Birth rates decreasing means the population decreasing. even the same number of death should increase the death rate.
Well... increasing death rate can be due to two causes:
1. Overall ageing of the population: The number of deaths remain the same, but since the total population is declining, the death rate will increase (the calculation is no. of deaths x 1,000 / population).
2. Overall increase in the no. of deaths: As the case with HIV-affected nations such as Zimbabwe and Swaziland. The no. of deaths increases, as a result the death rate also increases.