This is according to the Mail & Guardian:

During the period December 2013 to April 2018, we estimate that 1 177 600 deaths due to any cause occurred among people living in South Sudan, and that 794 600 deaths would have occurred under counterfactual assumptions. This yields an excess death toll of 382 900.

….. The first is that the researchers use different variables as proxies for mortality: proxies such as rainfall, climate, how much food is grown, the price of food (measured as “amount in kilogrammes of white flour that an average medium goat can be exchanged for”) and the presence of disease. This is how it works: if there is low rainfall, they know that people will struggle to get water and grow crops, so deaths are likely to go up. Using data from all around the world, they can make an ­educated guess about how many deaths were caused by a specific deficit of rainfall.

These proxies are combined with the limited survey data available to give an overall death toll for South Sudan in the relevant period. But the war didn’t cause all those deaths. It didn’t even cause most of them. Many deaths can be attributed to old age and natural causes; others to poverty and diseases such as malaria that would have happened regardless of the conflict.

Here is a summary of the state of the current iteration of the South Sudanese peace process.

And here is a documentary on the war economy and grand corruption in South Sudan.