scholarly journals Mathematical modelling of the effects of peer-educators’ campaign on the dynamics of HIV/AIDS in Rwanda

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Wellars Banzi ◽  
Titus K. Rotich ◽  
Jean Marie Ntaganda
Keyword(s):  
Equilibrium Points ◽  
Heterosexual Transmission ◽  
Preventive Strategy ◽  
Peer Educators ◽  
Subject Classifications ◽  
Educational Campaign ◽  
Educational Campaigns ◽  
Dynamics Stability ◽  
Disease Free ◽  
Hiv Aids

In this paper, we analyse the effects of peer-educator’s campaign on the dynamics of HIV. We present a sex-structured model for heterosexual transmission of HIV/AIDS in a community. The model is formulated using integro-differential equations, which help to account for a time delay due to incubation period of infective before developing AIDS. The sex-structured HIV/AIDS model divides the population into two subpopulations, namely; females and males. Both disease Free equilibrium and the endemic equilibrium points for the model are determined and their stability are examined. The model is extended to assess the effect of peer- educational campaigns in slowing or eradicating the epidemic. The exposure risk of infection after each intervention is obtained. Basic reproductive numbers for these models are computed and compared to assess the effectiveness of each intervention in a community. The models are numerically analyzed to assess the effectiveness of the treatment free measure, namely; peer educational campaign on the transmission dynamics of HIV/AIDS using demographic and epidemiological parameters of Rwanda. The study demonstrates the use of sex-structured HIV/AIDS models in assessing the effectiveness of educational campaigns as a preventive strategy in a heterosexually active populationMathematics Subject classifications (MSC 2010): 34D20, 34K60, 92D25, 34K25, 34K28Keywords: Population dynamics, Stability, Basic reproductive numbers, Equilibrium

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.

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 Stability Analysis of HIV/AIDS Model with Educated Subpopulation

CAUCHY ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 188-199
Author(s):  
Ummu Habibah
Keyword(s):  
Disease Transmission ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Hiv Positive ◽  
Asymptotically Stable ◽  
Transmission Coefficients ◽  
Two Stages ◽  
Susceptible Subpopulations ◽  
Disease Free ◽  
Hiv Aids

We had constructed mathematical model of HIV/AIDS with seven compartments. There were two different stages of infection and susceptible subpopulations. Two stages in infection subpopulation were an HIV-positive with consuming ARV such that this subpopulation can survive longer and an HIV-positive not consuming ARV.  The susceptible subpopulation was divided into two, uneducated and educated susceptible subpopulations.  The transmission coefficients from educated and uneducated subpopulations to infection stages were  where  ((  and ) (  and )) In this paper, we consider the case of  and  were zero.  We investigated local stability of the model solutions according to the basic reproduction number as a threshold of disease transmission. The disease-free and endemic equilibrium points were locally asymptotically stable when  and  respectively. To support the analytical results, numerical simulation was conducted.

scholarly journals HIV/AIDS-Pneumonia Coinfection Model with Treatment at Each Infection Stage: Mathematical Analysis and Numerical Simulation

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Shewafera Wondimagegnhu Teklu ◽  
Temesgen Tibebu Mekonnen
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Transmission Rates ◽  
Reproduction Numbers ◽  
Disease Free ◽  
The Basic Reproduction Number ◽  
Hiv Aids

In the paper, we have considered a nonlinear compartmental mathematical model that assesses the effect of treatment on the dynamics of HIV/AIDS and pneumonia coinfection in a human population at different infection stages. Our model revealed that the disease-free equilibrium points of the HIV/AIDS and pneumonia submodels are both locally and globally asymptotically stable whenever the associated basic reproduction numbers ( R H and R P ) are less than unity. Both the submodel endemic equilibrium points are locally and globally asymptotically stable whenever the associated basic reproduction numbers ( R P and R H ) are greater than unity. The full HIV/AIDS-pneumonia coinfection model has both locally and globally asymptotically stable disease-free equilibrium points whenever the basic reproduction number of the coinfection model R H P is less than unity. Using standard values of parameters collected from different kinds of literature, we found that the numerical values of the basic reproduction numbers of the HIV/AIDS-only submodel and pneumonia-only submodel are 17 and 7, respectively, and the basic reproduction number of the HIV/AIDS-pneumonia coinfection model is max 7 , 17 = 17 . Applying sensitive analysis, we identified the most influential parameters to change the behavior of the solution of the considered coinfection dynamical system are the HIV/AIDS and pneumonia transmission rates β 1 and β 2 , respectively. The coinfection model was numerically simulated to investigate the stability of the coinfection endemic equilibrium point, the impacts of transmission rates, and treatment strategies for HIV/AIDS-only, pneumonia-only, and HIV/AIDS-pneumonia coinfected individuals. Finally, we observed that numerical simulations indicate that treatment against infection at every stage lowers the rate of infection or disease prevalence.

