Farai Nyabadza - Profile on Academia.edu (original) (raw)

Papers by Farai Nyabadza

Theoretical analysis of mixed Plasmodium malariae and Plasmodium falciparum infections with partial cross-immunity

Journal of Theoretical Biology, 2010

A deterministic model for assessing the dynamics of mixed species malaria infections in a human p... more A deterministic model for assessing the dynamics of mixed species malaria infections in a human population is presented to investigate the effects of dual infection with Plasmodium malariae and Plasmodium falciparum. Qualitative analysis of the model including positivity and boundedness is performed. In addition to the disease free equilibrium, we show that there exists a boundary equilibrium corresponding to each species. The isolation reproductive number of each species is computed as well as the reproductive number of the full model. Conditions for global stability of the disease free equilibrium as well as local stability of the boundary equilibria are derived. The model has an interior equilibrium which exists if at least one of the isolation reproductive numbers is greater than unity. Among the interesting dynamical behaviours of the model, the phenomenon of backward bifurcation where a stable boundary equilibrium coexists with a stable interior equilibrium, for a certain range of the associated invasion reproductive number less than unity is observed. Results from analysis of the model show that, when cross-immunity between the two species is weak, there is a high probability of coexistence of the two species and when cross-immunity is strong, competitive exclusion is high. Further, an increase in the reproductive number of species i increases the stability of its boundary equilibrium and its ability to invade an equilibrium of species j. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.

Mathematical and Computer Modelling, 2011

Although cholera has existed for ages, it has continued to plague many parts of the world. In thi... more Although cholera has existed for ages, it has continued to plague many parts of the world. In this study, a deterministic model for cholera in a community is presented and rigorously analysed in order to determine the effects of malnutrition in the spread of the disease. The important mathematical features of the cholera model are thoroughly investigated. The epidemic threshold known as the basic reproductive number and equilibria for the model are determined, and stabilities are investigated. The disease-free equilibrium is shown to be globally asymptotically stable. Local stability of the endemic equilibrium is determined using centre manifold theory and conditions for its global stability are derived using a suitable Lyapunov function. Numerical simulations suggest that an increase in susceptibility to cholera due to malnutrition results in an increase in the number of cholera infected individuals in a community. The results suggest that nutritional issues should be addressed in impoverished communities affected by cholera in order to reduce the burden of the disease.

A graph theoretical perspective of a drug abuse epidemic model

Physica A: Statistical …, Jan 1, 2011

A drug use epidemic can be represented by a finite number of states and transition rules that gov... more A drug use epidemic can be represented by a finite number of states and transition rules that govern the dynamics of drug use in each discrete time step. This paper investigates the spread of drug use in a community where some users are in treatment and others are not in treatment, citing South Africa as an example. In our analysis, we consider the neighbourhood prevalence of each individual, ie, the proportion of the individual&amp;amp;#x27;s drug user contacts who are not in treatment amongst all of his or her contacts. We introduce ...

Models for the spread of HIV/AIDS: trends in southern Africa

Contemporary Mathematics, 2006

A tuberculosis model: The case of ‘reasonable’ and ‘unreasonable’ infectives

Physica A: Statistical Mechanics and its Applications, 2009

Epidemics such as tuberculosis (TB), can be represented by a finite number of states and transiti... more Epidemics such as tuberculosis (TB), can be represented by a finite number of states and transition rules that govern the spread of the disease in each discrete time step. This paper uses a graph theoretic approach to investigate TB interactions in a community where infectives are categorized. A threshold value, α= 1− 1n, for &amp;amp;amp;#x27;reasonable&amp;amp;amp;#x27;infectives is proposed. The results show that an epidemic will not ensue as long as the threshold is surpassed. Simulations presented show that unreasonable infectives can amplify the ...

