increased in some of these countries probably because of:– improved health care provisions, and– shortening periods of breast-feeding(3) THIRD STAGE (Late expanding)*Death rate declines further and*Birth rate now begins to fall.However, as the BR still exceeds the DR, there is an increase of populationThe fall in BR results mostly from access to contraceptives, women empowerment etc.India appears to be this stage.In some developing countries (e.g. China, Singapore) birth rates too have declined fast.(4) FOURTH STAGE (Low stationary)This stage is characterized withLow birth rate andLow death rateConsequently, the population remains stationary.An aging population is a feature of this stage.Japan, Sweden, Belgium, Denmark and Switzerland are in this stageMost industrialized countries have undergone a demographic transition*From a high BR and high DR*To low BR and low DR• Zero population growth has already been recorded in Austria during 1980- 85.• Growth rate as low as 0.1 was recorded in UK, Denmark, Sweden and Belgium during 1980-85. (5) FIFTH STAGE: (Declining)Birth rate is now lower than death rateHence the population begins to declineSome East European countries (e.g. Germany and Hungary) and some north European countries (e.g. Sweden, Norway) are now in this stage 
Beginning in the late 1700s, something remarkable happened: death rates declined. With new technologies in agriculture and production, and advancements in health and sanitation, a greater number of people lived through their adolescent years, increasing the average life expectancy and creating a new trajectory for population growth. This sudden change created a shift in understanding the correlation between birth and death rates, which up to that point had both been relatively equal, regardless of location. Over the past 300 years, population demographics have continued to evolve as a result of the relationship between the birth and death rates within a country. The observation and documentation of this global phenomenon has produced a model, the Demographic Transition Model, which helps explain and make sense of changes in population demographics. Using the Demographic Transition Model, demographers can better understand a country’s current population growth based on its placement within one of five stages and then pass on that data to be used for addressing economic and social policies within a country and across nations. 
Link.springer.com offers further information. Demographic Transition Theory (DTT) was developed by Frank Notestein in 1945. This theory provides an explanation of how fertility and mortality rates impact the age distribution and growth rate of populations. The ideals expressed in the DTT originate with the work of Warren Thompson in 1929, who described population growth using three categories of countries (groups A, B, and C). Group A includes Northern Europe, Western Europe, and the United States. These countries were predicted to experience a slow rate of population growth and eventually population aging and decline due to both low fertility and mortality rate. Group B includes Eastern and Southern Europe where both fertility and mortality rates decline; however, the decrease in mortality precedes that of fertility and occurs at a faster rate than that of fertility. Low rate of mortality coupled with higher fertility rate, would result in a period of rapid population growth and an increasing proportion of younger individuals…. (revised by Omero Abrams on April 7, 2020) 
Nhp.gov.in offers additional insight. Over time, the large bulge of population will move from working ages to old ages raising old age dependency. This would matter at the macro-level, but also at the micro or household level. Traditionally, supporting elderly parents has been the responsibility of working adults but low fertility means small families who would find it difficult to support elderly parents. This would then call for developing mechanism to provide old age support. At the national level, this matter does not seem urgent now but some states, the leaders in fertility transition, would face this issue soon. Population ageing will have a profound effect on the potential support ratio, defined here as the number of people of working age (25 to 64 years) per person aged 65 years or over. (a massive thanks to Abdiel Sharpe for bringing this to our attention).