scholarly journals A FRACTIONAL ORDER HIV/AIDS MODEL USING CAPUTO-FABRIZIO OPERATOR

2021 ◽  
Vol 15 (2s) ◽  
pp. 1-18
Author(s):  
Ebenezar Nkemjika Unaegbu ◽  
Ifeanyi Sunday Onah ◽  
Moses Oladotun Oyesanya
Keyword(s):  
Equilibrium Point ◽  
Fractional Order ◽  
Numerical Solutions ◽  
Fixed Point Theory ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Existence Of A Solution ◽  
Aids Model ◽  
Disease Free ◽  
Hiv Aids

Background: HIV is a virus that is directed at destroying the human immune system thereby exposing the human body to the risk of been affected by other common illnesses and if it is not treated, it generates a more chronic illness called AIDS. Materials and Methods: In this paper, we employed the fixed-point theory in developing the uniqueness and existence of a solution of fractional order HIV/AIDS model having Caputo-Fabrizio operator. This approach adopted in this work is not conventional when solving biological models by fractional derivatives. Results: The results showed that the model has two equilibrium points namely, disease-free, and endemic equilibrium points, respectively. We showed conditions necessitating the existence of the endemic equilibrium point and showed that the disease-free equilibrium point is locally asymptotically stable. We also tested the stability of our solution using the iterative Laplace transform method on our model which was also shown stable agreeing with the disease-free equilibrium. Conclusions: Numerical simulations of our model showed clear comparison with our analytical results. The numerical solutions show that given fractional operator like the Caputo-Fabrizio operator, it is less noisy and plays a major role in making a precise decision and gives room (‘freedom’) to use data of specific patients as the model can be easily adjusted to accommodate this, as it a better fit for the patients’ data and provide meaningful predictions. Finally, the result showed the advantage of using fractional order derivative in the analysis of the dynamics of HIV/AIDS over the classical case.

scholarly journals Dynamical Analysis of a Fractional Order HIV/AIDS Model

2021 ◽  
Vol 5 (1) ◽  
pp. 14
Author(s):  
Septiangga Van Nyek Perdana Putra ◽  
Agus Suryanto ◽  
Nur Shofianah
Keyword(s):  
Equilibrium Point ◽  
Fractional Order ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Dynamical Analysis ◽  
Order Model ◽  
Globally Asymptotically Stable ◽  
Fractional Order Model ◽  
Disease Free ◽  
Hiv Aids

This article discusses a dynamical analysis of the fractional-order model of HIV/AIDS. Biologically, the rate of subpopulation growth also depends on all previous conditions/memory effects. The dependency of the growth of subpopulations on the past conditions is considered by applying fractional derivatives. The model is assumed to consist of susceptible, HIV infected, HIV infected with treatment, resistance, and AIDS. The fractional-order model of HIV/AIDS with Caputo fractional-order derivative operators is constructed and then, the dynamical analysis is performed to determine the equilibrium points, local stability and global stability of the equilibrium points. The dynamical analysis results show that the model has two equilibrium points, namely the disease-free equilibrium point and endemic equilibrium point. The disease-free equilibrium point always exists and is globally asymptotically stable when the basic reproduction number is less than one. The endemic equilibrium point exists if the basic reproduction number is more than one and is globally asymptotically stable unconditionally. To illustrate the dynamical analysis, we perform some numerical simulation using the Predictor-Corrector method. Numerical simulation results support the analytical results.

scholarly journals Demographic Features of Identified PLWHA Infected through Commercial and Nonmarital Noncommercial Heterosexual Contact in China from 2015 – 2018: A Retrospective Cross-Sectional Study

2020 ◽  
Author(s):  
Zhilong Dong ◽  
Liying Ma ◽  
Chang Cai ◽  
George Fu Gao ◽  
Fan Lyu
Keyword(s):  
Marital Status ◽  
Educational Level ◽  
Hiv Transmission ◽  
Cross Sectional Study ◽  
Demographic Characteristics ◽  
Heterosexual Transmission ◽  
People Living With Hiv ◽  
Heterosexual Contact ◽  
Cross Sectional ◽  
Hiv Aids

