scholarly journals Modeling Schistosomiasis and HIV/AIDS Codynamics

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
S. Mushayabasa ◽  
C. P. Bhunu
Keyword(s):  
Positive Impact ◽  
Asymptotically Stable ◽  
Reproduction Numbers ◽  
Therapeutic Measures ◽  
Disease Threshold ◽  
Mathematical Techniques ◽  
Manifold Theory ◽  
Parameter Values ◽  
The Impact ◽  
Hiv Aids

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.

scholarly journals Mathematical Analysis of Malaria-Schistosomiasis Coinfection Model

2016 ◽  
Vol 2016 ◽  
pp. 1-19 ◽  
Author(s):  
E. A. Bakare ◽  
C. R. Nwozo
Keyword(s):  
Numerical Simulations ◽  
Endemic Equilibrium ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Reproduction Numbers ◽  
Mathematical Techniques ◽  
Parameter Values ◽  
The Impact ◽  
Number Of Individuals ◽  
Disease Free

We formulated and analysed a mathematical model to explore the cointeraction between malaria and schistosomiasis. Qualitative and comprehensive mathematical techniques have been applied to analyse the model. The local stability of the disease-free and endemic equilibrium was analysed, respectively. However, the main theorem shows that if RMS<1, then the disease-free equilibrium is locally asymptotically stable and the phase will vanish out of the host and if RMS>1, a unique endemic equilibrium is also locally asymptotically stable and the disease persists at the endemic steady state. The impact of schistosomiasis and its treatment on malaria dynamics is also investigated. Numerical simulations using a set of reasonable parameter values show that the two epidemics coexist whenever their reproduction numbers exceed unity. Further, results of the full malaria-schistosomiasis model also suggest that an increase in the number of individuals infected with schistosomiasis in the presence of treatment results in a decrease in malaria cases. Sensitivity analysis was further carried out to investigate the influence of the model parameters on the transmission and spread of malaria-schistosomiasis coinfection. Numerical simulations were carried out to confirm our theoretical findings.

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

2010 ◽  
Vol 18 (02) ◽  
pp. 277-297 ◽  
Author(s):  
C. P. BHUNU ◽  
J. M. TCHUENCHE ◽  
W. GARIRA ◽  
G. MAGOMBEDZE ◽  
S. MUSHAYABASA
Keyword(s):  
Positive Impact ◽  
Transmission Dynamics ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Epidemic Threshold ◽  
Schistosomiasis Control ◽  
Reproduction Numbers ◽  
Manifold Theory ◽  
Disease Free ◽  
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.

MODELING THE IMPACT OF VOLUNTARY TESTING AND TREATMENT ON TUBERCULOSIS TRANSMISSION DYNAMICS

2012 ◽  
Vol 05 (04) ◽  
pp. 1250029 ◽  
Author(s):  
S. MUSHAYABASA ◽  
C. P. BHUNU
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Positive Impact ◽  
Transmission Dynamics ◽  
Effective Control ◽  
Reproductive Number ◽  
Voluntary Testing ◽  
Manifold Theory ◽  
The Impact ◽  
Disease Free

A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemiological threshold, known as the reproduction number is derived and qualitatively used to investigate the existence and stability of the associated equilibrium of the model system. The disease-free equilibrium is shown to be locally-asymptotically stable when the reproductive number is less than unity, and unstable if this threshold parameter exceeds unity. It is shown, using the Centre Manifold theory, that the model undergoes the phenomenon of backward bifurcation where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The analysis of the reproduction number suggests that voluntary tuberculosis testing and treatment may lead to effective control of tuberculosis. Furthermore, numerical simulations support the fact that an increase voluntary tuberculosis testing and treatment have a positive impact in controlling the spread of tuberculosis in the community.

scholarly journals Modeling the effect of temperature variability on malaria control strategies

2020 ◽  
Vol 15 ◽  
pp. 65
Author(s):  
Salisu M. Garba ◽  
Usman A. Danbaba
Keyword(s):  
Control Strategies ◽  
Effect Of Temperature ◽  
Bed Nets ◽  
Asymptotically Stable ◽  
Temperature Changes ◽  
Offspring Number ◽  
Local Asymptotic Stability ◽  
Reproduction Numbers ◽  
The Impact ◽  
Disease Free

