Browsing by Author "Govinder, Keshlan Sathasiva."

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Analysis of multiple control strategies for pre-exposure prophylaxis and post-infection interventions on HIV infection.
(2016) Afassinou, Komi.; Chirove, Faraimunashe.; Govinder, Keshlan Sathasiva.
Abstract available in PDF file.
Analysis of shear-free spherically symmetric charged relativistic fluids.
(2011) Kweyama, Mandlenkosi Christopher.; Maharaj, Sunil Dutt.; Govinder, Keshlan Sathasiva.
We study the evolution of shear-free spherically symmetric charged fluids in general relativity. This requires the analysis of the coupled Einstein-Maxwell system of equations. Within this framework, the master field equation to be integrated is yxx = f(x)y2 + g(x)y3 We undertake a comprehensive study of this equation using a variety of ap- proaches. Initially, we find a first integral using elementary techniques (subject to integrability conditions on the arbitrary functions f(x) and g(x)). As a re- sult, we are able to generate a class of new solutions containing, as special cases, the models of Maharaj et al (1996), Stephani (1983) and Srivastava (1987). The integrability conditions on f(x) and g(x) are investigated in detail for the purposes of reduction to quadratures in terms of elliptic integrals. We also obtain a Noether first integral by performing a Noether symmetry analy- sis of the master field equation. This provides a partial group theoretic basis for the first integral found earlier. In addition, a comprehensive Lie symmetry analysis is performed on the field equation. Here we show that the first integral approach (and hence the Noether approach) is limited { more general results are possible when the full Lie theory is used. We transform the field equation to an autonomous equation and investigate the conditions for it to be reduced to quadrature. For each case we recover particular results that were found pre- viously for neutral fluids. Finally we show (for the first time) that the pivotal equation, governing the existence of a Lie symmetry, is actually a fifth order purely differential equation, the solution of which generates solutions to the master field equation.
An analysis of symmetries and conservation laws of some classes of PDEs that arise in mathematical physics and biology.
(2016) Okeke, Justina Ebele.; Narain, Rivendra Basanth.; Govinder, Keshlan Sathasiva.
In this thesis, the symmetry properties and the conservation laws for a number of well-known PDEs which occur in certain areas of mathematical physics are studied. We focus on wave equations that arise in plasma physics, solid physics and fluid mechanics. Firstly, we carry out analyses for a class of non-linear partial differential equations, which describes the longitudinal motion of an elasto-plastic bar and anti-plane shearing deformation. In order to systematically explore the mathematical structure and underlying physics of the elasto-plastic flow in a medium, we generate all the geometric vector fields of the model equations. Using the classical Lie group method, it is shown that this equation does not admit space dilation type symmetries for a speci fic parameter value. On the basis of the optimal system, the symmetry reductions and exact solutions to this equation are derived. The conservation laws of the equation are constructed with the help of Noether's theorem We also consider a generalized Boussinesq (GB) equation with damping term which occurs in the study of shallow water waves and a system of variant Boussinesq equations. The conservation laws of these systems are derived via the partial Noether method and thus demonstrate that these conservation laws satisfy the divergence property. We illustrate the use of these conservation laws by obtaining several solutions for the equations through the application of the double reduction method, which encompasses the association of symmetries and conservation laws. A similar analysis is performed for the generalised Gardner equation with dual power law nonlinearities of any order. In this case, we derive the conservation laws of the system via the Noether approach after increasing the order and by the use of the multiplier method. It is observed that only the Noether's approach gives a uni ed treatment to the derivation of conserved vectors for the Gardner equation and can lead to local or an in finite number of nonlocal conservation laws. By investigating the solutions using symmetry analysis and double reduction methods, we show that the double reduction method yields more exact solutions; some of these solutions cannot be recovered by symmetry analysis alone. We also illustrate the importance of group theory in the analysis of equations which arise during investigations of reaction-diffusion prey-predator mechanisms. We show that the Lie analysis can help obtain different types of invariant solutions. We show that the solutions generate an interesting illustration of the possible behavioural patterns.
Applications of Lie symmetries to gravitating fluids.
(2011) Msomi, Alfred Mvunyelwa.; Maharaj, Sunil Dutt.; Govinder, Keshlan Sathasiva.
