Modelling the Spread of Tuberculosis in South African Informal Settlements

Due to the high population density of informal settlements, the spread of communicable diseases is highly effective in this environment. South Africa has been on the World Health Organization’s list of 30 top tuberculosis-burdened countries in the world for the last two decades. The rate of individuals diseased with tuberculosis in informal settlements, however, is reported to be double that of the country. In order to succeed in reducing the number of tuberculosis cases, policy decision makers have a growing need to understand the risk factors surrounding tuberculosis and data which may inform their decision in a quantifiable manner. In this paper, agent-based simulation is employed in order to facilitate the understanding of the spread of tuberculosis in these environments. The simulation model developed models the personal characteristics, daily movements and interactions between informal settlement residents. This model is able, within a certain range of accuracy, to indicate the spread of tuberculosis given certain input parameters, such as population size, probability of treatment termination and percentage initially infected, amongst others. This may assist policy makers in making informed decisions based on quantitative targets. It is evident that population density has a great impact on the spread rate of the disease. This is supportive of the fact that 90% of residents in informal settlements have latent tuberculosis. Given that only 68% of people with the disease seek treatment, by increasing this likelihood through incentives, it is possible to drastically decrease the rate of death and unsuccessful treatment.


Introduction
As a result of the high cost of housing within cities, many individuals have no other option than to reside in informal settlements. In 2018, it is reported that approximately 26% of people living in urban areas in South Africa are residing in informal settlements [1]. As this percentage has increased from 23% in 2014, it supports the net migration patterns predicted by Statistics South Africa [2] in 2018 indicating an influx into provinces with large metropolitan areas such as Gauteng and the Western Cape hoping for work, given the steadily increasing unemployment rate. In 2021, the unemployment rate has reached a high of 34.9% since the start of the Quarterly Labour Force Survey [3], indicating that it is likely that the percentage of people living in South African informal settlements would have increased significantly from the reported 26% in 2018.
Informal settlements are characterised by "illegality and informality; inappropriate locations; restricted public and private sector investment; poverty and vulnerability; and social stress" [4]. They lack basic amenities, such as electricity, clean water and basic sanitation, resulting in a poor quality of life for residents within these settlements. This provides ideal conditions for disease to fester and spread which makes the chance of a pandemic likely and its consequence detrimental. Tuberculosis (TB) has been identified as being one of the leading causes of death in South Africa and the country is on the World Health Organization's (WHO) list of top 30 TB burden countries [5]. Furthermore, at the 5 th South African TB Conference held in 2018, several vulnerable groups were identified according to their living and working environment which included inmates, those residing in informal settlements and those working in the mining sector [6].
TB is an infectious disease which is caused by the Mycobacterium tuberculosis bacteria, typically presenting itself in the lungs, known as pulmonary TB. The disease spreads when those that have active pulmonary TB expel the bacterium into the air, through coughing or sneezing. An individual infected with the virus initially experiences latent TB, for which they are asymptomatic. It may become active when the individual's immune system is low, which can be caused by a multitude of factors relating to sanitation and nutrition. It is approximated that 5-10% of individuals who get infected with the virus will develop active TB after conception [7].
The risk of developing TB is amplified by certain factors, such as age, general health and human immunodeficiency virus (HIV) status. HIV infection is the most dangerous risk factor for latent TB to transition to active TB. This transition is 20 times more likely in an HIV-positive than an HIV-negative person with latent TB [8]. In addition, 26% of HIV-positive deaths are caused by TB [9]. TB is curable through a lengthy drug regime, depending on whether the individual is infected with a drug-susceptible TB (DS-TB) strain or a single or multidrugresistant TB (MDR-TB) strain. A more resistant strain of TB increases the length, cost and toxicity of the treatment process, whilst decreasing its effectiveness.
In this study, an agent-based model is developed to address the lack of information and understanding of the spread of infectious disease within informal settlements. With agent-based modelling (ABM), the interactions and contacts between individuals can be modelled to account for some of the complexities in social systems in which deterministic models are not able to capture. The model developed simulates the spread of TB, an airborne infectious disease, within a South African informal settlement by capturing characteristics of the disease and modelling the daily routine, personal characteristics and interactions of individuals residing within the settlement. In addition, by providing various input parameters, such as population size, percentage initially infected, percentage of infected individuals with MDR-TB, spread radius and probability of treatment termination, it visualises the spread of the disease. The model may assist policy makers in ascertaining which aspects to target using incentives, and which intervention strategies have the highest likelihood of being successful as the model can easily be restructured to conform to these new strategies.
In addition to the introductory section, the remainder of this paper encompasses a literature review on the spread of tuberculosis in the context of South African informal settlements and a review of existing epidemiology models, which is followed by the model development and a scenario analysis performed on the model. In conclusion, a discussion on the simulation model and the results acquired, as well as limitations and avenues for future research is provided.