In this study, a non-autonomous (temperature dependent) and autonomous (temperature independent) models for the transmission dynamics of malaria in a population are designed and rigorously analysed. The models are used to assess the impact of temperature changes on various control strategies. The autonomous model is shown to exhibit the phenomenon of backward bifurcation, where an asymptotically-stable disease-free equilibrium (DFE) co-exists with an asymptotically-stable endemic equilibrium when the associated reproduction number is less than unity. This phenomenon is shown to arise due to the presence of imperfect vaccines and disease-induced mortality rate. Threshold quantities (such as the basic offspring number, vaccination and host type reproduction numbers) and their interpretations for the models are presented. Conditions for local asymptotic stability of the disease-free solutions are computed. Sensitivity analysis using temperature data obtained from Kwazulu Natal Province of South Africa [K. Okuneye and A.B. Gumel. Mathematical Biosciences 287 (2017) 72–92] is used to assess the parameters that have the most influence on malaria transmission. The effect of various control strategies (bed nets, adulticides and vaccination) were assessed via numerical simulations.

THE EFFECTS OF VACCINATION AND TREATMENT ON THE SPREAD OF HIV/AIDS

2004 ◽  
Vol 12 (04) ◽  
pp. 399-417 ◽  
Author(s):  
M. KGOSIMORE ◽  
E. M. LUNGU
Keyword(s):  
Equilibrium Point ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Treatment Programs ◽  
Asymptotically Stable ◽  
Reproduction Numbers ◽  
Threshold Conditions ◽  
Existence And Stability ◽  
Disease Free ◽  
Hiv Aids

This study investigates the effects of vaccination and treatment on the spread of HIV/AIDS. The objectives are (i) to derive conditions for the success of vaccination and treatment programs and (ii) to derive threshold conditions for the existence and stability of equilibria in terms of the effective reproduction number R. It is found, firstly, that the success of a vaccination and treatment program is achieved when R0t<R0, R0t<R0v and γeRVT(σ)<RUT(α), where R0t and R0v are respectively the reproduction numbers for populations consisting entirely of treated and vaccinated individuals, R0 is the basic reproduction number in the absence of any intervention, RUT(α) and RVT(σ) are respectively the reproduction numbers in the presence of a treatment (α) and a combination of vaccination and treatment (σ) strategies. Secondly, that if R<1, there exists a unique disease free equilibrium point which is locally asymptotically stable, while if R>1 there exists a unique locally asymptotically stable endemic equilibrium point, and that the two equilibrium points coalesce at R=1. Lastly, it is concluded heuristically that the stable disease free equilibrium point exists when the conditions R0t<R0, R0t<R0v and γeRVT(σ)<RUT(α) are satisfied.

scholarly journals HIV/AIDS Model with Early Detection and Treatment

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Augustine S. Mbitila ◽  
Jean M. Tchuenche
Keyword(s):  
Early Detection ◽  
Disease Transmission ◽  
Deterministic Model ◽  
Positive Impact ◽  
Disease Status ◽  
Critical Threshold ◽  
Model Parameters ◽  
Case Detection ◽  
The Impact ◽  
Hiv Aids

A classical epidemiological framework is used to qualitatively assess the impact of early detection and treatment on the dynamics of HIV/AIDS. Within this theoretical framework, two classes of infected populations: those infected but unaware of their serological status and those who are aware of their disease status, are considered. In this context, we formulate and analyze a deterministic model for the transmission dynamics of HIV/AIDS and assess the potential population-level impact of early detection in curtailing the epidemic. A critical threshold parameter for which case detection will have a positive impact is derived. Model parameters sensitivity analysis indicates that the number of partners is the most sensitive (in increasing the average number of secondary transmission) parameter. However, the case detection coverage is the main drivers in reducing the initial disease transmission. Numerical simulations of the model are provided to support the analytical results. Early detection and treatment alone are insufficient to eliminate the disease, and other control strategies are to be explored.

scholarly journals Buddhists Care: Examining the Impact of Religious Elements on Reducing Discriminatory Attitudes toward People Living with HIV/AIDS

Religions ◽  
2019 ◽  
Vol 10 (7) ◽  
pp. 409 ◽  
Author(s):  
Song ◽  
Qin
Keyword(s):  
Positive Impact ◽  
Underlying Mechanism ◽  
People Living With Hiv ◽  
Infected People ◽  
Relevant Evidence ◽  
Positive Attitudes ◽  
Immunodeficiency Syndrome ◽  
The Impact ◽  
Perceived Religiosity ◽  
Hiv Aids

