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

A mathematical model for assessing the impact of poverty on yaws eradication

AbstractA neglected disease with a nearly forgotten name is making a comeback following a global control programme that almost eradicated it more than forty years ago. Until the 1970s the prevalence of non-venereal treponematosis, including yaws, was greatly reduced after worldwide mass treatment. In 2005, cases were again reported in the Democratic Republic of the Congo. A deterministic model is formulated to investigate the impact of poverty on yaws eradication. Threshold parameters are determined and stabilities analysed. The reproductive number was also used to assess the impact of birth rate in resource-constrained families on the dynamics of yaws. The model was shown to be globally stable whenever the associated reproductive number is less than a unity. Using the Lyapunov function it was proved that whenever the associated reproductive number is greater than a unity an endemic equilibrium exists and is globally asymptotically stable. Results from this theoretical study suggests that if the population of children in the community is dominated by those from resource-constrained families, then yaws eradication will remain difficulty to attain. Thus, more needs to be done in addressing issues such as high fertility rate, overcrowding, poor sanitation, etc. and poverty in general so that yaws epidemic which was successfully controlled several decades ago will cease to reemerge and can easily be eradicated

HSV-2 and Substance Abuse amongst Adolescents: Insights through Mathematical Modelling

Herpes simplex virus infection is mostly spread and occurs more commonly among substance abusing adolescents as compared to the nonsubstance abusing. In this paper, a mathematical model for the spread of HSV-2 within a community with substance abusing adolescents is developed and analysed. The impacts of condom use and educational campaigns are examined. The study suggests that condom use is highly effective among adolescents, when we have more of them quitting than becoming substance abusers. Measures such as educational campaigns can be put in place to try and reduce adolescents from becoming substance abusers. Further, we applied optimal control theory to the proposed model. The controls represent condom use and educational campaigns. The objective is based on maximising the susceptible nonsubstance abusing adolescents, while minimising the susceptible substance abusing adolescents, the infectious nonsubstance abusing adolescents, and the infectious substance abusing adolescents. We used Pontrygin’s maximum principle to characterise the optimal levels of the two controls. The resulting optimality system is solved numerically. Overall, the application of the optimal control theory suggests that more effort should be devoted to condom use as compared to educational campaigns

Cost-effectiveness of novel vaccines for tuberculosis control: a decision analysis study

<p>Abstract</p> <p>Background</p> <p>The development of a successful new tuberculosis (TB) vaccine would circumvent many limitations of current diagnostic and treatment practices. However, vaccine development is complex and costly. We aimed to assess the potential cost effectiveness of novel vaccines for TB control in a sub-Saharan African country - Zambia - relative to the existing strategy of directly observed treatment, short course (DOTS) and current level of bacille Calmette-Guérin (BCG) vaccination coverage.</p> <p>Methods</p> <p>We conducted a decision analysis model-based simulation from the societal perspective, with a 3% discount rate and all costs expressed in 2007 US dollars. Health outcomes and costs were projected over a 30-year period, for persons born in Zambia (population 11,478,000 in 2005) in year 1. Initial development costs for single vaccination and prime-boost strategies were prorated to the Zambian share (0.398%) of global BCG vaccine coverage for newborns. Main outcome measures were TB-related morbidity, mortality, and costs over a range of potential scenarios for vaccine efficacy.</p> <p>Results</p> <p>Relative to the status quo strategy, a BCG replacement vaccine administered at birth, with 70% efficacy in preventing rapid progression to TB disease after initial infection, is estimated to avert 932 TB cases and 422 TB-related deaths (prevention of 199 cases/100,000 vaccinated, and 90 deaths/100,000 vaccinated). This would result in estimated net savings of $3.6 million over 30 years for 468,073 Zambians born in year 1 of the simulation. The addition of a booster at age 10 results in estimated savings of$5.6 million compared to the status quo, averting 1,863 TB cases and 1,011 TB-related deaths (prevention of 398 cases/100,000 vaccinated, and of 216 deaths/100,000 vaccinated). With vaccination at birth alone, net savings would be realized within 1 year, whereas the prime-boost strategy would require an additional 5 years to realize savings, reflecting a greater initial development cost.</p> <p>Conclusions</p> <p>Investment in an improved TB vaccine is predicted to result in considerable cost savings, as well as a reduction in TB morbidity and TB-related mortality, when added to existing control strategies. For a vaccine with waning efficacy, a prime-boost strategy is more cost-effective in the long term.</p

Assessing the Impact of Vaccination on Controlling the Spread of Human Scabies

This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.,Scabies is among the infestations almost forgotten due to its association with poor communities. We formulate a deterministic model to assess the possible impact vaccination will have on scabies control.The Descartes?s rule of signs is used to show the nature of the endemic equilibria. Analysis of the reproduction number and numerical simulations suggest that vaccination in addition to treatment will help greatly in reducing the spread of scabies infestation.This suggests there is a strong need for researchers to come up with a possible vaccine in that order to effectively control scabies especially among the disadvantaged communities

A Computational Study of HSV-2 with Poor Treatment Adherence

Herpes simplex virus type 2 (HSV-2) is the most prevalent sexually transmitted disease worldwide, despite the availability of highly effective antiviral treatments. In this paper, a basic mathematical model for the spread of HSV-2 incorporating all the relevant biological details and poor treatment adherence is proposed and analysed. Equilibrium states of the model are determined and their stability has been investigated. The basic model is then extended to incorporate a time dependent intervention strategy. The aim of the control is tied to reducing the rate at which HSV-2 patients in treatment quit therapy before completion. Practically, this control can be implemented through monitoring and counselling all HSV-2 patients in treatment. The Pontryagin’s maximum principle is used to characterize the optimal level of the control, and the resulting optimality system is solved numerically. Overall, the study demonstrates that though time dependent control will be effective on controlling new HSV-2 cases it may not be sustainable for certain time intervals