A deterministic model for church growth with internal revival

Journal of Interdisciplinary Mathematics, 2008

ABSTRACT Churches have played an important role in the development and shaping of societies in th... more ABSTRACT Churches have played an important role in the development and shaping of societies in the world. An extension of a previously proposed theory for church growth is presented and analyzed using a mathematical modelling approach. The extension presented incorporates exposure before conversion and internal revival that results in the restoration of enthusiasm. The results are presented in terms of R 0 , the church reproduction potential. The incorporation of a class of the exposed and internal revival allowed the existence of a subcritical (backward) bifurcation at the critical value R 0 = 1 and hence the existence of multiple equilibria for R 0 < 1. The results suggest that having R 0 < 1 does not necessarily lead to a decline in church growth leading to extinction. Numerical results show that when internal revival is taken into account, R 0 does not accurately describe the invasion strength of the church.

Computational and Mathematical Methods in Medicine, 2014

The management of the Buruli ulcer (BU) in Africa is often accompanied by limited resources, dela... more The 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.

Mathematical Modelling and Analysis, 2008

In this paper problems associated with the modeling of HIV/AIDS in Southern Africa are presented.... more In this paper problems associated with the modeling of HIV/AIDS in Southern Africa are presented. A mathematical model is presented to highlight the three major challenges of modeling HIV/AIDS, i.e condom use, vertical transmission and treatment. The model analysis for the case, where the treatment parameter ρ = 0, is presented in terms of the model reproduction number R and threshold parameters RT and RA that show the contribution of vertical transmission. It is shown that if R, RT , RA < 1, then the disease free equilibrium point is both locally asymptotically and globally stable. Numerical simulations for the model are presented to determine the role of some key epidemiological parameters of the model.

Modelling the role of drug barons on the prevalence of drug epidemics

Mathematical Biosciences and Engineering, 2013

Substance abuse is a global menace with immeasurable consequences to the health of users, the qua... more Substance abuse is a global menace with immeasurable consequences to the health of users, the quality of life and the economy of countries affected. Although the prominently known routes of initiation into drug use are; by contact between potential users and individuals already using the drugs and self initiation, the role played by a special class of individuals referred to as drug lords can not be ignored. We consider a simple but useful compartmental model of drug use that accounts for the contribution of contagion and drug lords to initiation into drug use and drug epidemics. We show that the model has a drug free equilibrium when the threshold parameter R0 is less that unity and a drug persistent equilibrium when R0 is greater than one. In our effort to ascertain the effect of policing in the control of drug epidemics, we include a term accounting for law enforcement. Our results indicate that increased law enforcement greatly reduces the prevalence of substance abuse. In addition, initiation resulting from presence of drugs in circulation can be as high as seven times higher that initiation due to contagion alone.

A theoretical model for substance abuse in the presence of treatment

South African Journal of Science, 2012

ABSTRACT The production and use of addictive stimulants has been a major problem in South Africa.... more ABSTRACT The 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.

South African Journal of Science, 2013

A simulation age-specific tuberculosis model for the Cape Town metropole Tuberculosis (TB) contin... more A simulation age-specific tuberculosis model for the Cape Town metropole Tuberculosis (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.

Differential Equations and Dynamical Systems, 2011

A simple mathematical model for cholera is presented using a system of ordinary differential equa... more A simple mathematical model for cholera is presented using a system of ordinary differential equations. Comprehensive analysis of the important mathematical features of the model is carried out. The disease-free and endemic equilibria are obtained and their local stability investigated. We use the centre manifold theory to show the stability of the endemic equilibrium and suitable Lyapunov function for its global stability. Qualitative analysis of the model including positivity and boundedness of solutions are also presented. The cholera model is numerically analysed using published data to explore the effects of the recovery rate, rate of exposure to contaminated water and contribution of infected individuals to the population of Vibrio cholerae in the aquatic environment on the cumulative number of cholera infected individuals. The results demonstrate that proper management of the diseases will reduce the burden of cholera in endemic areas.

