# Detecting the sensitive spots of the African interurban transport network

ARAndrew Renninger  VMMValentina Marin Maureira  CC-ACarmen Cabrera-Arnau
RPCRafael Prieto-Curiel  Centre for Advanced Spatial Analysis (CASA),
University College London, Gower Stondon, WC1E 6AE London, UK  Department of
Geography and Planning University of Liverpool, Chatham St, L69 7ZT Liverpool,
UK  Complexity Science Hub, Josefstädter Str. 39, 1080 Vienna, Austria

###### Abstract

Transport systems are vulnerable to events that create disruptions. This
situation is particularly sensitive in parts of Africa with a low density of
highways and an increasing level of violence. Here, we measure the risk of the
African transport network based on two separate indices: the intensity of
future events $\mu$ and the impact $\nu$ of one event on the flow that travels
through the network. To estimate the intensity of future events happening in
city $i$, we construct a self-exciting point process. To estimate the impact
of an event, we consider a network of all highways in the continent and a
modelled flow between any pair of cities. Based on both indicators, we
construct the $\mu-\nu$ diagram and classify cities based on their combined
impact and intensity. Results show that certain cities in the network have a
high risk and increase the vulnerability of Africa’s infrastructure. These
cities have a high propensity for suffering subsequent violence against their
civilians, and given their connectivity structure, they also substantially
affect the overall regional functioning. Removing just ten edges would require
rerouting 32% of trips according to our model. The top 100 edges where
violence might happen account for 17% of the trips. We find that cities with
the highest $\mu-\nu$ risk are those characterised by small and medium size
and large degree, meaning they act as hubs. Vulnerable areas tend to be
characterised by the presence of terrorist groups like Boko Haram in Nigeria.

Research

##  1 Introduction

Transport systems are vulnerable to congestion, weather, and other events that
create delays and disruptions or isolate entire regions ganin2017resilience ;
maureira2017everyday . This situation is particularly relevant in parts of the
African transport network for three reasons. First, Africa has a vast and
fragmented territory, and the density of highways is reduced compared to other
parts of the world, so few alternatives exist in the case of a network
disruption. Second, the lack of resources and infrastructure makes the market
of goods in the continent susceptible to increases in transportation costs.
And thirdly, because of the increasing violence against civilians in the
region. It is estimated that between 2001 and 2021, the number of casualties
attributed to violence against civilians in Africa has increased 260%
raleigh2010introducing . Terrorist groups use the fragility of the network to
increase their control in some areas and the impact of their attacks. These
problems will likely intensify due to extreme weather conditions. Droughts and
extreme heat are correlated with violence, with a standard deviation rise in
annual temperatures corresponding to an 11.3% rise in the rate of intergroup
conflict, and a standard deviation rise in drought conditions corresponding to
1.3% rise in the chance of conflict in an area burke2015climate ;
harari2018conflict .

Here, we aim to measure the vulnerability of the African transport network
based on two separate indices: the intensity of events affecting a specific
location and the impact that an event has on the estimated flow that travels
through the network.

We use data from Africapolis and the network of all highways in the continent
constructed from OpenStreetMap Africapolis ; OpenStreetMap ;
prieto2022detecting ; prieto2022constructing . Major highways and roads are
considered within the urban network, so it is possible to compute a gravity-
based estimate for the flow between any pair of cities and assign it to the
shortest route between them based on existing infrastructure. We construct two
metrics to capture the vulnerability of different locations within the
network. First, the _impact_ that a violent event in a specific location could
have in terms of disrupting the flow. This impact is computed based on the
flow that would be observed if a node is removed. Second, the _intensity_ at
which violent events happen in that location. To estimate the intensity of
violent events, we use data from the Armed Conflict Location & Event Data
project (ACLED) that monitors political violence across Africa, and other
parts of the world, mainly from local media reports raleigh2010introducing .
We construct a self-exciting point process to determine the intensity of
events happening at some location based on previous events nearby. Thus, for
each node in the network, we construct its daily intensity $\mu_{i}(t)$ and
its impact on the network flow $\nu_{i}$.

We detect that a few nodes in the network are likely to suffer future events,
and their impact on the infrastructure is surprisingly high. We find that the
cities with the highest risk are those characterised by small and medium size
and high city degree, that is, cities which create transport shortcuts in the
network that otherwise do not exist. We show that these areas tend to be
characterised by terrorist groups like Boko Haram in Nigeria and Al-Shabaab in
Somalia.

