Markov Chain Models of Refugee Migration Data

TL;DR

This work presents a geography-aware, non-homogeneous Markov-chain framework to model local refugee movements on a daily timescale, using a graph of cities connected by roads and controlled by a distance threshold $D$. The approach computes transition probabilities from intermediate probabilities based on edge distances, enabling $B(t+1)=A(t)B(t)$ evolution and accommodating changing site types (Camp/Conflict/Neutral). Applied to the Burundi crisis with four variants (Initial Graph, Graph-adjusted, Camp-adjusted, Time-adjusted) and UNHCR data, the Camp-adjusted and Graph-adjusted variants yield improved long-term fit over the initial graph, with Time-adjusted removing the need for post-hoc rescaling while maintaining accuracy; the Camp-adjusted model achieves the best long-term ARD and outperforms a leading agent-based model by about 24% in long-term error. Overall, the Markov-chain framework offers a more efficient and scalable alternative to agent-based models for near-real-time refugee-flow forecasting and resource allocation.

Abstract

The application of Markov chains to modelling refugee crises is explored, focusing on local migration of individuals at the level of cities and days. As an explicit example we apply the Markov chains migration model developed here to UNHCR data on the Burundi refugee crisis. We compare our method to a state-of-the-art `agent-based' model of Burundi refugee movements, and highlight that Markov chain approaches presented here can improve the match to data while simultaneously being more algorithmically efficient.

Figures (7)

• Figure 1: (a). Location labels overlaid on a map of Burundi and surrounding regions (from Google Maps google). Note, Nakivale is located further north than illustrated. (b). A planar graph $G_P$ representing major roads connecting locations relevant to the Burundi refugee crisis as used in Suleimenova. (c). Non-planar graph representing additional routes connecting relevant locations, constructed by adding additional edges to the graph $G_P$ in panel (b), as detailed in Section \ref{['sec3']}.
• Figure 2: Plots of the population growth in each of the five major refugee camps relevant to Burundi refugee crisis predicted by each of our models as a function of timestamp (days). The four solid curves in each plot correspond to the four Markov chain models outlined in Section \ref{['sec4']} and the dashed curve is the UNHCR camp data from Suleimenova, the shading indicates a 10% error in the data.
• Figure 3: Total Averaged Relative Difference (ARD), as defined in eqns. (\ref{['ARD']}) & (\ref{['TARD']}), on each timestamp (day) for each of the Markov chain models. It can be seen that the refined graphs offer an improved fit of the data. Coloured curves match those in Figure \ref{['Fig2']}.
• Figure 4: The population of each camp at the final entry in the data set $(t=396)$ predicted by the Markov Chain: Camp Adjusted model as the maximum distance threshold $D$ is varied. The prediction for each camp is indicated by a different solid curve, the dashed lines indicate the population reported in the UNHCR data as given in Suleimenova. Notably, as $D$ is varied the number of edges in the graph varies as described in Section \ref{['sec2']}.
• Figure 5: Analogous to Figure \ref{['Fig2']} but here we compare our best model Markov chain: Camp-adjusted to the Flee model of SBG Suleimenova and also to Markov chain: Initial Graph. Note Flee and Markov chain: Initial Graph use the same graph, Figure \ref{['Fig1']}b, whereas the Camp-adjusted model uses the graph of Figure \ref{['Fig1']}c.