scholarly journals HIV/AIDS-Pneumonia Codynamics Model Analysis with Vaccination and Treatment

2022 ◽  
Vol 2022 ◽  
pp. 1-20
Author(s):  
Shewafera Wondimagegnhu Teklu ◽  
Koya Purnachandra Rao
Keyword(s):  
Disease Transmission ◽  
Transmission Rate ◽  
Progression Rate ◽  
Globally Asymptotically Stable ◽  
Standard Data ◽  
Reproduction Numbers ◽  
Manifold Theory ◽  
And Control ◽  
Disease Free ◽  
Hiv Aids

In this paper, we proposed and analyzed a realistic compartmental mathematical model on the spread and control of HIV/AIDS-pneumonia coepidemic incorporating pneumonia vaccination and treatment for both infections at each infection stage in a population. The model exhibits six equilibriums: HIV/AIDS only disease-free, pneumonia only disease-free, HIV/AIDS-pneumonia coepidemic disease-free, HIV/AIDS only endemic, pneumonia only endemic, and HIV/AIDS-pneumonia coepidemic endemic equilibriums. The HIV/AIDS only submodel has a globally asymptotically stable disease-free equilibrium if R 1 < 1 . Using center manifold theory, we have verified that both the pneumonia only submodel and the HIV/AIDS-pneumonia coepidemic model undergo backward bifurcations whenever R 2 < 1   and R 3 = max R 1 , R 2 < 1 , respectively. Thus, for pneumonia infection and HIV/AIDS-pneumonia coinfection, the requirement of the basic reproduction numbers to be less than one, even though necessary, may not be sufficient to completely eliminate the disease. Our sensitivity analysis results demonstrate that the pneumonia disease transmission rate   β 2 and the HIV/AIDS transmission rate   β 1 play an important role to change the qualitative dynamics of HIV/AIDS and pneumonia coinfection. The pneumonia infection transmission rate β 2 gives rises to the possibility of backward bifurcation for HIV/AIDS and pneumonia coinfection if R 3 = max R 1 , R 2 < 1 , and hence, the existence of multiple endemic equilibria some of which are stable and others are unstable. Using standard data from different literatures, our results show that the complete HIV/AIDS and pneumonia coinfection model reproduction number is R 3 = max R 1 , R 2 = max 1.386 , 9.69   = 9.69   at β 1 = 2 and β 2 = 0.2   which shows that the disease spreads throughout the community. Finally, our numerical simulations show that pneumonia vaccination and treatment against disease have the effect of decreasing pneumonia and coepidemic disease expansion and reducing the progression rate of HIV infection to the AIDS stage.

scholarly journals Dynamical analysis of a fractional order model incorporating fear in the disease transmission rate of COVID-19

2020 ◽  
Vol 99 (99) ◽  
pp. 1-17
Author(s):  
Debasis Mukherjee Debasis Mukherjee ◽  
Chandan Maji
Keyword(s):  
Fractional Order ◽  
Disease Transmission ◽  
Transmission Rate ◽  
Three Dimensional ◽  
Dynamical Analysis ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Fear Effect ◽  
And Control ◽  
Disease Free

This paper deals with a fractional-order three-dimensional compartmental model with fear effect. We have investigated whether fear can play an important role or not to spread and control the infectious diseases like COVID-19, SARS etc. in a bounded region. The basic results on uniqueness, non-negativity and boundedness of the solution of the system are investigated. Stability analysis ensures that the disease-free equilibrium point is locally asymptotically stable if carrying capacity greater than a certain threshold value.We have also derived the conditions for which endemic equilibrium is globally asymptotically stable that means the disease persists in the system. Numerical simulation suggests that the fear factor is an important role which is observed through Hopf-bifurcation.

scholarly journals A Two-Strain Deterministic Dengue Model With Seasonality Effect

2019 ◽  
Vol 1 (2) ◽  
pp. 13-15
Author(s):  
Afeez Abidemi ◽  
Mohd Ismail Abd Aziz ◽  
Rohanin Ahmad
Keyword(s):  
Disease Transmission ◽  
Birth Rate ◽  
Climatic Factors ◽  
Secondary Infection ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Dengue Disease ◽  
Reproduction Numbers ◽  
Disease Free

A compartmental model is proposed to describe the dynamics of vector-host interations for dengue disease transmission with coexistence of two virus serotypes. The model is modified to incorporate  seasonal-dependent mosquito birth rate in order to examine the influence of climatic factors such as rainfall and temperature on the dynamics of mosquito population and dengue disease transmission. The Next Generation Matrix method is used to obtain the basic reproduction number associated with the model without seasonality effect. The global dynamics of the model is analysed using the Comparison Theorem. The model is simulated in MATLAB with ode45 routine for two cases, namely: the less aggressive case (Case ) and the more aggressive case (Case ).  Analysis of the model shows that the Disease-Free Equilibrium (DFE) is locally asymptotically stable whenever both the basic reproduction numbers  R01 (associated with strain  only) and  R0j (associated with strain  only) are below unity. It is shown that the DFE is globally asymptotically stable when the susceptibility indices for secondary infection in strain  1 ( sigma1) and strain j ( sigmaj), and  are all less than 1.

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.