##  2 Literature review

###  2.1 Violence against civilians in Africa is increasing and concentrated

Data from the Armed Conflict Location & Event Data project (ACLED) is captured
mostly from local media and gives the location, dates, actors, fatalities, and
types of reported political violence and protest events worldwide
raleigh2010introducing . Between 2000 and 2021, ACLED reported over 250,000
events in Africa, with over half a million casualties, including nearly 64,000
events registered as violence against civilians. During 2021, 23 events daily
can be considered violence against civilians in Africa, causing nearly 43
fatalities. This means an increase of more than 400% in the past ten years.

Violence against civilians has four key aspects. First, few events account for
most casualties ZipfTerrorism ; guo2019common . Of the 8,000 events classified
as violence against civilians in 2021, the top 5% most violent account for 52%
of the casualties. Thus, roughly one daily event causes half of the civilian
casualties in Africa. Second, is that violence is primarily urban
radil2022urban . Most violent events happen inside or nearby cities and are
suffered directly by their population. Third, violence is highly
heterogeneous, meaning that some cities have high levels of violence, whilst
others are relatively peaceful ViolenceNorthWestAfrica ; buhaug2008contagion .
For example, Mogadishu (Somalia) had nearly 100 casualties in 2021 related to
violence against civilians, whilst Abuja (Nigeria), with a similar population,
had only one casualty raleigh2010introducing . Finally, violence has some
stability across time, meaning that if a city is peaceful for one year,
chances are that it will remain peaceful for the subsequent years. In
contrast, violent cities also tend to remain violent for years. For instance,
Mogadishu (Somalia) had nearly 100 casualties in 2021 related to violence
against civilians, but it had more than 100 casualties each year for more than
a decade, whilst Abuja (Nigeria) had only one casualty in 2021, and it had the
same low violence well over a decade. Thus, although violence against
civilians is increasing in Africa, it is due to some events highly
concentrated in a few cities. As observed in other parts, violence is highly
concentrated in a few locations, and they tend to be stable over time, meaning
that it is possible to use data from past events to forecast the intensity of
future ones LawCrimeConcentration ; CrimeConcentrationVaryingCitySize .

We use that violence against civilians is highly concentrated in a few
locations and is relatively stable over time to model its temporal patterns.
The Hawkes process is a mathematical model for a ‘self-exciting’ process
hawkes1971spectra ; chuang2019mathematical . The model is based on a counting
process of a sequence of ‘arrivals’ of some event over time, for example,
earthquakes, gang violence, trade orders, or bank defaults
MohlerExcitingPointProcess ; laub2015hawkes . It is based on the idea that
after a major shock, the probability of subsequent events is high. For
example, if an earthquake occurs, replicas are expected. Similarly, after a
recent attack, chances are that the circumstances that promoted it still
prevail, so more events are also expected porter2012self ; yuan2019fast ;
telesca2006global ; clauset2013estimating . The Hawkes process is a non-
Markovian extension of the Poisson process that records recent events. In a
Hawkes process, we assume a time-varying intensity $\mu_{i}(t)$ that depends
on all the events in city $i$ up to time $t$. The Hawkes process produces the
intensity function $\mu_{i}(t)$, which can be interpreted as the “temperature”
of city $i$. It is a combination of all recent events up to time $t$ that
enables us to obtain a daily description of events in city $i$. Furthermore,
the function $\mu_{i}(t)$ enables us to construct some metrics for that city,
for example, the per capita intensity.

Not all events cause the same impact. For example, in 2021, more than 8,000
events were classified as violence against civilians, but five events caused
more than 100 civilian casualties, whilst more than 4,000 events had no
casualties. Thus, one way to measure the severity of an attack is by the
number of deaths ZipfTerrorism . In a similar way in which an earthquake with
a higher seismic intensity is expected to have more replicas, we assume that
an event with more casualties causes a higher impact and likely more
subsequent reactions.

###  2.2 Urban networks are vulnerable

The location of cities relative to others has relevant socio-economic impacts.
Cities near major urban regions can benefit from borrowed agglomeration
economies meijers2016borrowing . Economic activities distribute themselves in
response to geographical centrality StreetNetw . Proximity, however, does not
accurately capture accessibility or travel distance, but details concerning
barriers, obstructions and the existing infrastructure are needed to capture
city interactions. Considering different cities as nodes and the road
infrastructure between them as the edges of a network is one of the most
natural ways to analyse city interactions barbosa2018human . Networks provide
a structured model and different conceptions and measurements of centrality.
As with every model, certain simplifications are made, favouring others, for
example, deciding which roads and which cities to analyse, defining when a
road passes through a city, or detecting when two road segments are connected.