This thesis is concerned with the application of Lie's group theoretic method to the Einstein field equations in order to find new exact solutions. We analyse the nonlinear partial differential equation which arises in the study of non- static, non-conformally flat fluid plates of embedding class one. In order to find the group invariant solutions to the partial differential equation in a systematic and comprehensive manner we apply the method of optimal subgroups. We demonstrate that the model admits linear barotropic equations of state in several special cases. Secondly, we study a shear-free spherically symmetric cosmological model with heat flow. We review and extend a method of generating solutions developed by Deng. We use the method of Lie analysis as a systematic approach to generate new solutions to the master equation. Also, general classes of solution are found in which there is an explicit relationship between the gravitational potentials which is not present in earlier models. Using our systematic approach, we can recover known solutions. Thirdly, we study generalised shear-free spherically symmetric models with heat flow in higher dimensions. The method of Lie generates new solutions to the master equation. We obtain an implicit solution or we can reduce the governing equation to a Riccati equation.
Applications of symmetry analysis to physically relevant differential equations.
(2005) Kweyama, Mandelenkosi Christopher.; Govinder, Keshlan Sathasiva.; Maharaj, Sunil Dutt.
We investigate the role of Lie symmetries in generating solutions to differential equations that arise in particular physical systems. We first provide an overview of the Lie analysis and review the relevant symmetry analysis of differential equations in general. The Lie symmetries of some simple ordinary differential equations are found t. illustrate the general method. Then we study the properties of particular ordinary differential equations that arise in astrophysics and cosmology using the Lie analysis of differential equations. Firstly, a system of differential equations arising in the model of a relativistic star is generated and a governing nonlinear equation is obtained for a linear equation of state. A comprehensive symmetry analysis is performed on this equation. Secondly, a second order nonlinear ordinary differential equation arising in the model of the early universe is described and a detailed symmetry analysis of this equation is undertaken. Our objective in each case is to find explicit Lie symmetry generators that may help in analysing the model.
Aspects of spherically symmetric cosmological models.
(1998) Moodley, Kavilan.; Maharaj, Sunil Dutt.; Govinder, Keshlan Sathasiva.
In this thesis we consider spherically symmetric cosmological models when the shear is nonzero and also cases when the shear is vanishing. We investigate the role of the Emden-Fowler equation which governs the behaviour of the gravitational field. The Einstein field equations are derived in comoving coordinates for a spherically symmetric line element and a perfect fluid source for charged and uncharged matter. It is possible to reduce the system of field equations under different assumptions to the solution of a particular Emden-Fowler equation. The situations in which the Emden-Fowler equation arises are identified and studied. We analyse the Emden-Fowler equation via the method of Lie point symmetries. The conditions under which this equation is reduced to quadratures are obtained. The Lie analysis is applied to the particular models of Herlt (1996), Govender (1996) and Maharaj et al (1996) and the role of the Emden-Fowler equation is highlighted. We establish the uniqueness of the solutions of Maharaj et al (1996). Some physical features of the Einstein-Maxwell system are noted which distinguishes charged solutions. A charged analogue of the Maharaj et al (1993) spherically symmetric solution is obtained. The Gutman-Bespal'ko (1967) solution is recovered as a special case within this class of solutions by fixing the parameters and setting the charge to zero. It is also demonstrated that, under the assumptions of vanishing acceleration and proper charge density, the Emden-Fowler equation arises as a governing equation in charged spherically symmetric models.
A classification of second order equations via nonlocal transformations.
(2000) Edelstein, R. M.; Govinder, Keshlan Sathasiva.
The study of second order ordinary differential equations is vital given their proliferation in mechanics. The group theoretic approach devised by Lie is one of the most successful techniques available for solving these equations. However, many second order equations cannot be reduced to quadratures due to the lack of a sufficient number of point symmetries. We observe that increasing the order will result in a third order differential equation which, when reduced via an alternate symmetry, may result in a solvable second order equation. Thus the original second order equation can be solved. In this dissertation we will attempt to classify second order differential equations that can be solved in this manner. We also provide the nonlocal transformations between the original second order equations and the new solvable second order equations. Our starting point is third order differential equations. Here we concentrate on those invariant under two- and three-dimensional Lie algebras.
Computer analysis of equations using Mathematica.
(2001) Jugoo, Vikash Ramanand.; Govinder, Keshlan Sathasiva.; Maharaj, Sunil Dutt.
