Limited containment options of COVID-19 outbreak revealed by regional agent-based simulations for South Africa

COVID-19 has spread from China across Europe and the United States and has become a global pandemic. In countries of the Global South, due to often weaker socioeconomic options and health care systems, effective local countermeasures remain debated. We combine large-scale socioeconomic and traffic survey data with detailed agent-based simulations of local transportation to analyze COVID-19 spreading in a regional model for the Nelson Mandela Bay Municipality in South Africa under a range of countermeasure scenarios. The simulations indicate that any realistic containment strategy, including those similar to the one ongoing in South Africa, may yield a manifold overload of available intensive care units (ICUs). Only immediate and the most severe countermeasures, up to a complete lock-down that essentially inhibits all joint human activities, can contain the epidemic effectively. As South Africa exhibits rather favorable conditions compared to many other countries of the Global South, our findings constitute rough conservative estimates and may support identifying strategies towards containing COVID-19 as well as any major future pandemics in these countries.

The first cases of the corona virus disease COVID-19 were confirmed on December 29, 2019 in China (1). Due to high contagiousness (2), the disease has spread rapidly (3,4) and the World Health Organization (WHO) has since confirmed (5) about 1.6 million cases worldwide, with its vast majority as of this writing ( April 11, 2020) in the United States and many countries in Europe. Most countries of the Global South are affected as well, often with reported case numbers just beginning to surge (6). However, the currently reported low numbers, e.g. about 9000 cases in all of Africa, may be biased as only few individuals have been tested, see (7) for the example of South Africa, and also (8). Furthermore, such countries operate under vastly different socio-economic conditions, with larger social inequality, distinct transportation options and weaker health care systems compared to those of most countries in the global north (9)(10)(11), such that core characteristics of potential COVID-19 spreading dynamics and thus the effectiveness of specific countermeasures remain largely unknown for countries of the Global South.
The transmission of COVID-19 is currently thought to occur through direct inter-person droplet-based infections through coughing and sneezing, with possible additional infection paths through aerosols and via contaminated surfaces. Symptoms often occur only after an incubation period of several days, with many infected responding entirely asymptomatic. Contagion may also occur via such symptom-free carriers, posing a challenge for tracing and estimating spreading patterns (12). Transmission predominantly occurs through interactions while being at home, being at work, using shared transportation modes or during group-based leisure activities. In many countries of the Global South, most of these social activities occur under conditions drastically different from those in, for example, Europe or the U.S.. For instance, these countries feature, on average, more people per household, higher unemployment rates, more manual and lower payed work (13,14) and much of publicly available transportation services used by the middle and low-income population are offered as paratransit shared-mobility services (15,16). Moreover, public health care services are different and often less well equipped than in countries of the Global North (11,17).
As a paradigmatic region offering large-scale data availability, we consider the Nelson Mandela Bay Municipality (NMBM) in South Africa to study scenarios of COVID-19 spreading dynamics and the impact of countermeasures. We combine socio-economic and travel survey data from more than 100,000 people (18), about 10% of the local population, based on employment status, household size, age group and income level together with a detailed 24-hour travel diary component integrated into an agent-based traffic simulation (see Materials and Methods). The resulting contact network forms the basis for extended Susceptible-Infected-Recovered (SIR) model dynamics with parameters adapted to COVID-19 (19). Such agent-based simulations capture the inhomogeneity among the agents and are capable of modeling intricate nonlinear dynamic relationships between them, including a spreading rate that depends on the individual agent's detailed activities, their modes of transportation used, and their distance to each other (20).
To evaluate the impact of various policy measures on the course of the disease, we systematically compare several scenarios by varying simulation parameters accordingly (see Materials and Methods). First, a baseline scenario without any countermeasures; second, a default scenario in line with the current measures implemented in South Africa as of early April 2020 (21).
These include the shutdown of childcare and educational institutions, the prohibition of leisure activities of any kind and cutting shopping activity options by about 70 %. Moreover, work related and "other" activities (for example trips to health care facilities and visits to public institutions) and travelling as passenger in a car are reduced by 80 % and formal and informal public transport is reduced by 30 %. Third, as a harsher variation of the lockdown that may be achievable in principle, we study the effect of a realistic lockdown scenario, increasing the restriction of activities related to work, shopping, leisure, and "other" by 90 % while childcare, educational activities as well as formal and informal public transport are completely shut down.