Based on a network, there are many ways to measure a node’s importance, for
example, by its degree or a combination of its degree and the degree of
neighbours or other node attributes buechel2013dynamics ; singh2020node . Node
betweenness is a commonly used metric that gives the number of times a node
occurs in the shortest paths between all possible pairs of nodes in a network
freeman1978centrality . However, we use a weighted node betweenness to detect
the importance of cities. The weights correspond to a combination of two urban
properties: the cities’ population and the distance between them. More
journeys are expected to happen to and from bigger cities, and fewer journeys
are expected between distant locations. Thus, we combine both factors using a
gravity model to estimate the number of interurban trips, which is one of the
most widely-used models for considering the strength of interactions between
spatial units, in this case the flow of people. The gravity model generally
uses population size and the physical distance, the road distance or the
travel time between origin and destination to estimate the number of journeys
between two cities Gravity . The procedure for obtaining the weighted
betweenness based on the gravity model is our method to asses the relevance
that a city has within a network. Cities with high intermediacy receive
considerable traffic. If traffic through a city with high intermediacy is
disrupted, consequences for inter-city travel are high.

Here, we aim to decode urban hierarchies by analysing the connectivity of
cities and detecting the impact of the flow between them when one is removed
from the system ArcautePercolation16 . The removal of cities from the system
aims to capture a scenario when journeys through a city are no longer possible
due to the presence of a violent group. If violence becomes dominant in a
city, then journeys that would be routed through that city must find an
alternative and frequently longer route. Thus, some journeys between cities
will ultimately be discouraged due to violence.

##  3 Methods

For the constructed network of African interurban highways, we compute two
metrics. One is used to proxy the intensity of violence or risk that a city
has a sizeable disruption, and the second metric is used to detect the impact
of a disruption in terms of the network. Both metrics are constructed at a
city level, so we have the intensity of events, $\mu_{i}(t)$ and the impact
$\nu_{i}$ for city $i$.

###  3.1 Measuring the intensity of events

Although there are many expressions for a Hawkes process laub2015hawkes , we
express the intensity for city $i$ as $\mu_{i}(t)$ as

$\mu_{i}(t)=\sum_{s:t\geq t_{s}}\kappa_{s}\exp(-\phi(t-t_{s})).$ (1)

Equation 1 only considers events that happened before some time $t$ measured
in days. The intensity $\mu_{i}(t)$ increases (jumps) in $\kappa_{s}>0$ units
immediately after the occurrence of an event at time $t_{s}$, and the
intensity decays exponentially with time at rate $\phi>0$. For an event taking
place at time $t_{s}$, we set the parameter $\kappa_{s}$ to be equal to the
reported number fatalities. Other definitions of $\kappa_{s}$ could depend on
the size of the event (number of protesters, for instance, or number of police
officers employed), the state intervention (number of arrests), the social
media impact (number of tweets related to the protest), or the media coverage
(the space devoted in the newspapers to such event). The parameter $\phi$ is
the “cooling” parameter of the Hawkes process and refers to the speed at which
one event is more or less significant in future days. With high values of
$\phi$, the process has a faster memory decay, in which case, $\mu_{i}(t)$
captures the number of casualties of recent days. The number $\mu_{i}(t)$ is
the expected number of casualties in city $i$ at time $t$ considering all
events in $[0,t]$. The value of $\phi$ used is the same for all cities
(assuming a homogeneous cooling-down effect), and it is estimated by
maximising the correlation between $\mu_{i}(t)$ and the observed number of
casualties in all cities during the two weeks after time $t$. Therefore, the
obtained $\mu_{i}(t)$ gives the best estimate of casualties in the upcoming 14
days. The estimated value of the cooling parameter is $\phi^{\star}=0.0987$.
More details about the estimation process are in the Supplementary
information. The result is $\mu_{i}$ for each city, which we then project to
the edges around it with a simple average to create $mu_{ij}.$

###  3.2 Estimating the flow between cities

To estimate the flows of goods and visitors along each path in the network, we
construct a gravity model based on available data. This assumes that the flow
between cities $i$ and $j$ is a function of the road distance between them and
their population. The predicted flow of people between location $i$ and
location $j$ is modelled as Equation 2