Literature Review
Traditionally, models in epidemiology followed a population-based, non-spatial approach. This method does not provide sufficient accuracy as the spread of infectious diseases is dependent on the geographic setting and thus must be analysed in a spatial environment [10]. The well-known deterministic Susceptible-Infected (SI) model developed by Kermack and McKendrick [11] has been expanded to include other states, allowing for the Susceptible-Infected-Recovered (SIR) model, the Susceptible-Exposed-Infected (SEI) model, the Susceptible-Exposed-Infected-Recovered (SEIR) model and the Susceptible-Exposed-Infected-Treatment-Recovered (SEITR) model.
These models are deterministic in nature and assume that the populations are uniformly mixed, which does not represent the true nature of social systems. Therefore, these models are inadequate for modelling complex social systems since they often neglect the effect of interactions between individuals and the spatial environment, both of which have a profound effect on the spread of disease [12]. Since interactions and contacts between individuals are a vital aspect when modelling the spread of diseases, this is a serious limitation [13]. ABM is a bottom-up approach which is able to model the interactions and contacts of individuals within a given geographical area. Therefore, ABM is more suitable for problems where the modelling of complex social systems is needed, such as in the field of epidemiology.
Perez and Dragicevic [14] simulated the spread of measles in an urban setting using ABM. Wang et al. [15] followed a similar approach by accounting for the spatial environment and associated mobility of agents. This was applied to the transmission of the H1N1 influenza virus using the 2009 pandemic in Kunming, Yunnan province of China, as a case study. Another study regarding the spread of 7 Page 4 of 17 influenza, executed by Aleman et al. [16], affirmed the ability of ABM to allow for the inclusion of more information with respect to the disease outbreak than in traditional non-homogenous mixing models. By including factors such as age, household interaction, casual interaction, geographic location, and transport use, the accuracy of the model improved. Macal et al. [17] used ABM in a study to model the transmission of community-associated methicillin-resistant Staphylococcus aureus.
The aforementioned studies have all been executed in urban settings, however, these settings did not focus on the incorporation of individuals residing in informal settlements who live in very different circumstances to those in formal housing. This disparity is evident in a study carried out by Adiga et al. [18] where the spread of the influenza virus in the city of Delhi was modelled. The intricacies of disease modelling within an informal setting are further captured in the study by Searle and Sutherland [19] which modelled the spread of the influenza virus within a Greek refugee camp.
The application of ABM to model TB is demonstrated in a study by Kasaie et al. [20] where the transmission of TB in settings with a high TB incidence rate is modelled. It was shown that the frequency of infection from a single source was high within the first year of infection (almost 50%) and decreased significantly thereafter, due to recovery of the individual. It was also noted that a need exists for more ABM models as the focus has historically been mathematical and analytical approaches.
In an effort to address this research gap, Badmus and Camorlinga [21] conducted a study whereby ABM was used to simulate the spread of TB in Nigerian slum areas. This study focused on incorporating the living conditions that would be characteristic of such areas, as well as certain health conditions, namely HIV, malnutrition and diabetes. The study included a model incorporating the various states of TB, namely latent, DS-TB and MDR-TB, which Kasaie et al. [20] failed to consider. Although neither Badmus and Camorlinga [21] nor Kasaie et al. [20] considered the effect of age or the movement of individuals based on daily routine. As expected, the study by Badmus and Camorlinga [21] further concluded that TB is a function of the person's immune system responding to the bacteria. Therefore, the individuals with diabetes and HIV were far more likely to develop the active TB disease and are thus an important factor which should be taken into account.
Countries are increasingly using modelling to determine TB policy options and intervention strategies. As each country has differing socio-economic climates, it is important to create models which take this climate into account. Country-specific models must be created [22]. In the context of South Africa there are high rates of HIV-TB co-infection, and different rates of defaulting on treatment compared to other countries which must be considered. It is noted that South Africa already uses mathematical modelling to support the TB allocation of R500 million [23]. As previously discussed, agent-based models are better suited to model complex social systems. Therefore, a need for agent-based models to simulate the spread of TB in such areas is identified in order to determine appropriate interventions to first control and, secondly, eradicate TB in high-burden TB countries.