Faith-based programs have been long regarded as influential social approaches to form positive attitudes to human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS) within the last few decades. However, recent scholars argue that religions serve a double role in supporting HIV-infected people. Moreover, relevant evidence is mainly collected from studies among participants of the Western religious traditions, such as Christianity. This study applies the theory of the attitude formation model to examine Buddhist factors impacting discriminatory attitudes towards HIV/AIDS and the causal path to positive behavior intention. To investigate its underlying mechanism, Buddhist elements, as an important antecedent, were introduced in the advertisement against HIV/AIDS-related discrimination to influence people’s attitudinal reaction. Results show that Buddhist advertising could significantly increase perceived religiosity and compassion. Then, both perceived religiosity and compassion jointly increase anti-prejudical attitudes towards HIV-infected people and have a positive impact on interaction intention at the end.

scholarly journals Exploring the Impact of Prostitution on HIV/AIDS Transmission

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
C. P. Bhunu ◽  
A. N. Mhlanga ◽  
S. Mushayabasa
Keyword(s):  
Mathematical Model ◽  
Antiretroviral Therapy ◽  
Condom Use ◽  
Numerical Simulations ◽  
Hiv Transmission ◽  
Safe Sex ◽  
Therapy Regimen ◽  
Reproduction Numbers ◽  
The Impact ◽  
Hiv Aids

HIV/AIDS has been somehow linked to prostitution for decades now. A mathematical model is presented to assess the link between prostitution and HIV transmission. The epidemic thresholds known as the reproduction numbers and equilibria for the model are determined and stabilities analyzed. Analysis of the reproduction numbers suggests that HIV/AIDS control using antiretroviral therapy is more effective in the absence of prostitution. Numerical simulations further show high levels of HIV/AIDS when percentage of prostitutes in the community is high. Results from this study suggest that effectively controlling HIV/AIDS requires strategies that address both prostitution and HIV/AIDS transmission. Addressing HIV/AIDS through condom use and antiretroviral therapy may not be enough to stem HIV/AIDS in the community as some drug/alcohol misusing prostitutes may not be able to negotiate for safe sex while they are in drunken stupor. Furthermore, prostitutes are likely to get infected by different HIV strains some of which may be resistant to the antiretroviral therapy regimen in use.

scholarly journals Local and global asymptotic behavior of malaria-filariasis coinfections in compliant and noncompliant susceptible pregnant women to antenatal medical program in the tropics

2019 ◽  
Vol 2019 (1) ◽  
pp. 31-54
Author(s):  
Oluwatayo M. Ogunmiloro
Keyword(s):  
Pregnant Women ◽  
Host Population ◽  
Control Measures ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Susceptible Host ◽  
Medical Program ◽  
Manifold Theory ◽  
The Tropics ◽  
Parameter Values

Abstract In this paper, a mathematical nonlinear model system of equations describing the dynamics of the co-interaction between malaria and filariasis epidemic affecting the susceptible host population of pregnant women in the tropics is formulated. The basic reproduction number Rmf of the coepidemic model is obtained, and we investigated that it is the threshold parameter between the extinction and persistence of the coepidemic disease. If Rmf < 1, then the disease-free steady state is both locally and globally asymptotically stable resulting in the disease dying out of the host. Also, if Rmf > 1, the disease lingers on. The center manifold theory is used to show that the unique endemic equilibrium is locally asymptotically stable. However, variations in the parameter values involved in the model build up will bring about appropriate control measures to curtail the spread of the coepidemic disease. Numerical simulations are carried out to confirm the theoretical results.

scholarly journals The Dynamic of Heterosexual Transmission of HIV-AIDS Model with Treatment

2017 ◽  
Vol 6 (2) ◽  
Author(s):  
Kehinde Adekunle Bashiru
Keyword(s):  
Mathematical Model ◽  
Equilibrium Points ◽  
Model System ◽  
Transmission Dynamics ◽  
Heterosexual Transmission ◽  
Asymptotically Stable ◽  
Effect Of Treatment ◽  
The Impact ◽  
Disease Free ◽  
Hiv Aids

A Mathematical Model of HIV/AIDS with Heterosexual transmission in the presence of treatment was examine in this paper, it ascertained the impact of treated individuals on the transmission dynamics of HIV/AIDS. Equilibrium points of the model system were found, stability analysis and numerical simulation were carried out, it was discovered that HIV/AIDS can die out with test of time as Ro < 1 . It was observed that the model had a disease free equilibrium which was asymptotically stable for Ro < 1 and unstable for Ro > 1. Graphical representations of the numerical analysis showing the effect of treatment on the model were also presented.

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