$F_{ij}=k\frac{P_{i}\times P_{j}}{d_{ij}^{\beta}}$ (2)

where $F_{ij}$ is the flow, $P_{i}$ and $P_{j}$ are the populations of the two
locations, respectively, and $d_{ij}$ is the road distance between them. $k$
is used to normalise all flows so they sum to 1, thus conveying a share of all
flows rather than the number of travellers using the road. We construct our
estimate without fitting to observed data, so we test the sensitivity of our
results to various values of $\beta$, including values obtained from the
literature on migration in Africa prieto2022detecting . For the purposes of
experiments that follow, we use $\beta=2.8$, but checks for robustness are
included in the supplementary information. We limit the maximum travel
distance in the model to 3,500 km, equivalent to the distance from Lagos (in
Nigeria) to Dakar (in Senegal). This value represents the span of an aspiring
economic corridor and an area of proposed economic cooperation
/content/publication/9789264265875-en . The gravity model gives us flows
between cities in the network. We then project flows between $i$ and $j$ for
all $F_{ij}$ along the shortest path $P_{ij}$ in the African urban network
described above to give us $\nu_{ij}$. The total flows into a city are summed
to construct $\nu_{i}$.

###  3.3 Percolation and violence

We use two approaches to understand the resilience of the interurban network
to shocks. The first samples edges in the network in proportion to conflict
intensity $\mu_{ij}(t)$ until we are left with an empty graph, with all cities
isolated from others. The remaining strategy assumes that violence is
correlated with the potential to spill from one location to another. A Mantel
test (a statistical test of the correlation between two matrices)
mantel1967detection  whether the distance between events in time is correlated
with the distance between those events in space and uses a simple Pearson
correlation between the spatial distance matrix and temporal distance matrix.
In our data, the location of violence in space and time is not correlated over
the entire period ($r=0.1$, $p<0.05$), when we split the data by country and
year, a third of the space-time partitions have $r>0.5$—likely because our
dataset covers such a long period that simple correlations do not capture the
peaks and troughs in violence. Knox tests (a test for space-time interaction
using space and time distances) Knox  also show that we see far more attacks
that are close in space and time than we would expect to occur by chance. We
can also look into the data and see that in 2013, militants took control of
three towns in Mali: Kidal, Gao and Timbuktu. In 2016, Djibo, Arbinda and Dori
in Burkina Faso came under the influence of militant groups. These tests
confirm other work, which shows that conflict in one area raises the chance of
conflict in adjacent areas harari2018conflict .

#### Percolation.

Here, we borrow from ArcautePercolation16 ; maureira2017everyday  to remove
nodes from the network and observe changes to its properties. Rather than
removing nodes at thresholds according to distance or risk, we use a
stochastic approach. At each step of our methodology, we sample an individual
edge in proportion to conflict intensity $\mu_{ij}(t)$, remove it from the
network, and monitor the changes to the network that are triggered by the
removal of the edge. We proceed, gradually removing edges according to
$\mu_{ij}(t)$ and thus —with some variance— move across the intensity
probability distribution. We allow the network to accumulate damage,
simulating the effect of prolonged and cascading conflict. Although a network
spanning the continent will not see broad enough conflict to disrupt the
network to the extremes we test here, the patterns shown can reveal aspects of
the network structure.

#### Cascading events.

We then use a form of bursty percolation, which assumes that violence can
spill over from one area to another in each round but does not allow damage to
accumulate as before: we reset the network each round and run repeated
simulations. In this approach, we draw an edge from the network with a
probability proportional to its intensity $\mu_{ij}(t)$ of conflict and remove
it. We then take all edges within 100km of the seed edge and perform Bernoulli
trails for each. In these trials, the probability of failure at proximate
edges is weighted by the intensity of conflict associated with each edge. This
is akin to performing a biased coin flip, where the level of violence
determines the coin’s bias. Each edge that “fails” is also removed from the
network along with the seed edge. At the end of each round, we compute a
series of statistics to measure the damage done. We reconstruct the entire
network after each round and observe the distributions of these statistics to
the network after 1000 rounds, simulating the effect of limited but cascading
conflict.

###  3.4 Measuring the impact of node removals

At each step of the percolation, we track the population of the largest
component as it fragments due to conflict along the network, the population of
all isolates created by the attacks on the network, and the percentage of all
flows that need to be rerouted to preserve trade and migration on the
continent. First, the largest component: by monitoring the size of largest
component —weighted as its total population— we look at threats to economic
integration on the continent, which requires trade and migration between
cities. Second, isolates: a simple measure of the affected population is the
total population of all isolates created at each step of the process as we
remove edges. Third, affected flows: what percentage of flows rely on edges
removed in the percolation?