In this thesis we analyse particular differential equations that arise in physical situations. This is achieved with the aid of the computer software package called Mathematica. We first describe the basic features of Mathematica highlighting its capabilities in performing calculations in mathematics. Then we consider a first order Newtonian equation representing the trajectory of a particle around a spherical object. Mathematica is used to solve the Newtonian equation both analytically and numerically. Graphical plots of the trajectories of the planetary bodies Mercury, Earth and Jupiter are presented. We attempt a similar analysis for the corresponding relativistic equation governing the orbits of gravitational objects. Only numerical results are possible in this case. We also perform a perturbative analysis of the relativistic equation and determine the amount of perihelion shift. The second equation considered is the Emden-Fowler equation of order two which arises in many physical problems, including certain inhomogeneous cosmological applications. The analytical features of this equation are investigated using Mathematica and the Lie analysis of differential equations. Different cases of the related autonomous form of the Emden-Fowler equation are investigated and graphically represented. Thereafter, we generate a number of profiles of the energy density and the pressure for a particular solution which demonstrates that a numerical approach for studying inhomogeneity, in cosmological models in general relativity, is feasible.
Continuous symmetries of difference equations.
(2011) Nteumagne, Bienvenue Feugang.; Govinder, Keshlan Sathasiva.
We consider the study of symmetry analysis of difference equations. The original work done by Lie about a century ago is known to be one of the best methods of solving differential equations. Lie's theory of difference equations on the contrary, was only first explored about twenty years ago. In 1984, Maeda [42] constructed the similarity methods for difference equations. Some work has been done in the field of symmetries of difference equations for the past years. Given an ordinary or partial differential equation (PDE), one can apply Lie algebra techniques to analyze the problem. It is commonly known that the number of independent variables can be reduced after the symmetries of the equation are obtained. One can determine the optimal system of the equation in order to get a reduction of the independent variables. In addition, using the method, one can obtain new solutions from known ones. This feature is interesting because some differential equations have apparently useless trivial solutions, but applying Lie symmetries to them, more interesting solutions are obtained. The question arises when it happens that our equation contains a discrete quantity. In other words, we aim at investigating steps to be performed when we have a difference equation. Doing so, we find symmetries of difference equations and use them to linearize and reduce the order of difference equations. In this work, we analyze the work done by some researchers in the field and apply their results to some examples. This work will focus on the topical review of symmetries of difference equations and going through that will enable us to make some contribution to the field in the near future.
Differential equations for relativistic radiating stars.
(2013) Abebe, Gezahegn Zewdie.; Maharaj, Sunil Dutt.; Govinder, Keshlan Sathasiva.
We consider radiating spherical stars in general relativity when they are conformally flat, geodesic with shear, and accelerating, expanding and shearing. We study the junction conditions relating the pressure to the heat flux at the boundary of the star in each case. The boundary conditions are nonlinear partial differential equations in the metric functions. We transform the governing equations to ordinary differential equations using the geometric method of Lie. The Lie symmetry generators that leave the equations invariant are identified, and we generate the optimal system in each case. Each element of the optimal system is used to reduce the partial differential equations to ordinary differential equations which are further analyzed. As a result, particular solutions to the junction conditions are presented for all types of radiating stars. New exact solutions, which are group invariant under the action of Lie point infinitesimal symmetries, are found. Our solutions contain families of traveling wave solutions, self-similar variables, and other forms with different combinations of the spacetime variables. The gravitational potentials are given in terms of elementary functions, and the line elements can be given explicitly in all cases. We show that the Friedmann dust model is regained as a special case in particular solutions. We can connect our results to earlier investigations and we show explicitly that our models are generalizations. Some of our solutions satisfy a linear equation of state. We also regain previously obtained solutions for the Euclidean star as a special case in our accelerating model. Our results highlight the importance of Lie symmetries of differential equations for problems arising in relativistic astrophysics.
Ermakov systems : a group theoretic approach.
(1993) Govinder, Keshlan Sathasiva.; Leach, Peter Gavin Lawrence.