Model Development
ABM allows for the desired level of detail to be captured. Within the agent-based model, agents are assigned certain characteristics and are able to interact with each other as well as the environment. During a simulation run, the spread of TB may be modelled as a result of agent characteristics and interactions or behaviour which is governed by the agent statechart.
An agent-based simulation model is developed to understand the spread of TB in informal settlements in South Africa and to evaluate different intervention strategies. Both the characteristics of the individuals living in informal settlements and the disease itself are modelled. These core modelling aims are conveyed by means of a graphical user interface to allow for user interaction.
The agent-based simulation model is developed in the AnyLogic simulation software and is of a dynamic and stochastic nature. Agents represent informal settlement residents and are differentiated through their assigned characteristics, including gender, age, employment, and current health status, amongst others. The model is geographically based on a section of Khayelitsha, an informal settlement located in Cape Town. Given that only a portion of the informal settlement is addressed in the model, it may provide a more granular representation of the movements of individuals within the settlement.
Agents are able to interact with each other and, based on their proximity, they may become exposed to the TB bacilli. This exposure may result in the agent remaining in their current state of health or becoming infected, given a certain probability. This infection may present as a latent infection or evolve to the active disease based on their general health status. The type of active disease can be DS-TB or MDR-TB depending on the initial strain of TB to which an agent was exposed. The model is largely based on the SEITR approach, where the agent moves from the stages of being susceptible, exposed, infected (which can present as a latent or active infection) and then receives treatment, after which they may recover, depending on certain probabilities associated with the state of the various parameters the agent adopts.

Model Assumptions
There are many assumptions made in developing a model which represents the spread of TB in an informal settlement. This includes gathering accurate qualitative and quantitative data regarding the conditions within informal settlements and the spread of the disease. Primary assumptions are made with respect to the location, the spatial arrangement of the informal settlement, the agent attributes, and the disease.

Location
When modelling the spread of disease, one must consider the interactions between individuals and their environment. Considering the poor living conditions in 7 Page 6 of 17 informal settlements, it was important to consider an informal settlement which represents the worst-case scenario. Site B in Khayelitsha was chosen as it is located in one of the largest informal settlements in the country and it has been identified as one of the most densely populated areas within the settlement. Several areas on the map were identified as areas where individuals would congregate at varying times of day depending on their activities, such as waiting for a taxi at the taxi rank for work or work seeking purposes, visiting shopping centres and hospitals, and attending school. It is important to note that this model only serves to simulate the spread of TB within the bounds of the informal settlement. As such, these agents can only spread or become infected with TB whilst they remain within the bounds of the settlement.

Agent Attributes
Various attributes of the agent influence their daily movement and susceptibility to illness. Characteristics, including age, gender, employment, and the presence of comorbidities, such as diabetes, HIV and malnutrition, impact the agent's probability of transitioning into the active form of TB from the latent form.
An analysis of South Africa's population percentage with respect to age and gender of the entire South African population, from 2018 as adapted from Statistics South Africa [2], and the South African population infected with TB, reported in 2017 as adapted from the World Health Organisation [24] was completed. It was found that for every female, 1.42 males have the disease, indicating that males are more likely than females to develop the active form of the disease. It is argued that this is the case due to behavioural habits usually associated with males: unhealthy habits such as drinking and smoking, and spending time in settings such as bars which are conducive to the transmission of communicable diseases [25].
Regarding age, there is a clear difference between the age distribution of the general population, and the distribution of the age of TB-infected individuals, therefore age does play a role in an individual's susceptibility to the TB infection. It is further evident that those within the ages of 25-44 are most at risk. The co-morbidities with the highest impact are diabetes, malnutrition and HIV. It has been reported that 27% of the Khayelitsha population is HIV-positive [26], 10% are diagnosed with diabetes [27] and 19% suffer from malnutrition [28].
The agent attributes are included as parameters of which an agent is assigned a parameter value based on a certain probability distribution. The set of agent attributes and associated probabilities depicting these attributes are shown in Table 1.
As shown in Table 1, the 2011 census data [29] revealed that 49% of the Khayelitsha population is male. The age distribution shown is according to the 2018 population estimates provided by Statistics South Africa [2]. The employment status of an agent dictates whether they will leave the settlement during the day. The type of employment is recorded as an integer parameter and remains consistent throughout the length of the simulation run. It may have a value of 0 if the agent is employed, a value of 1 if the agent is seeking work, a value of 2 if the agent is unemployed or has chosen not to attend school, and a value of 3 if the agent is a child that attends school. The associated probabilities, as given in Table 1, were extracted from The Housing Development Agency report on the informal settlement status in 2013 [30].

