Steady Mushayabasa

Is HIV infection associated with an increased risk for cholera? Insights from a mathematical model

Cholera, a waterborne gastroenteric infection, remains a significant threat to public health in sub-Saharan Africa, the region most heavily affected by HIV. It is biologically plausible that immune suppression caused by HIV infection predisposes to cholera. In this paper, a simple mathematical model is developed and comprehensively analyzed to assess whether HIV infection is associated with an increased risk for cholera or not. Analytical results of the model show that the quantities R(c) and R(h), which represents the reproductive number for cholera and HIV infection, respectively, provide threshold conditions that determine cumulative new single and dual infection cases. These threshold conditions can be used to gain important insights on the epidemiological consequences of HIV and cholera coexistence in the community. Numerical results are provided to support the analytical findings. The findings suggest that in a cholera-endemic area, HIV infection is associated with an increased risk for cholera.

A Theoretical Analysis of Smoking and Alcoholism

A mathematical model for the spread of alcoholism and smoking is designed and analysed to gain insights into this growing health and social problem. The reproduction number and equilibria states of the model are determined and their local asymptotic stabilities investigated. Analysis of the reproduction number have shown conditions under which encouraging and supporting moderate alcohol drinkers (smokers) to quit alcohol consumption (smoking) is more effective in the control of alcoholism (smoking) than supporting and encouraging alcoholics (smoking addicts) to quit and vice-versa. Numerical simulations show that smoking greatly enhances alcoholism and vice-versa. Thus, as shown by the numerics encouraging and supporting all smokers (alcohol drinkers) to quit smoking (alcohol drinking) also contribute meaningfully to alcohol (smoking) control programmes.

Mathematical analysis of hepatitis C model for intravenous drug misusers: Impact of antiviral therapy, abstinence and relapse

Despite advances in hepatitis C therapy and better knowledge of viral/host factors related to disease progression, hepatitis C virus (HCV) remains the leading cause of chronic liver disease, causing progression to end-stage liver disease (ESLD) as well as the development of hepatocellular carcinoma. In this paper a mathematical model for assessing the impact of antiviral therapy, abstinence and relapse on the transmission dynamics of HCV is formulated and analyzed. A threshold quantity known as the reproductive number has been computed, and the stability of the steady states has been investigated. The dynamical analysis reveals that the model has globally asymptotically stable steady states. The impacts of antiviral therapy, abstinence and relapse on the transmission dynamics of HCV are discussed through the basic reproductive number and numerical simulations.

Modelling the effects of chemotherapy and relapse on the transmission dynamics of leprosy

PurposeAlthough there is a declining trend in the global burden of leprosy, there are 15 countries in Asia and Africa which account for 94% of the global total of the new-case detection rate. Here, we assess the impact of different intervention strategies aimed at leprosy eradication through targeting non-symptomatic and symptomatic individuals.MethodsWe develop a mathematical model of leprosy transmission and treatment amongst symptomatic and non-symptomatic, in order to investigate the effects of leprosy relapse cases, case finding of non-symptomatic individuals and compliance to therapy of individuals administered with treatment. Comparison theory has been qualitatively used to analyze the global stability of the disease-free equilibrium. With the aid of centre manifold theory, the local stability of the endemic equilibrium has been investigated. Population-level effects of increased case findings and high treatment rate (guaranteed by compliance and completion of therapy via educational campaigns) are evaluated through numerical simulations and presented in support of the analytical results.ResultsComprehensive and qualitative mathematical analysis of the model reveals that, the disease-free equilibrium is globally, asymptotically stable whenever the reproductive number is less than unity. Further, we have established that the model has a locally, asymptotically stable endemic equilibrium when the reproductive number is greater, but close to unity. Numerical simulation suggests that case finding of non-symptomatic leprosy carriers, greater that 40% is necessary for reducing leprosy prevalence and maybe useful on attaining leprosy eradication.ConclusionsAt its best, the study suggests that high level of case finding targeting non-symptomatic and symptomatic individuals, together with high level of compliance by individuals on treatment, may have a substantial effect on controlling leprosy relapses and possible may assist on attaining leprosy eradication.