The physical world is, for the most part, modelled using second order ordinary differential equations. The time-dependent simple harmonic oscillator and the Ermakov-Pinney equation (which together form an Ermakov system) are two examples that jointly and separately describe many physical situations. We study Ermakov systems from the point of view of the algebraic properties of differential equations. The idea of generalised Ermakov systems is introduced and their relationship to the Lie algebra sl(2, R) is explained. We show that the 'compact' form of generalized Ermakov systems has an infinite dimensional Lie algebra. Such algebras are usually associated only with first order equations in the context of ordinary differential equations. Apart from the Ermakov invariant which shares the infinite-dimensional algebra of the 'compact' equation, the other three integrals force the dimension of the algebra to be reduced to the three of sl(2, R). Subsequently we establish a new class of Ermakov systems by considering equations invariant under sl(2, R) (in two dimensions) and sl(2, R) EB so(3) (in three dimensions). The former class contains the generalized Ermakov system as a special case in which the force is velocity-independent. The latter case is a generalization of the classical equation of motion of the magnetic monopole which is well known to possess the conserved Poincare vector. We demonstrate that in fact there are three such vectors for all equations of this type.
Exact solutions for spherical relativistic models.
(2011) Nyonyi, Yusuf.; Govinder, Keshlan Sathasiva.; Maharaj, Sunil Dutt.
In this thesis we study relativistic models of gravitating uids with heat ow and electric charge. Firstly, we derive the model of a charged shear-free spherically symmetric cosmological model with heat ow. The solution of the Einstein-Maxwell equations of the system is governed by the pressure isotropy condition. This condition is a highly nonlinear partial di erential equation. We analyse this master equation using Lie's group theoretic approach. The Lie symmetry generators that leave the equation invariant are found. We provide exact solutions to the gravitational potentials using the rst symmetry admitted by the equation. Our new exact solutions contain the earlier results of Msomi et al (2011) without charge. Using the second symmetry we are able to reduce the order of the master equation to a rst order highly nonlinear di erential equation. Secondly, we study a shear-free spherically symmetric cosmological model with heat ow in higher dimensions. We establish the Einstein eld equations and nd the governing pressure isotropy condition. We use an algorithm due to Deng (1989) to provide several new classes of solutions to the model. The four-dimensional case is contained in our general result. Solutions due to Bergmann (1981), Maiti (1982), Modak (1984) and Sanyal and Ray (1984) for the four-dimensional case are regained. We also establish a new class of solutions that contains the results of Deng (1989) from four dimensions.
Extensions and generalisations of Lie analysis.
(1995) Govinder, Keshlan Sathasiva.; Leach, Peter Gavin Lawrence.
The Lie theory of extended groups applied to differential equations is arguably one of the most successful methods in the solution of differential equations. In fact, the theory unifies a number of previously unrelated methods into a single algorithm. However, as with all theories, there are instances in which it provides no useful information. Thus extensions and generalisations of the method (which classically employs only point and contact transformations) are necessary to broaden the class of equations solvable by this method. The most obvious extension is to generalised (or Lie-Backlund) symmetries. While a subset of these, called contact symmetries, were considered by Lie and Backlund they have been thought to be curiosities. We show that contact transformations have an important role to play in the solution of differential equations. In particular we linearise the Kummer-Schwarz equation (which is not linearisable via a point transformation) via a contact transformation. We also determine the full contact symmetry Lie algebra of the third order equation with maximal symmetry (y'''= 0), viz sp(4). We also undertake an investigation of nonlocal symmetries which have been shown to be the origin of so-called hidden symmetries. A new procedure for the determination of these symmetries is presented and applied to some examples. The impact of nonlocal symmetries is further demonstrated in the solution of equations devoid of point symmetries. As a result we present new classes of second order equations solvable by group theoretic means. A brief foray into Painleve analysis is undertaken and then applied to some physical examples (together with a Lie analysis thereof). The close relationship between these two areas of analysis is investigated. We conclude by noting that our view of the world of symmetry has been clouded. A more broad-minded approach to the concept of symmetry is imperative to successfully realise Sophus Lie's dream of a single unified theory to solve differential equations.
Generalized travelling wave solutions for a microscopic chemotaxis model.
(2014) Djomegni, Patrick Mimphis Tchepmo.; Govinder, Keshlan Sathasiva.
