MODELING AND ANALYSIS OF HIV AND HEPATITIS C CO-INFECTIONS

Infection with the hepatitis C virus (HCV) is the most common coinfection in people with the human immunodeficiency virus (HIV), and hepatitis C is categorized as an HIV-related illness. The study of the joint dynamics of HIV and HCV present formidable mathematical challenges in spite the fact that they share similar routes of transmission. A deterministic model for the co-interaction of HCV and HIV in a community is presented and rigorously analyzed. 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 the unity. The Centre Manifold theory is used to show that the HCV only and HIV/AIDS only endemic equilibria are locally asymptotically stable when their associated reproduction numbers are greater than the unity. We compute two coexistence thresholds for the stability of boundary equilibria. Numerical results are presented to validate analytical results.

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

Journal of Biological System ◽

10.1142/s0218339010003196 ◽

2010 ◽

Vol 18 (02) ◽

pp. 277-297 ◽

Cited By ~ 8

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.

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Mathematical Modeling and Analysis of an Alcohol Drinking Model with the Influence of Alcohol Treatment Centers

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2020/4903168 ◽

2020 ◽

Vol 2020 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

Bouchaib Khajji ◽

Abderrahim Labzai ◽

Omar Balatif ◽

Mostafa Rachik

Keyword(s):

Alcohol Drinking ◽

Addiction Treatment ◽

Reproduction Number ◽

Dynamical Behavior ◽

Model Parameters ◽

Asymptotically Stable ◽

Globally Asymptotically Stable ◽

Modeling And Analysis ◽

Private And Public ◽

The Stability

In this paper, we present a continuous mathematical model PMHTrTpQ of alcohol drinking with the influence of private and public addiction treatment centers. We study the dynamical behavior of this model and we discuss the basic properties of the system and determine its basic reproduction number R0. We also study the sensitivity analysis of model parameters to know the parameters that have a high impact on the reproduction number R0. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at drinking-free equilibrium E0 when R0≤1. When R0>1, drinking present equilibrium E∗ exists and the system is locally as well as globally asymptotically stable at alcohol present equilibrium E∗.

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Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics

Journal of Applied Mathematics ◽

10.1155/2020/5109841 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13

Author(s):

Haileyesus Tessema Alemneh

Keyword(s):

Optimal Control ◽

Center Manifold ◽

Necessary Conditions ◽

Deterministic Model ◽

Integrated Control ◽

Modeling Analysis ◽

The Stability ◽

Manifold Theory ◽

The Impact ◽

Control Of Corruption

In this paper, a nonlinear deterministic model for the dynamics of corruption is proposed and analysed qualitatively using the stability theory of differential equations. The basic reproduction number with respect to the corruption-free equilibrium is obtained using next-generation matrix method. The conditions for local and global asymptotic stability of corruption-free and endemic equilibria are established. From the analysis using center manifold theory, the model exhibits forward bifurcation. Then, the model was extended by reformulating it as an optimal control problem, with the use of two time-dependent controls to assess the impact of corruption on human population, namely, campaigning about corruption through media and advertisement and exposing corrupted individuals to jail and giving punishment. By using Pontryagin’s maximum principle, necessary conditions for the optimal control of the transmission of corruption were derived. From the numerical simulation, it was found that the integrated control strategy must be taken to fight against corruption.

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Mathematical Modelling of HIV-HCV Coinfection Dynamics in Absence of Therapy

Computational and Mathematical Methods in Medicine ◽

10.1155/2020/2106570 ◽

2020 ◽

Vol 2020 ◽

pp. 1-27

Author(s):

Edison Mayanja ◽

Livingstone S. Luboobi ◽

Juma Kasozi ◽

Rebecca N. Nsubuga

Keyword(s):

Deterministic Model ◽

Spontaneous Clearance ◽

Model Formulation ◽

Chronic Stage ◽

Long Run ◽

Reproduction Numbers ◽

Immunodeficiency Virus ◽

Next Generation Matrix ◽

Hcv Coinfection ◽

Number Of Individuals

Globally, it is estimated that of the 36.7 million people infected with human immunodeficiency virus (HIV), 6.3% are coinfected with hepatitis C virus (HCV). Coinfection with HIV reduces the chance of HCV spontaneous clearance. In this work, we formulated and analysed a deterministic model to study the HIV and HCV coinfection dynamics in absence of therapy. Due to chronic stage of HCV infection being long, asymptomatic, and infectious, our model formulation was based on the splitting of the chronic stage into the following: before onset of cirrhosis and its complications and after onset of cirrhosis. We computed the basic reproduction numbers using the next generation matrix method. We performed numerical simulations to support the analytical results. We carried out sensitivity analysis to determine the relative importance of the different parameters influencing the HIV-HCV coinfection dynamics. The findings reveal that, in the long run, there is a substantial number of individuals coinfected with HIV and latent HCV. Therefore, HIV and latently HCV-infected individuals need to seek early treatment so as to slow down the progression of HIV to AIDS and latent HCV to advanced HCV.

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Dynamics of an infection model with two delays

International Journal of Biomathematics ◽

10.1142/s1793524515500680 ◽

2015 ◽

Vol 08 (05) ◽

pp. 1550068 ◽

Cited By ~ 3

Author(s):

Xinguo Sun ◽

Junjie Wei

Keyword(s):

Viral Infection ◽

Asymptomatic Carrier ◽

Infection Model ◽

Asymptotically Stable ◽

Stability Switches ◽

Globally Asymptotically Stable ◽

Ctl Response ◽

Reproduction Numbers ◽

Two Delays ◽

The Stability

In this paper, a HTLV-I infection model with two delays is considered. It is found that the dynamics of this model are determined by two threshold parameters R0 and R1, basic reproduction numbers for viral infection and for CTL response, respectively. If R0 < 1, the infection-free equilibrium P0 is globally asymptotically stable. If R1 < 1 < R0, the asymptomatic-carrier equilibrium P1 is globally asymptotically stable. If R1 > 1, there exists a unique HAM/TSP equilibrium P2. The stability of P2 is changed when the second delay τ2 varies, that is there exist stability switches for P2.

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Modeling Schistosomiasis and HIV/AIDS Codynamics

Computational and Mathematical Methods in Medicine ◽

10.1155/2011/846174 ◽

2011 ◽

Vol 2011 ◽

pp. 1-15 ◽

Cited By ~ 14

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.

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