Abstract Background:Understanding the demographic characteristics of people living with HIV/AIDS (PLWHA) infected through commercial heterosexual contact (CHC) or nonmarital noncommercial heterosexual contact (NMNCHC) is important for HIV/AIDS prevention and control.Methods:Cases reported through the Chinese HIV/AIDS Case Reporting System (CRS) from 2015 to 2018 were analyzed. A descriptive and preliminary inferential analysis were performed for those demographic characteristics deemed of interest.Results:Overall, 523,121 identified PLWHA between 2015 and 2018 in the CRS were analyzed. The constituent ratio of heterosexual transmission increased from 66.25% in 2015 to 71.48% in 2018. The proportion of CHC heterosexual transmission decreased from 40.18% in 2015 to 37.99% in 2018, while that of NMNCHC increased from 46.33% in 2015 to 49.02% in 2018. PLWHA infected through NMNCHC were significantly younger than those who were infected through CHC (Student’s t test, P<0.0001), with an average age gap ranging from 5.63 (2015) to 7.46 (2018) years, and the average age of both groups increased annually. The frequency of newly identified PLWHA who were infected through CHC had a remarkable increase among the ages of 65 and above. Gender distribution was significantly different between CHC and NMNCHC (χ2 = 8909.00(2015), 9941.90(2016), 11004.00 (2017), 12836.00(2018), all P < 0.0001), and the ratio of men to women in the NMCHC group was 1.50:1 (2015), 1.51:1 (2016), 1.54:1 (2017), and 1.52:1 (2018), while in the commercial heterosexual contact (CHC) group, these ratios were 11.45:1 (2015), 12.08:1 (2016), 12.53:1 (2017), and 13.28:1 (2018). Marital status was significantly different between CHC and NMNCHC (χ2 = 94.67 (2015), 109.88(2016), 58.18(2017), 152.38(2018), all P < 0.0001). As the educational level improved, the proportion of NMNCHC also increased (Cochran - Armitage test, P<0.0001).Conclusions:We found that heterosexual transmission was the primary mode of HIV transmission in China from 2015 to 2018. PLWHA infected through CHC and NMNCHC had different characteristics in age, gender, marital status, and educational level. The frequency of PLWHA infected through CHC increased substantially in the age group of 65 and above. This study provides useful baseline data for future studies on the heterosexual transmission of HIV in China.

scholarly journals On an SEIR Epidemic Model with Vaccination of Newborns and Periodic Impulsive Vaccination with Eventual On-Line Adapted Vaccination Strategies to the Varying Levels of the Susceptible Subpopulation

2020 ◽  
Vol 10 (22) ◽  
pp. 8296 ◽  
Author(s):  
Malen Etxeberria-Etxaniz ◽  
Santiago Alonso-Quesada ◽  
Manuel De la Sen
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Impulsive Vaccination ◽  
Disease Free ◽  
The Basic Reproduction Number

This paper investigates a susceptible-exposed-infectious-recovered (SEIR) epidemic model with demography under two vaccination effort strategies. Firstly, the model is investigated under vaccination of newborns, which is fact in a direct action on the recruitment level of the model. Secondly, it is investigated under a periodic impulsive vaccination on the susceptible in the sense that the vaccination impulses are concentrated in practice in very short time intervals around a set of impulsive time instants subject to constant inter-vaccination periods. Both strategies can be adapted, if desired, to the time-varying levels of susceptible in the sense that the control efforts be increased as those susceptible levels increase. The model is discussed in terms of suitable properties like the positivity of the solutions, the existence and allocation of equilibrium points, and stability concerns related to the values of the basic reproduction number. It is proven that the basic reproduction number lies below unity, so that the disease-free equilibrium point is asymptotically stable for larger values of the disease transmission rates under vaccination controls compared to the case of absence of vaccination. It is also proven that the endemic equilibrium point is not reachable if the disease-free one is stable and that the disease-free equilibrium point is unstable if the reproduction number exceeds unity while the endemic equilibrium point is stable. Several numerical results are investigated for both vaccination rules with the option of adapting through ime the corresponding efforts to the levels of susceptibility. Such simulation examples are performed under parameterizations related to the current SARS-COVID 19 pandemic.

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