In biology cell migration is one of the most critical processes, for it is decisive in the mechanisms leading to the beginning of life. The collective migration of cells via wave motion plays a key role in understanding many essential steps in developmental processes. It is often modelled as a system of partial differential equations (PDEs). We investigate in a one-dimensional microscopic model, the formation of travelling bands (via wave motion) of bacteria E coli, caused by the chemotactic response of cells to a signal moving with constant speed. We also look at the impact of cell growth and unbiased turning rate on the behaviour of our system. The model derives from the experimental observation reported in Budrene and Berg (1991, 1995). In the first problem we tackle, we overlook the proliferation of the cells and we search for travelling wave solutions in the case where the cells do not starve. We show that, using a group theoretical approach, a larger class of travelling wave solutions than that obtained from the standard ansatz is possible. By applying realistic initial and boundary conditions, we restrict the general solutions appropriately. This is the first time that explicit travelling wave solutions have been obtained for this system of equations. In particular, we treat the full system, including non-zero diffusivity terms, unlike previous approaches. Importantly, we provide biologically relevant solutions. The second problem focuses on the metabolism effect in the case of starvation. It was observed experimentally that a low concentration of nutrients may not cause the band to break up, but rather impel the cells to consume the excreted signal. Here cell growth is allowed with constant rate. We use asymptotic methods to prove the existence of travelling wave solutions in both the case of diffusivity and non diffusivity. Significant results have been obtained. In the last problem we incorporate the proliferation of the cells in the case of non-limiting resources. Constant cell growth and a nutrient dependent proliferation rate are considered. We combine a dynamical systems analysis with other analytic methods to investigate the behaviour of the solutions. Travelling wave solutions have been obtained both for high chemotactic sensitivity, and also in the case of no chemotaxis. Explicit, biologically and pertinent solutions have been provided, confirming the validation of the model.
Group analysis of equations arising in embedding theory.
(2010) Okelola, Michael.; Govinder, Keshlan Sathasiva.
Embedding theories are concerned with the embedding of a lower dimensional manifold (dim = n, say) into a higher dimensional one (usually dim = n+1, but not necessarily so). We are concerned with the particular case of embedding 4D spherically symmetric equations into 5D Einstein spaces. This scenario is of particular relevance to contemporary cosmology and astrophysics. Essentially, they are 5D vacuum field equations with initial data given on a 4D spacetime hypersurface. The equations that arise in this framework are highly nonlinear systems of ordinary differential equations and they have been particularly resistant to solution techniques over the past few years. As a matter of fact, to date, despite theoretical results for the existence of solutions for embedding classes of 4D space times, no general solutions to the local embedding equations are known. The Lie theory of extended groups applied to differential equations has proved to be very successful since its inception in the nineteenth century. More recently, it has been successfully utilized in relativity and has provided solutions where none were previously found, as well as explaining the existence of ad hoc methods. In our work, we utilize this method in an attempt to find solutions to the embedding equations. It is hoped that we can place the analysis of these equations onto a firm theoretical basis and thus provide valuable insight into embedding theories.
Group theoretic approach to heat conducting gravitating systems.
(2013) Nyonyi, Yusuf.; Maharaj, Sunil Dutt.; Govinder, Keshlan Sathasiva.
We study shear-free heat conducting spherically symmetric gravitating fluids defined in four and higher dimensional spacetimes. We analyse models that are both uncharged and charged via the pressure isotropy condition emanating from the Einstein field equations and the Einstein-Maxwell system respectively. Firstly, we consider the uncharged model defined in higher dimensions, and we use the algorithm due to Deng to generate new exact solutions. Three new metrics are identified which contain the results of four dimensions as special cases. We show graphically that the matter variables are well behaved and the speed of sound is causal. Secondly, we use Lie's group theoretic approach to study the condition of pressure isotropy of a charged relativistic model in four dimensions. The Lie symmetry generators that leave the equation invariant are found. We provide exact solutions to the gravitational potentials using the symmetries admitted by the equation. The new exact solutions contain earlier results without charge. We show that new charged solutions related to the Lie symmetries, that are generalizations of conformally at metrics, may be generated using the algorithm of Deng. Finally, we extend our study to find models of charged gravitating fluids defined in higher dimensional manifolds. The Lie symmetry generators related to the generalized pressure isotropy condition are found, and exact solutions to the gravitational potentials are generated. The new exact solutions contain earlier results obtained in four dimensions. Using particular Lie generators, we are able to provide forms for the gravitational potentials or reduce the order of the master equation to a first order nonlinear differential equation. Exact expressions for the temperature pro les, from the transport equation for both the causal and noncausal cases, in higher dimensions are obtained, generalizing previous results. In summary, the Deng algorithm and Lie analysis prove to be useful approaches in generating new models for gravitating fluids.
The interplay of dynamical systems analysis and group theory.
(2011) Djomegni, Patrick Mimphis Tchepmo.; Govinder, Keshlan Sathasiva.