We also compute a detour (in km) resulting from rerouting flows between a pair
or origin and destination nodes which can no longer take place through the
shortest path due to road disruption. This measure does not use gravity
estimates and it is based strictly on the network road network.

##  4 Results

The intensity $\mu_{i}(t)$ of future events is estimated by adding the number
of casualties in city $i$. Each event is affected by memory decay. One
casualty in the city at time $t_{s}$ has an immediate effect of adding one
unit to the intensity, so $\mu_{i}(t_{s})=\mu_{i}(t_{s}-1)+1$. However, as new
events happen, the value of past information decreases. We obtain that after
one week, one casualty adds only 0.5 units to
$\mu_{i}(t_{s}+7)=\mu_{i}(t_{s}-1)+0.5$. After one month, one casualty at time
$t_{s}$ only adds 0.05 units to the intensity, so
$\mu_{i}(t_{s}+30)=\mu_{i}(t_{s}-1)+0.05$. Thus, unless more casualties occur
in the city, the intensity $\mu_{i}(t)$ cools down after time $t_{s}$.

Figure 1: Observed values of the intensity of events $\mu_{i}(t)$ (vertical
axis) between 2013 and 2022 in four major cities in Africa, with recurrent
violence in Mogadisho and fluctuations elsewhere.

For some cities, such as Mogadisho (Somalia), the intensity $\mu_{i}(t)$ is
maintained with high levels, indicating an intense and stable violent process.
In other cases, the intensity $\mu_{i}(t)$ reflects specific moments, such as
elections or conflict. High values of $\mu_{i}(t)$ correspond to significant
outbreaks of violence in that city. For example, the rate in Cairo (Egypt) had
values above 500 in 2013 during Egypt’s coup d’état, indicating more than 500
casualties per day (Figure 1). A similar value was observed in Mogadisho
(Somalia) in 2015 during its bombings. In Bangui (Central African Republic),
roughly 300 casualties were observed daily between 2013 and 2014,
corresponding to its conflict. During the 2020 national elections in Ivory
Coast, there was also an increase in the daily casualties in its main city,
Abidjan, but the daily number of casualties was below ten units during the
whole period. Figure 9 in supplementary information shows how conflict is
evolving as violence increases in West Africa, decreases after the Arab Spring
in North Africa, and persists in the Horn of Africa.

###  4.1 Relationship between impact and intensity

We identify edges and nodes with a high impact disrupting the network
$\nu_{i}$. Edge impact is derived from flows along those roads; for node
impact, we recast these weights so that each node is assigned an impact
according to the sum of flows to and through it according to the gravity
model. Generally, cities with high traffic are characterised by a high
centrality, creating shortcuts in the network between big cities. Because of
its population, most cities in Egypt have a high impact on the network, as
removing them would reduce integration in the country. The same pattern occurs
in parts of Nigeria. Cities with a low impact are more isolated, tend to have
a smaller degree, or are adjacent to redundant travel options. For example,
cities in South Africa tend to have a small impact, as well as cities in
Ethiopia. They reflect either high isolation from the network or rich
connection to it (Figure 2).

Figure 2: Relationship between conflict intensity and mobility aggregated to
cities, with the size of the dot indicating the size of the city, showing the
confluence of high intensity and high mobility in West Africa, while in
populous areas in North Africa there is the flow between cities but—especially
in Egypt in recent years—the absence of violence. Violence in Ethiopia and
Nigeria rose between 2014 and 2022.

We analyse the intensity of cities $\mu_{i}(t)$ for $t=2022$. That is, we
observe the 2022 year and analyse the expected levels of violence for future
days. Most cities in North Africa have low intensity, reflecting fewer violent
outbreaks in the region. However, cities in Nigeria, Burkina Faso, Somalia or
Ethiopia have higher intensity, reflecting recent episodes of violence (Figure
2). By looking at different periods we can look at how these patterns are
changing; we map $\mu_{i}(t)$ for $t=2014$ for comparison. Conflict in
Nigeria, in particular, is growing.

Based on the propensity for future events and the impact that an intervention
could have, we identify nine groups according to their $\mu-\nu$ colour
(Figure 2). The colour assigned to each city is the $\mu-\nu$ diagram of
cities. Group 1-1 are cities with low impact and low intensity, meaning that
due to violence, there are few events expected there, but also, if some
outbreak of violence occurs, the impact will be reduced. In Africa, there are
280 cities with a population of 18 million in this group. In total, cities
with the lowest risk of conflict represent 13.5% of the continent’s urban
population. We report disaggregate these results by class and region in Table
1.

