C. P. Bhunu

The impact of media coverage on the transmission dynamics of human influenza

BackgroundThere is an urgent need to understand how the provision of information influences individual risk perception and how this in turn shapes the evolution of epidemics. Individuals are influenced by information in complex and unpredictable ways. Emerging infectious diseases, such as the recent swine flu epidemic, may be particular hotspots for a media-fueled rush to vaccination; conversely, seasonal diseases may receive little media attention, despite their high mortality rate, due to their perceived lack of newness.MethodsWe formulate a deterministic transmission and vaccination model to investigate the effects of media coverage on the transmission dynamics of influenza. The population is subdivided into different classes according to their disease status. The compartmental model includes the effect of media coverage on reporting the number of infections as well as the number of individuals successfully vaccinated.ResultsA threshold parameter (the basic reproductive ratio) is analytically derived and used to discuss the local stability of the disease-free steady state. The impact of costs that can be incurred, which include vaccination, education, implementation and campaigns on media coverage, are also investigated using optimal control theory. A simplified version of the model with pulse vaccination shows that the media can trigger a vaccinating panic if the vaccine is imperfect and simplified messages result in the vaccinated mixing with the infectives without regard to disease risk.ConclusionsThe effects of media on an outbreak are complex. Simplified understandings of disease epidemiology, propogated through media soundbites, may make the disease significantly worse.

Modeling HIV/AIDS and Tuberculosis Coinfection

An HIV/AIDS and TB coinfection model which considers antiretroviral therapy for the AIDS cases and treatment of all forms of TB, i.e., latent and active forms of TB, is presented. We begin by presenting an HIV/AIDS-TB coinfection model and analyze the TB and HIV/AIDS submodels separately without any intervention strategy. The TB-only model is shown to exhibit backward bifurcation when its corresponding reproduction number is less than unity. On the other hand, the HIV/AIDS-only model has a globally asymptotically stable disease-free equilibrium when its corresponding reproduction number is less than unity. We proceed to analyze the full HIV-TB coinfection model and extend the model to incorporate antiretroviral therapy for the AIDS cases and treatment of active and latent forms of TB. The thresholds and equilibria quantities for the models are determined and stabilities analyzed. From the study we conclude that treatment of AIDS cases results in a significant reductions of numbers of individuals progressing to active TB. Further, treatment of latent and active forms of TB results in delayed onset of the AIDS stage of HIV infection.

Tuberculosis transmission model with chemoprophylaxis and treatment.

A tuberculosis model which incorporates treatment of infectives and chemoprophylaxis is presented. The model assumes that latently infected individuals develop active disease as a result of endogenous re-activation, exogenous re-infection and disease relapse, though a small fraction is assumed to develop active disease soon after infection. We start by formulating and analyzing a TB model without any intervention strategy that we extend to incorporate chemoprophylaxis and treatment of infectives. The epidemic thresholds known as reproduction numbers and equilibria for the models are determined, and stabilities analyzed. The reproduction numbers for the models are compared to assess the possible community benefits achieved by treatment of infectives, chemoprophylaxis and a holistic approach of these intervention strategies. The study shows that treatment of infectives is more effective in the first years of implementation (≈ 10 years) as treatment results in clearing active TB immediately and there after chemoprophylaxis will do better in controlling the number of infectives due to reduced progression to active TB.

Mathematical Analysis of a Two Strain HIV/AIDS Model with Antiretroviral Treatment

A two strain HIV/AIDS model with treatment which allows AIDS patients with sensitive HIV-strain to undergo amelioration is presented as a system of non-linear ordinary differential equations. The disease-free equilibrium is shown to be globally asymptotically stable when the associated epidemic threshold known as the basic reproduction number for the model is less than unity. The centre manifold theory is used to show that the sensitive HIV-strain only and resistant HIV-strain only endemic equilibria are locally asymptotically stable when the associated reproduction numbers are greater than unity. Qualitative analysis of the model including positivity, boundedness and persistence of solutions are presented. The model is numerically analysed to assess the effects of treatment with amelioration on the dynamics of a two strain HIV/AIDS model. Numerical simulations of the model show that the two strains co-exist whenever the reproduction numbers exceed unity. Further, treatment with amelioration may result in an increase in the total number of infective individuals (asymptomatic) but results in a decrease in the number of AIDS patients. Further, analysis of the reproduction numbers show that antiretroviral resistance increases with increase in antiretroviral use.

Mathematical Analysis of an HIV/AIDS Model: Impact of Educational Programs and Abstinence in Sub-Saharan Africa

We formulate a deterministic HIV/AIDS model to theoretically investigate how counselling and testing coupled with the resulting decrease in sexual activity could affect the HIV epidemic in resource-limited communities. The threshold quantities are determined and stabilities analyzed. Theoretical analysis and numerical simulations support the idea that increase in the number of sexually inactive HIV positive individuals who voluntarily abstain from sex has a positive impact on HIV/AIDS control. Results from this theoretical study suggest that effective counselling and testing have a great potential to partially control the epidemic (especially when HIV positive individuals either willingly withdraw from risky sexual activities or disclose their status beforehand) even in the absence of antiretroviral therapy (ART). Therefore, more needs to be done in resource-limited settings, such as sub-Saharan Africa, as far as the HIV/AIDS epidemic is concerned and a formalized information, education, and communication strategy should be given prominence in educational campaigns.