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 The Global Behavior of a Periodic Epidemic Model with Travel between Patches

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Luosheng Wen ◽  
Bin Long ◽  
Xin Liang ◽  
Fengling Zeng
Keyword(s):  
Epidemic Model ◽  
Transmission Rate ◽  
Global Behavior ◽  
Uniform Persistence ◽  
Basic Reproduction Ratio ◽  
Globally Asymptotically Stable ◽  
Reproduction Ratio ◽  
Periodic Transmission ◽  
Theoretical Results ◽  
Disease Free

We establish an SIS (susceptible-infected-susceptible) epidemic model, in which the travel between patches and the periodic transmission rate are considered. As an example, the global behavior of the model with two patches is investigated. We present the expression of basic reproduction ratioR0and two theorems on the global behavior: ifR0< 1 the disease-free periodic solution is globally asymptotically stable and ifR0> 1, then it is unstable; ifR0> 1, the disease is uniform persistence. Finally, two numerical examples are given to clarify the theoretical results.

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 Mathematical Epidemic Model of HIV/AIDS in Pakistan

2018 ◽  
Vol 18 (1) ◽  
pp. 14-23 ◽  
Author(s):  
Syed Rizwan Ul Haq Tirmizi ◽  
Nasiruddin Khan ◽  
Syed Talha Tirmizi ◽  
Syeda Amara Tirmizi
Keyword(s):  
Labor Migration ◽  
Medical Science ◽  
Equation Model ◽  
Population Mobility ◽  
Nonlinear Fractional Differential Equation ◽  
Rapid Spread ◽  
Fractional Differential ◽  
And Control ◽  
Disease Free ◽  
Hiv Aids

In Pakistan the effect population mobility, specifically labor migration and refugees is also thought to have been important in explaining the rapid spread of HIV/AIDS. One of the effects labor migration is likely to have had increased the prevalence of the overlap of sexual partnership. A nonlinear fractional differential equation model is discussed for transmission and control of HIV/AIDS in Pakistan. We shall also discuss the disease free equilibrium and stability behavior of the model Bangladesh Journal of Medical Science Vol.18(1) 2019 p.14-23

scholarly journals A MODEL FOR CONTROL OF HIV/AIDS WITH PARENTAL CARE

2013 ◽  
Vol 06 (02) ◽  
pp. 1350006 ◽  
Author(s):  
GBENGA JACOB ABIODUN ◽  
NIZAR MARCUS ◽  
KAZEEM OARE OKOSUN ◽  
PETER JOSEPH WITBOOI
Keyword(s):  
Mathematical Model ◽  
Parental Care ◽  
Optimal Strategies ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Qualitative And Quantitative ◽  
Aids Epidemic ◽  
Quantitative Analyses ◽  
Disease Free ◽  
Hiv Aids

In this study we investigate the HIV/AIDS epidemic in a population which experiences a significant flow of immigrants. We derive and analyze a mathematical model that describes the dynamics of HIV infection among the immigrant youths and how parental care can minimize or prevent the spread of the disease in the population. We analyze the model with both screening control and parental care, then investigate its stability and sensitivity behavior. We also conduct both qualitative and quantitative analyses. It is observed that in the absence of infected youths, disease-free equilibrium is achievable and is globally asymptotically stable. We establish optimal strategies for the control of the disease with screening and parental care, and provide numerical simulations to illustrate the analytic results.

scholarly journals Mathematical Modeling of Echinococcosis in Humans, Dogs, and Sheep

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Getachew Bitew Birhan ◽  
Justin Manango W. Munganga ◽  
Adamu Shitu Hassan
Keyword(s):  
Cystic Echinococcosis ◽  
Transmission Rate ◽  
Interaction Model ◽  
Transmission Dynamics ◽  
Human Populations ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Predator Prey ◽  
Prey Interaction ◽  
Disease Free

In this paper, a model for the transmission dynamics of cystic echinococcosis in the dog, sheep, and human populations is developed and analyzed. We first model and analyze the predator-prey interaction model in these populations; then, we propose a mathematical model of the transmission dynamics of cystic echinococcosis. We calculate the basic reproduction number R 0 and prove that the disease-free equilibrium is globally asymptotically stable, and hence, the disease dies out if R 0 > 1 . We further show that the endemic equilibrium is globally asymptotically stable, and hence, the disease persists if R 0 < 1 . Numerical simulations are performed to illustrate our analytic results. We give sensitivity analysis of the key parameters and give strategies that are helpful to control the transmission of cystic echinococcosis, from which the most sensitive parameter is the transmission rate of Echinococcus’ eggs from the environment to sheep ( β es ). Thus, the effective controlling strategies are associated with this parameter.

ON THE GLOBAL STABILITY OF CHOLERA MODEL WITH PREVENTION AND CONTROL

2018 ◽  
Vol 3 (1) ◽  
pp. 28
Author(s):  
M O Ibrahim ◽  
A A Ayoade ◽  
O J Peter ◽  
F A Oguntolu
Keyword(s):  
Global Stability ◽  
Prevention And Control ◽  
Control Measures ◽  
Extended Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
First Order ◽  
Prevention And Control Measures ◽  
And Control ◽  
Disease Free

In this study, a system of first order ordinary differential equations is used to analyse the dynamics of cholera disease via a mathematical model extended from Fung (2014) cholera model. The global stability analysis is conducted for the extended model by suitable Lyapunov function and LaSalle’s invariance principle. It is shown that the disease free equilibrium (DFE) for the extended model is globally asymptotically stable if 𝑅0 𝑞 < 1 and the disease eventually disappears in the population with time while there exists a unique endemic equilibrium that is globally asymptotically stable whenever 𝑅0 𝑞 > 1 for the extended model or 𝑅0 > 1 for the original model and the disease persists at a positive level though with mild waves (i.e few cases of cholera) in the case of𝑅0 𝑞 > 1. Numerical simulations for strong, weak, and no prevention and control measures are carried out to verify the analytical results and Maple 18 is used to carry out the computations.

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