The Spread of TB
TB is mainly spread via coughing and sneezing, upon which droplets containing thousands of TB bacilli are released into the surrounding air at a high velocity, which may reach individuals standing as far as 2 metres away from the infected individual. Due to the lightweight nature of the bacteria, TB may remain in the air long after the infected individual has left the area. For this reason, a spread radius was incorporated to simulate this characteristic [31]. Only infected individuals with an active infection, i.e. displaying symptoms, can spread the disease. The infected individual will have the same form of TB as the individual that infected them with it. This may be either DS-TB or MDR-TB. An individual with DS-TB may, however, transition to having MDR-TB with a probability of 7.1% if they stop their treatment before they are cured as the bacteria have been exposed to treatment and may become resistant to it [24].

Simulating Agent Movement
As the model considers the spread of disease only within the informal settlement, only the movement of agents within the informal settlement are considered. Upon model initialisation, agents are given a designated home within the region identified as being living area within the map of Site B. Within the informal settlements, agents are able to move between the bathrooms, the hospital, the taxi rank, the schools, the shops, and their home. There are several conditions which govern these movements of which the most notable is that these movements may only take place if the agent is within the settlement. The daily movements of an agent are influenced by their attributes, such as age and employment, and the state that they are in according to their statechart. Note that exact data are not available to accurately model the movement of individuals and the model represents a simplification of the real world. It is assumed that individuals may leave the settlement if they have been identified as employed or work seeking. The time they leave for work is determined by a triangular distribution with a minimum value of 5 (i.e. 5 am), a maximum value of 10 (i.e. 10 am) and a mode of 8 (i. e. 8 am). Similarly, the time that they return to the settlement is determined using a triangular distribution with a minimum value of 15 (i.e. 3 pm), a maximum value of (i.e. 11 pm) and a mode of (i.e. 5 pm). During this time period, their state of infection remains the same and they are unable to infect other individuals within the settlement. A similar mechanism is used to govern school attendance in children. The time that agents move to school varies, and thus this is determined using a triangular distribution with a minimum of 6 (i.e. 6 am), a maximum of 8 (i.e. 8 am) and a mode of 7 (i.e. 7 am) and the time that school ends is a function of the agent's age, 12:30 pm for primary school, alternatively, 2:45 pm for high school. The movement for tertiary education is assumed negligible as less than 5% of the overall population in Khayelitsha have completed higher education [29].
Individuals infected with the virus who are receiving treatment are modelled to visit the hospital once a day. It is assumed that agents will only visit the hospital for TB treatment. Finally, the three activities common to all agents in the settlement are going to the bathroom, going to the shops and heading back home again. The agents are prompted to visit the shopping area, containing several shops and a library, twice a week during daytime hours and to go to the bathroom 6 times a day which is modelled as within a 250m radius since the exact location of the bathrooms could not be determined. To ensure that agents do not spend an exorbitant amount of time at the bathrooms or shopping area, they are called home every 3 h. The agent movement involves a number of basic assumptions which allows for a stochastic model that may capture emergence.