Finally, we consider a theoretical complete lockdown where all travel and outside activities are prohibited.
All countermeasures come into effect 7 days after an initial infection of 100 people. We furthermore investigate additional simulations that start with the (currently enacted) default measures and introduce the realistic lockdown scenario after a number of days. The results presented below may inform and complement the ongoing discussion around tightening, loosening, introducing or repealing certain countermeasures. In all four scenarios, the outbreak strongly overloads the available intensive care unit (ICU) beds, with ten-to 100-fold overload in default and baseline scenario, respectively (see Figure   2A). Out of the total 267 ICU beds available in (public and private) hospitals in the whole Eastern Cape Province (data from 2008, (22)), only about 50 would be available for critical cases from the NMBM (scaled proportional to the relative population counts in 2011 (23,24)).
We additionally quantify the sustained pressure on the health care system by computing the cumulative overload λ of the health system as the total number of person days critical patients go without intensive care ( Figure 2B), where Θ(·) denotes the Heaviside step function, Θ(x) = 1 for x ≥ 0 and Θ(x) = 0 otherwise, c(t) the number of critical cases at time t and c max the available ICU capacity. The integral is taken over the entire time of simulation, 64 days after the 100 people are infected in NMBM.
This cumulative measure λ thus quantifies the total long term overload of intensive care health services (and may be large even if the peak overload is small).
The potential severity of the outbreak in NMBM even with strong countermeasures, is especially evident when compared to that of the United Kingdom (UK) ( Figure 2C). In the UK, ICU Realistic or complete lockdown offer options of greatly reducing the pressure on the health care system if enacted rapidly enough. However, economic boundary conditions and in particular the large inequality in South Africa -and similarly in many other countries of the Global South -pose additional problems. Thus, in our opinion, in particular complete lockdown seems hardly enforceable and would appear unsustainable especially for a large share of people with lower income, as already weaker containment will likely lead to severe economic consequences in addition to disease related deaths (26,27).
How can the number of critical cases be confined given that the default scenario is already enacted? On April 9th, 2020, the number of cases reported in NMBM was 30 (28). As the number of reported cases seem to systematically underestimate their actual number by at least a factor of three, as predicted for Austria on April 10, 2020 (8), we estimate that on 9th of April, at least 100 cases existed in NMBM and take that as our initial condition. Starting simulations with the default scenario active, we find that critical cases are likely to vastly exceed the available ICU capacity ( Figure 3A) within two months. In contrast, introducing the realistic lockdown scenario immediately, i.e. starting April 13th, might support a successful confinement of the number of critical COVID-19 patients in NMBM to manageable numbers ( Figure 3B). In this scenario, the simulations suggest that there is about 80% likelihood that ICU capacity becomes overloaded at some time and that ,if overload occurs, it will be relatively mild (factor of 2-3 of the capacity, in contrast to factor of about 30 when keeping the default measures as they are). We remark that the success of such lockdown countermeasures crucially relies on several restrictions and our simulations likely under-rather than overestimate future case numbers. First in our simulations, activities are immediately reduced to the set low values (complete shutdown of public transport, child care and educational facilities, 90% reduction of all other activities) and all inhabitants fully comply with these restrictions. Second, our simulations are based on estimated parameters that thereby come with uncertainties, and stochastic dynamics may create large deviations from the predicted values, in particular also earlier growth and larger total num-ber of critical patients, not last due to an exponential growth of the outbreak in its initial phase without severe lockdown (compare (29)). Third, our estimates assume that all ICU beds would be available exclusively for COVID-19 patients during the entire time of the outbreak. Those and other constraints call for a more conservative, especially earlier introduction of realistic countermeasures.
Across all scenarios studied, the results thus indicate that it may be hard to enact realistic, socially and economically feasible countermeasures without exceeding ICU capacity and that more drastic measures beyond the current default are rapidly needed. Finally, it seems reasonable to assume that the consequences of countermeasures would be qualitatively the same across South Africa as well as many countries of the Global South.

