A Stochastic Model for Population Dynamics in Sudan During the Recent Armed Conflict

Entisar Alrasheed Sidahmed, Associate Professor

Abstract

In this study and in order to provide a theoretical framework to understand the behavior of the population dynamics under conflict we formulate and solve analytically the linear stochastic population model that describes the population dynamics in Sudan during the recent armed conflict. The war interval  defined as

   where   represent the start and end times of the war period respectively.

Before conflict the population dynamics are modeled stochastically using Geometric Brownian Motion (GBM), The conflict period is then captured by introducing the time depending negative drift term  to represent mortality, displacement and forced migration introduced in modelling of the population dynamics during the conflict. By applying Itô’s lemma, we derived the population trajectory, expected value and the variance during the war.

The analysis shows clearly that the conflict reduces the effective growth rate from r to r − , lowers the expected population size and increases demographic uncertainty which completely matched the reports on Sudan’s ongoing humanitarian crisis.