Exploring the benefits of antibody immune response in HIV-1 infection using a discrete model

Mathematical Medicine and Biology, 2015

The role of antibodies in HIV-1 infection is investigated using a discrete-time mathematical mode... more The role of antibodies in HIV-1 infection is investigated using a discrete-time mathematical model that considers cell-free and cell-associated transmission of the virus. Model analysis shows that the effect of each type of antibody is dependent on the stage of the infection. Neutralizing antibodies are efficient in controlling the viral levels in the early days after seroconversion and antibodies that coat HIV-1-infected cells and recruit effector cells to either kill the HIV-1-infected cells or inhibit viral replication are efficient when the infection becomes established. Model simulations show that antibodies that inhibit viral replication are more effective in controlling the infection than those that recruit Natural Killer T cells after infection establishment. The model was fitted to subjects of the Tsedimoso study conducted in Botswana and conclusions similar to elasticity analysis results were obtained. Model fitting results predicted that neutralizing antibodies are more efficient in controlling the viral levels than antibodies that coat HIV-1-infected cells and recruit effector cells to either kill the HIV-1-infected cells or inhibit viral replication in the early days after seroconversion.

A metapopulation model for cholera transmission dynamics between communities linked by migration

Applied Mathematics and Computation, 2014

ABSTRACT A metapopulation model is developed to describe the spread of cholera between two commun... more ABSTRACT A metapopulation model is developed to describe the spread of cholera between two communities connected by migratory movement. Disease threshold ratios specific to the communities are given, considering a case when the communities are isolated and when the communities are connected. The connection of the threshold ratios to disease spread and stability is discussed. The disease free equilibrium is globally stable whenever, the corresponding community specific disease threshold ratios are less than one and unstable otherwise. Community specific endemic equilibrium points are unique, locally asymptotically stable, and only exist when the corresponding disease thresholds are greater than unit. Disease spread is explosive in nature at the beginning of the outbreak but more severe in a community with poor facilities relative to a community with more improved facilities. In isolated communities, in the case of endemic cholera, the infection is characterised by a big outbreak, followed by a small episode of the infection. Only one typically big outbreak is observed in the community with improved facilities with no recurrence of the epidemic. In connected communities, movement of individuals across communities not only influences persistence of the infection but also results in more pronounced outbreak in a relatively well facilitated community in the long term. Synchronous fluctuation of the population is observed when there is unrestricted movement of both immunologically naive and infected individuals across the communities. Our results suggest that during times of cholera, movement to and fro cholera endemic areas should be avoided if the outbreak is to be contained. Otherwise, with continued migration, the infection may potentially worsen even in communities with relatively good facilities.

Journal of Theoretical Biology, 2011

Preventing and managing the HIV/AIDS epidemic in South Africa will dominate the next decade and b... more Preventing and managing the HIV/AIDS epidemic in South Africa will dominate the next decade and beyond. Reduction of new HIV infections by implementing a comprehensive national HIV prevention programme at a sufficient scale to have real impact remains a priority. In this paper, a deterministic HIV/AIDS model that incorporates condom use, screening through HIV counseling and testing (HCT), regular testing and treatment as control strategies is proposed with the objective of quantifying the effectiveness of HCT in preventing new infections and predicting the long-term dynamics of the epidemic. It is found that a backward bifurcation occurs if the rate of screening is below a certain threshold, suggesting that the classical requirement for the basic reproduction number to be below unity though necessary, is not sufficient for disease control in this case. The global stabilities of the equilibria under certain conditions are determined in terms of the model reproduction number R 0 . Numerical simulations are performed and the model is fitted to data on HIV prevalence in South Africa. The effects of changes in some key epidemiological parameters are investigated. Projections are made to predict the long-term dynamics of the disease. The epidemiological implications of such projections on public health planning and management are discussed.

