Browsing by Author "Nyabadza, Farai"
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- ItemA comparison of elasticities of viral levels to specific immune response mechanisms in human immunodeficiency virus infection(BioMed Central, 2014-10) Showa, Sarudzai P.; Nyabadza, Farai; Hove-Musekwa, Senelani D.; Magombedze, GeshamBackground The presence of an asymptomatic phase in an HIV infection indicates that the immune system can partially control the infection. Determining the immune mechanisms that contribute significantly to the partial control of the infection enhance the HIV infection intervention strategies and is important in vaccine development. Towards this goal, a discrete time HIV model, which incorporates the life cycle aspects of the virus, the antibody (humoral) response and the cell-mediated immune response is formulated to determine immune system components that are most efficient in controlling viral levels. Ecological relationships are used to model the interplay between the immune system components and the HIV pathogen. Model simulations and transient elasticity analysis of the viral levels to immune response parameters are used to compare the different immune mechanisms. Results It is shown that cell-mediated immune response is more effective in controlling the viral levels than the antibody response. Killing of infected cells is shown to be crucial in controlling the viral levels. Our results show a negative correlation between the antibody response and the viral levels in the early stages of the infection, but we predicted this immune mechanism to be positively correlated with the viral levels in the late stage of the infection. A result that suggests lack of relevance of antibody response with infection progression. On the contrary, we predicted the cell-mediated immune response to be always negatively correlated with viral levels. Conclusion Neutralizing antibodies can only control the viral levels in the early days of the HIV infection whereas cell-mediated immune response is beneficial during all the stages of the infection. This study predicts that vaccine design efforts should also focus on stimulating killer T cells that target infected cells.
- ItemComputational and theoretical analysis of human diseases associated with infectious pathogens(Hindawi, 2015) Noutchie, Suares Clovis Oukouomi; Kwuimy, Cedrick Aurelien Kitio; Tewa, Jean Jules; Nyabadza, Farai; Bildik, NecdetMathematical models and computer simulations are useful experimental tools for building and testing theories, assessing quantitative conjectures, answering specific questions, determining sensitivities to changes in parameter values, and estimating key parameters from data. Understanding the transmission characteristics of infectious diseases in communities, regions, and countries can lead to better approaches to decreasing the transmission of these diseases.
- ItemModelling the potential role of media campaigns in ebola transmission dynamics(Hindawi Publishing Corporation, 2017) Njankou, Sylvie Diane Djiomba; Nyabadza, FaraiA six-compartment mathematical model is formulated to investigate the role of media campaigns in Ebola transmission dynamics. The model includes tweets or messages sent by individuals in different compartments. The media campaigns reproduction number is computed and used to discuss the stability of the disease states. The presence of a backward bifurcation as well as a forward bifurcation is shown together with the existence and local stability of the endemic equilibrium. Results show that messages sent through media have a more significant beneficial effect on the reduction of Ebola cases if they are more effective and spaced out.
- ItemOn the transmission dynamics of Buruli ulcer in Ghana : insights through a mathematical model(BioMed Central, 2015-11-06) Nyabadza, Farai; Bonyah, EbenezerBackground: Mycobacterium ulcerans is know to cause the Buruli ulcer. The association between the ulcer and environmental exposure has been documented. However, the epidemiology of the ulcer is not well understood. A hypothesised transmission involves humans being bitten by the water bugs that prey on mollusks, snails and young fishes. Methods: In this paper, a model for the transmission of Mycobacterium ulcerans to humans in the presence of a preventive strategy is proposed and analysed. The model equilibria are determined and conditions for the existence of the equilibria established. The model analysis is carried out in terms of the reproduction number R0. The disease free equilibrium is found to be locally asymptotically stable for R0 < 1. The model is fitted to data from Ghana. Results: The model is found to exhibit a backward bifurcation and the endemic equilibrium point is globally stable when R0 > 1. Sensitivity analysis showed that the Buruli ulcer epidemic is highly influenced by the shedding and clearance rates of Mycobacterium ulcerans in the environment. The model is found to fit reasonably well to data from Ghana and projections on the future of the Buruli ulcer epidemic are also made. Conclusions: The model reasonably fitted data from Ghana. The fitting process showed data that appeared to have reached a steady state and projections showed that the epidemic levels will remain the same for the projected time. The implications of the results to policy and future management of the disease are discussed.