Transport simulation
For the transport simulation, we employ the latest version (version 12.0-SNAPSHOT) of MAT-Sim (30). The analysis relies on the population data file provided by Joubert (18). It processes travel diaries from the 2004 Travel Survey to compute a synthetic population sample of the Nelson Mandela Bay Municipality (NMBM).  We employ the Demand Responsive Transport (DRT) framework for MATSim (32) to include the informal minibus taxi transit. In the underpinning MATSim, agents walk to a bus stop and request a DRT vehicle (in this case a minibus taxi). Their ride is pooled with rides of other agents with similar destinations. The simulated routing is more flexible than in reality, since the minibus taxis operate on a stop-based system with routes. Due to a lack of detailed data, this mode was implemented based on a door-to-door based operating scheme and pick ups waiting passengers from the stops. Consequently the vehicles are less frequented on the one hand but travel longer distances with passengers on board to pick up customers in the city on the other. This reduces the likelihood of being on a minibus with an infected person, but increases the contact time if an infected person is actually on board. The formal bus transport services in NMBM are provided by Algoa Bus Company (34). Due to limited data on frequencies and schedules, the formerly bus passengers are assigned to the minibus taxis in the simulation.

Transport parameters
Due to the 10 % population sample, the total capacity of the minibus taxis vehicles must be adapted to reflect the proportions in reality. In 2014, a total of 2,374 minibus taxis operated in NMBM with an average capacity of 15 persons (31). As scaling the capacity of minibus taxis to 1.5 passengers would strongly underestimate the infections during minibus taxi trips, several test scenarios with different fleet sizes and passenger capacities were carried out.
Due to the operating scheme of door-to-door DRT a reduction either in fleet size and/or passenger capacity of the vehicles would lead to a high rejection rate and accordingly high infection numbers at home facilities that could bias the simulation results. For this reason, the number of vehicles has been chosen with respect to the trade-off between capacity utilisation and the rejection rate. A fleet of 2,300 vehicles with a capacity of 15 optimises these criteria and was introduced into the model. The vehicles were placed randomly in the area at the beginning of the simulation, although in reality they wait for customers at designated places at the beginning of the day and start their tour when a certain degree of occupancy is reached.
Public minibus taxis are assumed to take an important role in the epidemic simulation, as both the probability and the intensity of contact are assumed to be high. Moreover, people with different places of work and residence mix up at this small space.

Epidemic simulation
The model relies on the MATSim-based Episim-framework to simulate the epidemic spreading in the research area. The following briefly summarises both the functionality of the default Episim configuration and the parametric adaptions to the NMBN. It is important to note that the package is still in a very early stage of development. For the following simulations, we used the latest version (master in GitHub) dated April 11, 2020 (see also https://github.com/matsimorg/matsim-episim).
Episim is based on a traditional SIR model, which is a common model for the analysis of epidemics (35) and has been continuously improved, e.g. by (36-38). The basic mechanism is that people go through different stages during an epidemic, and have different characteristics with each transition. In short, initially all persons are susceptible for a disease and, over time, become infected with a given probability, partly influenced by individual characteristics. Later on, they recover. The states and transitions are usually extended to a more complex framework and include quarantine, seriously sick and critical patients in order to account for policy measures and the need for either hospital beds or ICUs.
The infection process is based on a probabilistic model and occurs in "containers". These containers represent locations where several agents may interact, such as households, workplaces or transport vehicles, and are computed based on the information from NMBM MATSim simulation output event data. These chronicle all trajectories covered by agents during the day and the vehicles and facilities they visited and stayed at. Once a susceptible and a contagious agent stay in the same container, an infection occurs with a certain probability, which is described by equation S1 (see below).

Epidemic parameters
At the beginning of the simulation, 10 randomly selected agents (corresponding to 100 people) are initially infected. After 7 days of uncontrolled spread, various countermeasures are implemented. We consider the dynamics until the countermeasures are in effect for 60 days.
In Episim, infected agents undergo several state transitions before their infection is terminated. Since not all humans suffer equally from COVID-19, the agents follow different paths from infection to recovery. In the beginning of the simulation, all agents except the "Patients Zero" are initially healthy and thus susceptible. After an infection, an agent's state changes to infected but not contagious, due to incubation time. With the beginning of the fourth day after an infection, the agent's state changes to contagious. From this step on, the agent's differ in their behaviour. In the default scenario, 20 % of the agents put themselves into quarantine. The idea of the simulation model is that only a certain share of those suffering from COVID-19 notices symptoms. In addition, it is to be expected that some infected persons will go into public despite symptoms. The self-quarantine lasts 14 days and is assumed to mitigate social contacts completely, even within the household. 4.5 % of all infected agents become seriously sick on day 10 and of these, 25 % become critical the following day. In this way, a distinction is made between patients who require regular medical care and those who are dependent on ICUs. Contagious agents recover 16 days after infection, whereas the infection of patients with severe conditions terminates after 23 days.
In reality, an infection would end by recovery or death. For usability reasons, every infected agent recovers in Episim. As recovered agents are assumed to be immune and no longer contagious, omitting death does not bias the further course. The same mechanism is applied for self-quarantined, who remain mobile in the simulation but are neither contagious nor susceptible.
The probability of agent n becoming infected at time t when leaving a container is given by where q denotes the shedding rate (infectivity-parameter for the virus), i the contact intensity and τ the interaction duration of two persons, summed over all persons in contact with agent n. i is assumed to scale as d −3 , thus declining very fast with increasing distance. θ is introduced as a calibration parameter to shape the infection curve in a realistic way. Based on current infection data a tenfold increase of infected persons in 7 days is quite realistic for most countries without any interventions. In our framework, we thus set θ N M BM = 0.000003 in order to meet this condition.
Most of the contact intensities were left at their default since it is reasonable to assume, that the contact intensities of most activities do not differ significantly from the values determined by (19). The activities work, shopping, dropby and other were introduced so that the first two have the same contact intensity as leisure (5) and the other two take the values 7 and 3. It is assumed that due to the available space and seating arrangements in the minibus taxis, the contact between passengers in the minibus taxis is much higher than in formal public transport in Berlin. Since no reliable data on the contact intensity of passengers are available, we take the interaction intensity to be 20, compared to 10 in the default setting. Likewise, the contact intensity of being at home is doubled from 3 to 6 due to limited space, larger households and general living conditions.

Policy Parameters
The countermeasures in the default setting, realistic lockdown and complete lockdown are described by modifiers to the activity rates of the agents, describing the reduction in the frequency of the respective activity.

Simulation results
Here we provide additional measures recorded from the simulations presented in the main manuscript on the location of infection events (Table S3) and exact values of the health care system overload (Table S4) Table S3).