Modelling People and the Spread of Tuberculosis
At the start of the simulation, each agent is assigned attributes according to the respective probabilities summarised in Table 1. Additionally, each agent is assigned an initial health status represented by a triangular distribution which includes the gender and HIV status of the agent, as summarised in Table 2.  This initial health status of an agent is then modified by taking the other parameters into account. The modified health status H of an agent is calculated based on the agent's employment status E, risk associated as a combination of age and gender A, malnutrition M and diabetes D. The employment status is omitted in the case of school children (i.e. for the case where the variable has a value of 3). A is a value from 0 to 8 depending on the risk per age and gender group based on an analysis from the data by Statistics South Africa [2] and the WHO [24] as summarised in Table 3.
Furthermore, M ∈ 0, 1 and D ∈ 0, 1 based on the prevalence of an agent being malnourished or having diabetes. The modified health status H of an agent is therefore calculated as where , , , is determined by means of qualitative derivation. For the purpose of the model, it is assumed that = 0.005, = 0.01, = 0.03, = 0.04.
The agent statechart is a mechanism which defines the agent's state and governs the progression from one state to another using a variety of triggers. The agent statechart utilised in this model is depicted in Fig. 1. In transitioning between states, the conditional triggers are used for probabilistic events, whilst timeout triggers are used to allow for a waiting period before transitioning occurs and message triggers are used to indicate exposure.
For each simulation run, the user is able to specify the initial proportion of individuals infected for each strain of TB. At the start of the simulation run, agents are selected at random until the specified proportion of infections are reached. The remainder of the agents are uninfected, i.e. healthy. Starting off as a healthy individual that has been exposed to a TB-infected individual, they will move to the exposed state. Once in this state, they have a 30% chance of progressing to the latent TB state; otherwise, they will remain healthy. Once in the latent TB state, they will transition to the form of the active infection that they were exposed to, i.e. either DS-TB or MDR-TB, given that the value of their health status is less than 0.5. Once in this state, they may die or remain in this state if they default on treatment, or if the treatment is ineffective. The probabilities of death and treatment effectiveness are used as a function of HIV status as this seems to be the largest contributing factor. If they default on treatment and if it is a case of DS-TB, they may also transition to MDR-TB due to drug-resistant bacteria with a 7.1% probability. If, however, the agent does not default on treatment and the treatment is effective, they may transition to the active not contagious state after 1.5-3 months of treatment and they will no longer be able to infect others. After the given time duration of treatment, they will return to a healthy state. The time duration is determined using a uniform distribution of 6-9 months for DS-TB and 1-2 years for MDR-TB. Fig. 1 The statechart pertaining to the agents in the people agent class

Graphical User Interface
The graphical user interface is made up of text boxes and sliders which allow the user to input data which facilitates the evaluation of various scenarios. This allows the user of the simulation model to interact with the model in an informative way, making it applicable for the desired purpose. The user-input parameters to the model include the initial population size, the portion of the agent population infected with TB and MDR-TB respectively, the spread radius, and the probability of an infected individual defaulting after seeking treatment. Once the user has configured the input Table 4 Mapping agent states to colours of agents Fig. 2 A screenshot of the running simulation model parameters and initiated a simulation run, the screen as displayed in Fig. 2 will be visible to the user. The colour of an agent depicts the state of the agent as summarised in Table 4. The model output is shown in three graphs capturing the number of agents in different states over time. This includes a stack chart of agents within the MDR-TB, DS-TB, latent TB, active not contagious, and healthy state, along with two other graphs presenting those diseased with DS-TB and MDR-TB, respectively, and those receiving treatment for the respective strains.

Model Analysis
The simulation allows for adaptation of the initial population size. The average population density in Khayelitsha is approximately 32 000 people per km 2 [32], which would be too computationally expensive. Therefore, the environment and agent avatar scale were readjusted to accommodate a similar population density whilst using an agent population size of 2 000. Thus, the initial population size is set to 2 000. Furthermore, the portions of the agent population infected with TB and MDR-TB are set to 2.5% and 6% respectively, representing the current situation in informal settlements in South Africa as confirmed by Marx [33]. The default spread radius is set to 2 metres whilst the default probability of an infected individual defecting after seeking treatment is set to 20%.
A sensitivity analysis was performed on the spread rate and the spread radius in order to determine the effect of these two parameters on the results of the model and to determine sufficiently accurate values. The parameters which are determined to be sensitive should be calibrated such that they are sufficiently accurate for the intended use of the developed model. The model parameter specifically useful in evaluating strategies for policy makers is the probability of defaulting on treatment, therefore, a scenario analysis is performed in varying this parameter.

Impact of the Spread Rate
Whilst varying the spread rate, the spread radius and probability of treatment termination are kept constant at 2 metres and 20%, respectively. It is observed that as the spread rate increases, the initial number of individuals becoming diseased as a result of first-time exposure follows a steeper increase. This does, however, exhibit less sensitivity for a spread rate of 0.8-1 time(s) per hour. The interacting dynamics of the model seem to suggest that the spread rate resulting in the most favourable outcome regarding a realistic proportion of MDR-TB is when the spread rate is set to 0.6 times per hour. Given that the results more closely resemble the real-world situation, this suggests that a value of 0.6 is the most appropriate. It is vital to consider that the spread radius has a direct impact on the rate at which healthy agents become infected.