- ItemA simulation age-specific tuberculosis model for the Cape Town metropole(Academy of Science of South Africa, 2013-09-18) Nyabadza, Farai; Winkler, DieterTuberculosis (TB) continues to present an insurmountable health burden in the Western Cape Province of South Africa. TB dynamics in adults is different from that in children, with the former determining the latter. Because the dynamics of TB are largely dependent on age, planning for interventions requires reasonable and realistic projections of the incidence across ages. It is thus important to model the dynamics of TB using mathematical models as predictive tools. We considered a TB compartmental model that is age dependent and whose parameters are set as functions of age. The model was fitted to the TB incidence data from the Cape Town metropole. The effective contact rate, a function of both age and time, was changed to fit the model to the notification rates of active TB disease cases. Our simulations illustrate that age structure plays an important role in the dynamics of TB. Projections on the future of the epidemic were made for each age group. The projected results show that TB incidence is likely to increase in the lower age groups of the population. It is clearly evident that even very simple models when applied to limited data can actually give valuable insights. Our results show that the age groups who have the highest incidence rates of active TB disease have the highest contribution in the transmission of TB. Furthermore, interventions should be targeted in the age group 25–34 years.
- ItemA systems dynamic model for drug abuse and drug-related crime in the Western Cape Province of South Africa(Hindawi Publishing Corporation, 2017) Nyabadza, Farai; Coetzee, LezanieThe complex problem of drug abuse and drug-related crimes in communities in the Western Cape province cannot be studied in isolation but through the system they are embedded in. In this paper, a theoretical model to evaluate the syndemic of substance abuse and drug-related crimes within the Western Cape province of South Africa is constructed and explored. The dynamics of drug abuse and drug-related crimes within the Western Cape are simulated using STELLA software. The simulation results are consistent with the data from SACENDU and CrimeStats SA, highlighting the usefulness of such a model in designing and planning interventions to combat substance abuse and its related problems.
- ItemA theoretical model for substance abuse in the presence of treatment(Academy of Science of South Africa, 2012-03-16) Kalula, Asha Saidi; Nyabadza, FaraiThe production and use of addictive stimulants has been a major problem in South Africa. Although research has shown increased demand for drug abuse treatment, the actual size of the drug-abusing population remains unknown. Thus the prevalence of drug abuse requires estimation through available tools. Many questions remain unanswered with regard to interventions, new cases of substance abuse and relapse in recovering persons. A six-state compartmental model including a core and non-core group, with fast and slow progression to addiction, was formulated with the aim of qualitatively investigating the dynamics of substance abuse and predicting drug abuse trends. The analysis of the model was presented in terms of the substance abuse epidemic threshold R0. Numerical simulations were performed to fit the model to available data for methamphetamine use in the Western Cape and to determine the role played by some key parameters. The model was also fitted to data on methamphetamine users who enter rehabilitation using the least squares curve fitting method. It was shown that the model exhibits a backward bifurcation where a stable drug-free equilibrium coexists with a stable drug-persistent equilibrium for a certain defined range of values of R0. The stabilities of the model equilibria were ascertained and persistence conditions established. It was found that it is not sufficient to reduce R0 below unit to control the substance abuse epidemic. The reproduction number should be brought below a determined threshold, R0c. The results also suggested that the substance abuse epidemic can be reduced by intervention programmes targeted at light drug users and by increasing the uptake rate into treatment for those addicted. Projected trends showed a steady decline in the prevalence of methamphetamine abuse until 2015.
- ItemA Theoretical model for the transmission dynamics of the Buruli Ulcer with saturated treatment(Hindawi Publishing Corporation, 2014-08) Bonyah, Ebenezer; Dontwi, Isaac; Nyabadza, FaraiThe management of the Buruli ulcer (BU) in Africa is often accompanied by limited resources, delays in treatment, and macilent capacity in medical facilities. These challenges limit the number of infected individuals that access medical facilities. While most of the mathematical models with treatment assume a treatment function proportional to the number of infected individuals, in settings with such limitations, this assumption may not be valid. To capture these challenges, a mathematical model of the Buruli ulcer with a saturated treatment function is developed and studied. The model is a coupled system of two submodels for the human population and the environment. We examine the stability of the submodels and carry out numerical simulations. The model analysis is carried out in terms of the reproduction number of the submodel of environmental dynamics. The dynamics of the human population submodel, are found to occur at the steady states of the submodel of environmental dynamics. Sensitivity analysis is carried out on the model parameters and it is observed that the BU epidemic is driven by the dynamics of the environment. The model suggests that more effort should be focused on environmental management. The paper is concluded by discussing the public implications of the results.