Transmission dynamics of Trichomonas vaginalis: A mathematical approach

AbstractDespite the availability of treatment that is effective, Trichomonas vaginalis infections are still high. A deterministic model for transmission dynamics of Trichomonas vaginalis is presented as a system of non-linear differential equations. Analysis of the reproduction number has shown that an increase in the number of straight women (non-lesbians) infected result in an increase in the number of lesbians infected. This suggests that straight women are turning into lesbians already infected. The disease-free equilibrium is shown to be globally asymptotically stable when the corresponding reproduction number is less than unity. Analytical results and numerical simulations both show that treatment is able to control Trichomonas vaginalis infections. This suggests an effective control of trichomoniasis rests in encouraging and persuading sexual partners of those displaying symptoms to seek treatment. Failure for the asymptomatic to seek treatment (mostly males given that the majority of males does not show symptoms) will continue to fuel the infection

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

A model of population dynamics of TB in a prison system and application to South Africa

BACKGROUND: Tuberculosis (TB) continues to spread in South African prisons in particular, as prisons are over-capacitated and have poor ventilation. The awaiting trial detainees are not screened on admission and are at high risk of getting infected with TB. RESULTS: We propose a compartmental model to describe the population dynamics of TB disease in prisons. Our model considers the inflow of susceptible, exposed and TB infectives into the prison population. Removal of individuals out of the prison population can be either by death or by being released from prison, as compared to a general population in which removal is only by death. We describe conditions, including non-inflow of infectives into the prison, which will ensure that TB can be eradicated from the prison population. The model is calibrated for the South African prison system, by using data in existing literature. The model can be used to make quantitative projections of TB prevalence and to measure the effect of interventions. Illustrative simulations in this regard are presented. The model can be used for other prison populations too, if data is available to calculate the model parameters. CONCLUSIONS: Various simulations generated with our model serve to illustrate how it can be utilized in making future projections of the levels of prevalence of TB, and to quantify the effect of interventions such as screening, treatment or reduction of transmission parameter values through improved living conditions for inmates. This makes it particularly useful as there are various targets set by the World Health Organization and by governments, for reduction of TB prevalence and ultimately its eradication. Towards eradication of TB from a prison system, the theorem on global stability of the disease-free state is a useful indicator

Modelling the effects of heavy alcohol consumption on the transmission dynamics of gonorrhea

Journal Article (peer reviewed),Prior studies have indicated that heavy al- cohol drinkers are likely to engage in risky sexual behaviours and thus, more likely to get sexually transmitted infections (STIs) than social drinkers. Here, we formulate a deterministic model for evaluating the im- pact of heavy alcohol drinking on the reemerging gonorrhea epidemic. The model is rigorously analysed,showing the existence of a globally asymptotically stable disease-free equilibrium whenever the reproductive number is less than unity. If the disease threshold number is greater than unity, a unique endemic equilibrium exists and is globally asymptotically stable in the interior of the feasible region and the disease persists at endemic proportions if it is initially present.Both analytical and numerical results are provided to ascertain whether heavy alcohol drinking has an impact on the transmission dynamics of gonorrhe

Impact of Vaccination and Culling on Controlling Foot and Mouth Disease: A Mathematical Modelling Approach

Published Online November 2011 (http://www.SciRP.org/journal/wjv),Foot and mouth disease (FMD) is a major threat, not only to countries whose economies rely on agricultural exports, but also to industrialized countries that maintain a healthy domestic livestock industry by eliminating major infectious diseases from their livestock populations. In this paper a simple mathematical model is formulated and comprehen- sively analyzed to assess the impact of vaccination and culling on controlling FMD. Overally the study demonstrates that vaccination and culling are essential on controlling FMD if they are all implemented. Furthermore the study illus- trates that culling latently infected (early detection of infected animals) is extremely important on controlling FMD dy- namics