Group | Africa | North | West | East | Central | South
---|---|---|---|---|---|---
($\mu-\nu$) | cities | pop | cities | pop | cities | pop | cities | pop | cities | pop | cities | pop
1-1 | 280 | 18 | 110 | 8 | 48 | 2 | 34 | 2 | 40 | 2 | 48 | 3
1-2 | 207 | 15 | 85 | 7 | 39 | 2 | 24 | 2 | 18 | 1 | 41 | 3
1-3 | 161 | 23 | 114 | 18 | 17 | 1 | 6 | 1 | 3 | 0 | 21 | 2
2-1 | 181 | 19 | 37 | 3 | 46 | 4 | 41 | 6 | 26 | 3 | 31 | 4
2-2 | 178 | 24 | 42 | 7 | 54 | 7 | 28 | 4 | 15 | 1 | 39 | 5
2-3 | 190 | 81 | 119 | 61 | 24 | 4 | 11 | 2 | 6 | 0 | 30 | 14
3-1 | 118 | 15 | 11 | 4 | 42 | 3 | 10 | 2 | 14 | 2 | 41 | 4
3-2 | 217 | 54 | 17 | 3 | 87 | 22 | 19 | 2 | 13 | 2 | 81 | 25
3-3 | 241 | 164 | 11 | 10 | 121 | 66 | 31 | 31 | 25 | 20 | 53 | 37
Table 1: Number of cities and population (in millions) assigned to separate
$\mu-\nu$ groups per continent region.

Many cities in the highest $\mu-\nu$ class have the largest populations, so
the 241 cities in this group represent 163 million inhabitants or 39% of the
total. There is significant violence in West Africa, a populous and busy
economic corridor home to Africa’s largest economy (Nigeria) and largest city
(Lagos), and many cities at risk in East Africa. There are some cities with a
high impact $\nu_{i}$ and a high intensity $\mu_{i}(t)$, reflecting locations
where a violent outbreak is likely to happen and where the impact in the
network could be huge. This is the case, for example, for cities in Kenya,
such as Nairobi. Although its levels of violence are smaller than elsewhere
(including cities in Somalia), its network position creates a higher impact.
There are just 23 million people in the low risk, high flow—and thus
peacefully integrated—condition.

We check pairwise correlations between $\mu_{i}$ and $\nu_{i}$ along the edges
in 2022 to see if the conflict is associated with the flow on the network. We
can imagine a world where conflict occurs peripherally because people may be
drawn to violence or terrorism when economic opportunities are limited
harari2018conflict , but it may also be the case that conflict requires people
as well as activity and is thus centrally located. Without a more robust
empirical strategy, we cannot decompose cause and effect, but we can explore
whether or not the important corridors are also prone to conflict. This is
important because it indicates whether or not violence poses a risk to or is
limiting Africa’s integration and economy. Figure 3 shows this relationship on
aggregate and by region.

The strongest correlation is in the South, including a high $\mu-\nu$ along an
edge connecting Johannesburg, in South Africa, to the network—a path
facilitating 16% of all flows. Many of the highest combined $\mu-\nu$ values
are in the West, with a road between Ikorodu and Lagos in Nigeria. This road
accounts for 4% of all flows according to the gravity model. Both of these
cities are important hubs in the network and vital centres of activity in the
economy.

Figure 3: Intensity of conflict $\mu_{i}(t)$ (horizontal axis) and impact
$\nu_{i}$ (vertical axis) in 2022 according to the region. Areas where
violence and mobility interact are represented by points in the top right
quadrant. Critically, many edges in the network that bridge regions have high
levels of conflict.

We also look at the detour resulting from the removal of an edge. This is the
change in average shortest path (km) on the network after removing that edge.
This varies from 1 km to 10 thousand km. Most of the largest detours,
highlighted in Figure 4, cross regions, indicating that economic integration
would become more costly if violence occurs in these areas. Aside from
crossing roads, the highest detours are in the North and East, while the South
and West have redundancy.

Figure 4: A The relationship between conflict, impact and detours, defined and
the change in the average shortest path (km) after removing the edge, along
with the distribution of detours. The five largest detours—including the
largest two crossing the Sahara—are highlighted. B The distribution of
detours: most are just a few hundred or thousand km, but some reach 10
thousand.