ISRN Biomathematics, 2014

Malaria remains by far the world's most important tropical disease, killing more people than any ... more Malaria remains by far the world's most important tropical disease, killing more people than any other communicable disease. A number of preventive and control measures have been put in place and most importantly drug treatment. The emergence of drug resistance against the most common and affordable antimalarials is widespread and poses a key obstacle to malaria control. A mathematical model that incorporates evolution of drug resistance and treatment as a preventive strategy is formulated and analyzed. The qualitative analysis of the model is given in terms of the effective reproduction number, √ . The existence and stability of the disease-free and endemic equilibria of the model are studied. We establish the threshold parameters below which the burden due to malaria can be brought under control. Numerical simulations are done to determine the role played by key parameters in the model. The public health implications of the results are twofold; firstly every effort should be taken to minimize the evolution of drug resistance due to treatment failure and secondly high levels of treatment and development of immunity are essential in reducing the malaria burden.

Journal of Biological Systems, 2010

Primary prevention measures designed to alter susceptibility and/or reduce exposure of 23 suscept... more Primary prevention measures designed to alter susceptibility and/or reduce exposure of 23 susceptible individuals to diseases, remain the mainstay in the fight against HIV/AIDS. A model for HIV/AIDS, that investigates the reduction in infection by advocating for 31 the rate of dissemination of effective public-health information campaigns results in a decrease in the prevalence of the disease. Similarly, an increase in the fraction of individ-33 uals with AIDS who withdraw from sexual activities reduces the burden of the disease.

MODELING THE IMPACT OF REHABILITATION, AMELIORATION AND RELAPSE ON THE PREVALENCE OF DRUG EPIDEMICS

Journal of Biological Systems, 2013

ABSTRACT Substance abuse remains a global menace in spite of recurrent warnings, seizures, social... more ABSTRACT Substance abuse remains a global menace in spite of recurrent warnings, seizures, social and pharmacological effects associated with addiction to drugs. In this paper, we use a mathematical model which is a combination of the classical SIS and SIR models to investigate the dynamics of substance abuse. Initiation into drug use is based on contact of those at risk (the susceptible population) with drug users at different levels of drug use. We evaluate the threshold number and use it to analyze the model. We show that when this threshold number is less than unity, the drug-free steady state is globally asymptotically stable and when this threshold number is greater than unity the drug-persistent steady state is also globally stable. The impact of amelioration, rehabilitation and re-initiation on drug epidemics is investigated. Amelioration in presence of quitting for light users is observed to reduce the prevalence of substance abuse and this is supported by numerical simulations. The results show that both prevention and treatment/rehabilitation are necessary strategies for reduction of drug epidemics. Our recommendation is that preventive strategies should be directed toward reducing the contact rate and treatment should be combined with psychotherapy to accelerate quitting and reduce re-initiation.

Modelling the Dynamics of Crystal Meth (‘Tik’) Abuse in the Presence of Drug-Supply Chains in South Africa

Bulletin of Mathematical Biology, 2013

Substance abuse remains a global problem, with immense health and social consequences. Crystal me... more Substance abuse remains a global problem, with immense health and social consequences. Crystal meth, known as &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;tik&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39; in South Africa, is a growing problem, and its supply chains have equally grown due to increased numbers of &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;tik&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39; users, especially…

A MATHEMATICAL MODEL FOR COMBATING HIV/AIDS IN SOUTHERN AFRICA: WILL MULTIPLE STRATEGIES WORK?

Journal of Biological Systems, 2006

... Title: A MATHEMATICAL MODEL FOR COMBATING HIV/AIDS IN SOUTHERN AFRICA: WILL MULTIPLE STRATEGI... more ... Title: A MATHEMATICAL MODEL FOR COMBATING HIV/AIDS IN SOUTHERN AFRICA: WILL MULTIPLE STRATEGIES WORK? Author(s): FARAI NYABADZA Department of Mathematics, University of Botswana, P. Bag UB 00704, Gaborone, Botswana. ...