Dynamics and Stability Analysis of a Brucellosis Model with Two Discrete Delays

We present a mathematical model for brucellosis transmission that incorporates two discrete delays and culling of infected animals displaying signs of brucellosis infection. The first delay represents the incubation period while the second account for the time needed to detect and cull infectious animals. Feasibility and stability of the model steady states have been determined analytically and numerically. Further, the occurrence of Hopf bifurcation has been established. Overall the findings from the study, both analytical and numerical, suggest that the two delays can destabilize the system and periodic solutions can arise through Hopf bifurcation.

Global Stability of an Anthrax Model with Environmental Decontamination and Time Delay

Anthrax occurs worldwide and is associated with sudden death of cattle and sheep. This paper considers an epidemic model of anthrax in animal population, only. The susceptible animal is assumed to be infected, only, through ingestion of the disease causing pathogens. The proposed model incorporates time delay and environmental decontamination by humans. The time delay represents the period an infected animal needs to succumb to anthrax-related death. By constructing suitable Lyapunov functionals, we demonstrate that the global dynamics of this model fully hinges on whether the associated reproductive number is greater or less than unity. The effectiveness of environmental decontamination on eradication of anthrax in the community is explored through the reproductive number.

Assessing the effects of drug misuse on HIV/AIDS prevalence.

Drug misuse (injecting drug users-IDU) has been recognized to have a significant effect on the spread of HIV/AIDS epidemic. A deterministic model to assess the contribution of drug misuse and sex in the spread of HIV/AIDS is investigated. The threshold parameters of the model are determined and stabilities are analysed. Analysis of the reproduction number has shown that increase in drug misuse results in an increase in HIV infections. Furthermore, numerical simulations of the model show that drug misuse enhances HIV transmission and progression to AIDS. Thus, in a population with intravenous drug users, advocating for safe sex alone will not be enough to control the HIV/AIDS epidemic.

On the dynamics of brucellosis infection in bison population with vertical transmission and culling

We introduce a new mathematical modeling framework that seek to improve our quantitative understanding of the influence of chronic brucellosis and culling control on brucellosis dynamics in periodic and non-periodic environments. We conduct both epidemic and endemic analysis, with a focus on the threshold dynamics characterized by the basic reproduction numbers. In addition, we also perform an optimal control study to explore optimal culling strategy in periodic and non-periodic environment.

A Mathematical Model for Assessing the Impact of Intravenous Drug Misuse on the Dynamics of HIV and HCV within Correctional Institutions

Unsafe injecting practices, blood exchange, the use of nonsterile needles, and other cutting instruments for tattooing are common in correctional institutions, resulting in a number of blood transmitted infections. A mathematical model for assessing the dynamics of HCV and HIV coinfection within correctional institutions is proposed and comprehensively analyzed. The HCV-only and HIV-only submodels are first considered. Analytical expressions for the threshold parameter in each submodel and the cointeraction are derived. Global dynamics of this coinfection shows that whenever the threshold parameter for the respective submodels and the coinfection model is less than unity, then the epidemics die out, the reverse condition implies disease persistence within correctional institutions. Numerical simulations using a set of plausible parameter values are provided to support analytical findings.

Modeling the Effects of Spatial Heterogeneity and Seasonality on Guinea Worm Disease Transmission

Guinea worm disease is one of the neglected tropical diseases that is on the verge of elimination. Currently the disease is endemic in four countries, namely, Ethiopia, Mali, Chad, and South Sudan. Prior studies have demonstrated that climate factors and limited access to safe drinking water have a significant impact on transmission and control of Guinea worm disease. In this paper, we present a new mathematical model to understand the transmission dynamics of Guinea worm disease in South Sudan. The model incorporates seasonal variations, educational campaigns, and spatial heterogeneity. Both qualitative and quantitative analysis of the model have been carried out. Utilizing Guinea worm disease surveillance data of South Sudan (2007-2013) we estimate the model parameters. Meanwhile, we perform an optimal control study to evaluate the implications of vector control on long-term Guinea worm infection dynamics. Our results demonstrate that vector control could play a significant role on Guinea worm disease eradication.