###  4.2 How robust is the system?

The impact of a network intervention is measured by the number of people that
would be removed from the connected component (Figure 5). Results show that
East Africa has the highest vulnerability since a network disruption would
disconnect more people. Many of the most prosperous and populous cities are in
North and West Africa, so even though we see these regions less prevalent
across simulations—compared to the East—they represent a disproportionate
amount of potential damage to the network when conflict does occur in those
regions. That is, the conflict that isolates entire cities is rarer in the
North and West compared to the East, but when it does occur, the
damage—quantified in terms of millions of people removed from Africa’s
integrated economy—tends to be more significant.

Figure 5: A Results of an attack percolation simulating the effect of limited
but cascading conflict, we see that even though West and East Africa are most
prone to violence, the combination of a sparse road network and growing
conflict on the Horn of Africa results in more isolates—stranded cities with
no connections to the broader continent—in the East across simulations. We can
interpret thicker bars as repeat events across simulations, showing that much
of the largest isolated cities come from rarer events in the North. B The
results in order of occurrence during 10.000 runs.

Results of a cumulative percolation simulating prolonged conflict, cutting
edges with probability proportionate to conflict intensity, shows that in some
scenarios, it only takes a few hundred events to strand millions of residents,
disrupt a quarter or more of interurban traffic and fragment the network
(Figure 6). Although there is little risk of correlated violence across the
continent, the threat of it could disrupt trade and discourage integration. As
Figures 2 and 9 show, conflict is becoming more growing in some areas and
persisting in others, leading to prolonged threats that could change the
relationships between cities. As we shift down the risk curve in 6, we produce
maps like those in Figure 7. We remove all links above a given threshold and
observe the size of the largest component as we do so, finding that the
continent fragments even a high values of risk, indicating that we could see
effects from violence if it escalates on the continent.

Figure 6: A Number of people of the largest component (vertical axis) as the
number of edges is removed (horizontal axis). Each grey line represents a
single simulation, while the blue shows the average; the dispersion of grey
lines shows that in the worst cases, the comment can break during a few
hundred conflict events. B The percentage of total flow along the network,
according to our gravity model, is disrupted by rising conflict, with some key
edges disrupted early on in many of the simulations. C The number of people in
cities in isolated nodes at each step, showing monotonic growth across steps
with few deviations across simulations, again shown with a grey line. Figure
7: The result cummulative effect of violence on the integrity of Africa’s
interurban network. Blue here represents new isolates or new components broken
off from the largest component. As we remove links at a given level of risk,
we see the size of the largest component shrink and the continent fragment
into isolated areas.

##  5 Conclusions

Road transportation is the most dominant mode of motorised transport in
Africa, accounting for 80% of goods traffic and 90% of passenger traffic.
However, in 2005, only 22.7% of the African road network was paved,
highlighting the need for infrastructure development in some regions
UNTransportAfrica09 . Even though there is some regional variation in the road
density and quality, the road transport network in Africa is sparse and
frequently characterised by relatively long delays at borders, high transit
tariffs, market access barriers and transport restrictions. These shortcomings
are especially prevalent in some of Africa’s least developed regions,
hindering their economic development efforts AfricaEUCoop-Transport  and
creating a cyclic relationship between poverty and the state of the road
network. Furthermore, terrorist groups operating in some regions take
advantage of the fragility of the road network to increase their control in an
area. Through their attacks, they may seek to create additional disruption in
the roads prieto2020uncovering , hence exacerbating the already existing
issues. It is estimated that between 2001 and 2021, the number of casualties
attributed to violence against civilians in Africa increased 260%
raleigh2010introducing .

In this work, we have quantified the impact that disruptions in the road
network would have at different locations. The impact measure is based on the
magnitude of the traffic flow at a given location, so the impact would be
higher for disrupted at locations with more traffic. We have also quantified
the risk or intensity at which a location experiences disruption due to
violent conflict at a given point in time. Combining these two measures, we
observe that low-risk but high-impact locations are mostly concentrated in
North African cities. Importantly, our analysis suggests that high-risk and
high-impact cities are concentrated in West Africa and Ethiopia, leading to
higher vulnerability in this region. High-risk, low-impact areas are in
Somalia and other isolated parts of the network.

Specifically, we find that as a result of road disruption caused by violent
attacks, a larger population is more likely to become isolated from the rest
of the road network in West Africa and Ethiopia. In addition, if all journeys
were to go ahead despite the disruption, the fragmentation of the road network
would force a relatively higher percentage of traffic flows to be rerouted in
West Africa. This could result in longer travel times, subject to additional
delays and congestion as well as an increase in vehicle emissions.