Impact of Spread Radius
A variation in the spread radius indicates that the model output is less sensitive to the spread radius when it is given values between 5-10 metres. When varying the spread radius between 0.5-2 metres, however, there is a notable difference in output, thus indicating sensitivity for this parameter at values between 0.5-2 metres. Although it may seem reasonable to increase the spread radius to capture the effect of TB bacteria lingering in the atmosphere even after a person has moved, this is only true given that sunlight is not present. In the context of an informal settlement, the majority of contact would occur in open areas, thus preventing the survival of TB bacteria in the atmosphere. For this reason, coupled with the fact that the majority of individuals are likely to cover their mouths when coughing, a lower spread radius is applied, i.e. having a maximum of 0.5 metres, to mimic the progression as evident in the real world.

Scenario Analysis for Defecting on Treatment
Scenario analysis is performed for four different scenarios that examine the effect of defecting on or terminating treatment. These four scenarios are as follows: 1. Running the model with 10% probability of treatment termination 2. Running the model with 30% probability of treatment termination 3. Running the model with 50% probability of treatment termination 4. Running the model with 70% probability of treatment termination The analysis of treatment termination is relevant in that it is likely to be influenced by policy makers as it is often a consequence of the socio-economic climate in South Africa. Other strategies and initiatives which fit within the scope of the model may also be evaluated.
Refer to Fig. 3 for the resulting graphs from the respective scenarios. It is evident that as the probability of treatment termination increases, fewer agents enter the state of being actively infected, yet not contagious. By referring to leftmost stack chart, in Fig. 3c, d the output seems to be less sensitive, although from Fig. 3a-d, there is a clear difference in those in the active not contagious state. The increase in the proportion of those diseased with either DS-TB or MDR-TB is evident with an increasing probability of treatment termination. The danger with respect to terminating treatment is the risk of developing MDR-TB.
As indicated in Fig. 3a, b, an increase in the probability of treatment termination from 10% to 30% results in a percentage increase of 40.74% of MDR-TB patients not receiving successful treatment at the end of the 600 day simulated period. A default model value for this case study of less than 15% is suggested. This corresponds with the approximately 9.6% default rate for the city of Cape Town in 2017 [27]. This, however, covers a large area inclusive of wealthier areas, therefore, in Khayelitsha, this figure may be further inflated. From this analysis, the prominent effect of an increase in treatment termination in the development of MDR-TB cases within a community should be noted.

Conclusion
Due to the deteriorating economic climate in South Africa, with official unemployment rate at an all-time high, informal settlements have likely expanded significantly whilst in a pandemic, making it more and more important to have models which are tailored to represent such communities. Furthermore, given that TB kills almost Fig. 3 An illustration of the scenario analysis pertaining to parameter variation of the probability of treatment termination with a 10%, b 30%, c 50%, and d 70% 2 million people per year [5], it is an important disease to model in order to determine intervention strategies, particularly in vulnerable communities such as informal settlements.
The proposed model is able to simulate the spread of TB within an informal settlement by modelling the movement and behaviour of individuals based on their daily routines and demographics. The analysis performed on the effect of terminating treatment is useful as it provides a clear visual representation indicating that even a small decrease in the number of treatment termination may lead to overall better health of the entire community and curb the spread of MDR-TB.
The proposed model serves as a concept demonstrator of a tool which can be used by policy makers to make decisions based on analytical evidence. By providing various input parameters, such as population size, percentage initially infected, percentage of infected individuals with MDR-TB, spread radius and probability of treatment termination, the user can visualise the spread of the disease. As such, policy makers may be able to ascertain which aspects to target using incentives, and which intervention strategies have the highest likelihood of being successful.
It should, however, be noted that a number of simplifying assumptions were made in an attempt to mimic the real world and that it remains but a representation thereof. There is also a number of limitations to the model which should be noted. First, the model relates to a specific geographic area and the results should not be generalised, but considered in relation to the area under investigation. Future research may endeavour to create a generic model for which the geographic area of consideration may be adapted for different scenarios. Secondly, the assumptions relating to the movement of individuals may have been oversimplified and may be further refined in future research to more closely resemble the real world, for example by including sleep patterns and visits to the hospital for general illness as well as for the treatment of TB. Finally, it is assumed that the presence of multiple comorbidities is linear; however, this may not be the case. Thus, the calculation of the health status could also be further refined by investigating the impact that multiple co-morbidities could have on the overall health of an agent. Future research may further involve developing decision support systems whereby policy makers will have the opportunity to evaluate multiple intervention strategies in an effort to curb the spread of TB.

Data Availability
The authors declare that the data supporting the findings of this study are available within the article.

Declarations
Ethics Approval Not applicable.

Conflict of Interest
The authors declare no competing interests.

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