Modelling the effects of pre-exposure and post-exposure vaccines in tuberculosis control

Epidemic control strategies alter the spread of the disease in the host population. In this paper, we describe and discuss mathematical models that can be used to explore the potential of pre-exposure and post-exposure vaccines currently under development in the control of tuberculosis. A model with bacille Calmette-Guerin (BCG) vaccination for the susceptibles and treatment for the infectives is first presented. The epidemic thresholds known as the basic reproduction numbers and equilibria for the models are determined and stabilities are investigated. The reproduction numbers for the models are compared to assess the impact of the vaccines currently under development. The centre manifold theory is used to show the existence of backward bifurcation when the associated reproduction number is less than unity and that the unique endemic equilibrium is locally asymptotically stable when the associated reproduction number is greater than unity. From the study we conclude that the pre-exposure vaccine currently under development coupled with chemoprophylaxis for the latently infected and treatment of infectives is more effective when compared to the post-exposure vaccine currently under development for the latently infected coupled with treatment of the infectives.

Modeling Schistosomiasis and HIV/AIDS Codynamics

We formulate a mathematical model for the cointeraction of schistosomiasis and HIV/AIDS in order to assess their synergistic relationship in the presence of therapeutic measures. Comprehensive mathematical techniques are used to analyze the model steady states. The disease-free equilibrium is shown to be locally asymptotically stable when the associated disease threshold parameter known as the basic reproduction number for the model is less than unity. Centre manifold theory is used to show that the schistosomiasis-only and HIV/AIDS-only endemic equilibria are locally asymptotically stable when the associated reproduction numbers are greater than unity. The impact of schistosomiasis and its treatment on the dynamics of HIV/AIDS is also investigated. To illustrate the analytical results, numerical simulations using a set of reasonable parameter values are provided, and the results suggest that schistosomiasis treatment will always have a positive impact on the control of HIV/AIDS.

Optimal control for HIV-1 multi-drug therapy

Optimal control theory is applied to a mathematical model that describes the interaction of the immune system with the human immunodeficiency virus (HIV) and that permits the administration of triple HIV drug therapy. The optimal control represents a percentage effect the chemotherapy consisting of fusion inhibitors (FIs), reverse transcriptase inhibitors (RTIs), and protease inhibitors (PIs) has on the interaction of CD4+T-cells with the virus. First, we maximize the benefit based on the T-cell count and minimize the systemic cost based on the percentage of chemotherapies given and then build an objective functional to minimize the viral replication and treatment systemic costs. Our results indicate that highly toxic drugs and small dosage sizes have the potential for improving the quality of life and reducing economic costs of therapy. An optimal control strategy that seeks to maximize CD4+ T-cells has the potential to provide better treatment results over the optimal treatmet strategy that seeks to minimize the viral production. The addition of FIs to the current HIV treatment strategy of RTIs and PIs improves to relax both concentration and dose sizes of RTIs and PIs.

Mathematical modelling of immune regulation of type 1 diabetes

Type 1 diabetes is a disease characterized by progressive loss of β cell function due to an autoimmune reaction affecting the islets of Langerhans. Two types of T cells are involved in diabetes: turncoat auto-reactive T cells, or T cells gone bad, that kill the insulin-producing cells, and regulatory T cells that are unable to control the auto-reactive T cells. We formulate a mathematical model that incorporates the role of cytotoxic T cells and regulatory T cells in type 1 diabetes. This study shows that onset of type 1 diabetes is due to a collective, dynamical instability, rather than being caused by a single etiological factor. It is also a numbers game between regulatory T cells and auto-reactive T cells. The problem in the onset of this disease is that there are not enough of the regulatory cells that suppress the immune response against the bodys insulin-producing pancreatic islet cells.

MODELING THE EFFECTS OF SCHISTOSOMIASIS ON THE TRANSMISSION DYNAMICS OF HIV/AIDS

A schistosomiasis and HIV/AIDS co-infection model is presented as a system of nonlinear ordinary differential equations. Qualitative analysis (properties) of the model are presented. The disease-free equilibrium is shown to be locally asymptotically stable when the associated epidemic threshold known as the basic reproduction number for the model is less than unity. The Centre Manifold theory is used to show that the schistosomiasis only and HIV/AIDS only endemic equilibria are locally asymptotically stable when the associated reproduction numbers are greater than unity. The model is numerically analyzed to assess the effects of schistosomiasis on the dynamics of HIV/AIDS. Analysis of the reproduction numbers and numerical simulations show that an increase of schistosomiasis cases result in an increase of HIV/AIDS cases, suggesting that schistosomiasis control have a positive impact in controlling the transmission dynamics of HIV/AIDS.