The network analysis approach that we take here offers several benefits over
traditional Geographic Information Systems (GIS) for the study of the
vulnerability of certain locations within the African road system. The most
obvious advantage is the ability of spatial networks to capture the
interactions between different places, allowing us to better understand the
complexity of the system and ask questions such as ‘if there is a violent
event in a certain location, how does this affect the road transport system as
a whole?’. Therefore, our work constitutes a step forward in the direction of
understanding the resilience of the road transport network against occurrences
of violent conflict in the African continent. Our work also highlights the
need to increase the quality, and more specifically, the connectivity of the
road network in Africa, with the West African region being a priority area.

##  6 Supplementary information

###  6.1 The network of all African highways

Primary roads, highways and trunks were obtained from OpenStreetMap
OpenStreetMap , and data from Africapolis Africapolis  was used to obtain the
location and size of all urban agglomerations with more than 100,000
inhabitants and also smaller cities near major roads to construct a connected
network of all cities. A connected and simplified network of African cities is
constructed. Unlike other infrastructure networks (for example, a railway
network), the road network is not clearly defined. For example, considering
train stations and the railways between them is a natural way to determine the
nodes and the edges of the railway network. Road networks need transport nodes
representing road crossings.

Cities and road data were spatially aligned and integrated into a single
network. Then, disconnected components of the network were joined based on the
proximity of the roads prieto2022constructing ; prieto2022detecting . Then,
the network is simplified by dissolving nodes with a degree of two that
connect the same type of road at both ends. The node is replaced by a “longer”
edge, where the length corresponds to the sum of the two edges. The urban
network comprises 9,159 edges and 7,361 nodes. The labelled network represents
2,162 cities in the continent and 5,199 transport nodes. The edges correspond
to an existing highway between any two nodes. The type of road is used to
estimate the speed and travel time to cross it. Any edge with its extremes on
different countries is a border crossing, so 120 minutes are added for
crossing it. Similarly, extra time for travelling through an urban
agglomeration is added, proportional to the population of that city. For each
edge, it is identified its road length, whether it crosses an international
border and a city in any of its two extremes, resulting in a proxy of the
estimated minutes to travel through that edge.

###  6.2 The Hawkes process and its parameters

We use a Hawkes point process to model the intensity of events in city $i$.
The rate $\mu_{i}(t)$ for city $i$ at some time $t$ is calculated by

$\mu_{i}(t)=\sum_{s:t\geq t_{s}}\kappa_{s}\exp{-\phi(t-t_{s})},$ (3)

where $t_{s}$ indicates the time in which event $s$ happened, $\kappa_{s}$ is
the impact of event $s$, and $\phi>0$ is the model parameter that captures
memory decay. With small values of $\phi$ the model keeps the impact for many
days, but with high values, the $\mu_{i}(t)$ has almost no memory of past
events. The sum is only for the time $t$ after the event (so $t\geq t_{s}$),
so the values inside the exponential drop to zero as time passes.

We take $\kappa_{s}$ to be the number of event fatalities. We estimate the
values of $\phi$, so the Hawkes process provides the most future information
as follows. For some test value of $\phi$, we compute the corresponding Hawkes
process for city $i$ and compute the lagged correlation between the
$\mu_{i}(t)$ and the events in city $i$ for the next $t+14$ days. Thus, the
objective is that $\mu_{i}(t)$ should inform as close as possible what will
happen in the city two weeks after its value is computed. We compute the
correlation between $\mu_{i}(t)$ and $E_{i}(t)$, where $E_{i}(t)$ is the
average daily impact experienced in city $i$ between $t$ and $t+14$. A high
correlation indicates that $\mu_{i}(t)$ informs the intensity of future
(unknown) events. We add the correlation obtained for all cities into the
value $\theta(\phi)$. Then, we vary the parameter $\phi$ and follow the same
procedure, obtaining different values of $\theta(\phi)$. We keep the value of
$\phi^{\star}=0.0987$ since it maximises $\theta^{\star}(\phi)$ (Figure 8).

Figure 8: Values of $\phi$ (horizontal axis) and its corresponding
$\theta(\phi)$ (vertical axis). We keep $\phi^{\star}=0.0987$ that maximise
the correlation between $\mu_{i}(t)$ and $E_{i}(t)$ Figure 9: Observed values
of the intensity of events $\mu_{i}(t)$ over time across all cities in Africa.

## Competing interests

The authors declare that they have no competing interests.

## Funding

The research was funded by the Austrian Federal Ministry for Climate Action,
Environment, Energy, Mobility, Innovation and Technology (2021-0.664.668) and
the Austrian Federal Ministry of the Interior (2022-0.392.231).

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