We investigate the relationship between the Dynamical Systems analysis and the Lie Symmetry analysis of ordinary differential equations. We undertake this investigation by looking at a relativistic model of self-gravitating charged fluids. Specifically we look at the impact of specific parameters obtained from Lie Symmetries analysis on the qualitative behaviour of the model. Steady states, stability and possible bifurcations are explored.
Lie group analysis of exotic options.
(2013) Okelola, Michael.; Govinder, Keshlan Sathasiva.; O'Hara, John Gerard.
Exotic options are derivatives which have features that makes them more complex than vanilla traded products. Thus, finding their fair value is not always an easy task. We look at a particular example of the exotic options - the power option - whose payoffs are nonlinear functions of the underlying asset price. Previous analyses of the power option have only obtained solutions using probability methods for the case of the constant stock volatility and interest rate. Using Lie symmetry analysis we obtain an optimal system of the Lie point symmetries of the power option PDE and demonstrate an algorithmic method for finding solutions to the equation. In addition, we find a new analytical solution to the asymmetric type of the power option. We also focus on the more practical and realistic case of time dependent parameters: volatility and interest rate. Utilizing Lie symmetries, we are able to provide a new exact solution for the terminal pay off case. We also consider the power parameter of the option as a time dependent factor. A new solution is once again obtained for this scenario.
Lie symmetries of junction conditions for radiating stars.
(2011) Abebe, Gezahegn Zewdie.; Govinder, Keshlan Sathasiva.; Maharaj, Sunil Dutt.
We consider shear-free radiating spherical stars in general relativity. In particular we study the junction condition relating the pressure to the heat flux at the boundary of the star. This is a nonlinear equation in the metric functions. We analyse the junction condition when the spacetime is conformally flat, and when the particles are travelling in geodesic motion. We transform the governing equation using the method of Lie analysis. The Lie symmetry generators that leave the equation invariant are identifed and we generate the optimal system in each case. Each element of the optimal system is used to reduce the partial differential equation to an ordinary differential equation which is further analysed. As a result, particular solutions to the junction condition are presented. These exact solutions can be presented in terms of elementary functions. Many of the solutions found are new and could be useful in the modelling process. Our analysis is the first comprehensive treatment of the boundary condition using a symmetry approach. We have shown that this approach is useful in generating new results.
Mathematical modelling of the Ebola virus disease.
(2024) Abdalla, Suliman Jamiel Mohamed.; Govinder, Keshlan Sathasiva.; Chirove, Faraimunashe.
Despite the numerous modelling efforts to advise public health physicians to understand the dynamics of the Ebola virus disease (EVD) and control its spread, the disease continued to spread in Africa. In the current thesis, we systematically review previous EVD models. Further, we develop novel mathematical models to explore two important problems during the 2018-2020 Kivu outbreak: the impact of geographically targeted vaccinations (GTVs) and the interplay between the attacks on Ebola treatment centres (ETCs) and the spread of EVD. In our systematic review, we identify many limitations in the modelling literature and provide brief suggestions for future work. Our modelling findings underscore the importance of considering GTVs in areas with high infections. In particular, we find that implementing GTVs in regions with high infections so that the total vaccinations are increased by 60% decreases the cumulative cases by 15%. On the other hand, we need to increase the vaccinations to more than 1000% to achieve the 15% decrease in EVD cases if we implement GTVs in areas with low infections. On the impact of the attacks on ETCs, we find that due to the attacks on ETCs, the cumulative cases increased by more than 17% during the 2018-2020 Kivu outbreak. We also find that when 10% of the hospitalised individuals flee the attacks on ETCs after spending only three days under treatment, the cumulative cases increased by more than 30% even if these individuals all returned to the ETCs three days later. On the other hand, if only half of these individuals returned to ETCs for treatment, the cumulative cases increase by approximately 50%. Further, when these patients spend one more day in the community, after which they all return to ETCs, the cumulative cases rise by an additional 10%. Global sensitivity analysis also confirmed these findings. To conclude, our literature systematic review is used to identify many critical factors which were overlooked in previous EVD models. Our modelling findings show that the attacks on ETCs can be destructive to the efforts of EVD response teams. Hence, it is important for decision-makers to tackle the reasons for community distrust and address the roots of the hostility towards ETCs. We also find that GTVs can be used to contain the spread of EVD when ring vaccinations, contact tracing and antiviral treatments cannot successfully control the spread of EVD.