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.

A mathematical analysis of a tuberculosis epidemic model with two treatments and exogenous re-infection

2020 ◽  
pp. 2050082
Author(s):  
Mehdi Lotfi ◽  
Azizeh Jabbari ◽  
Hossein Kheiri
Keyword(s):  
Mathematical Model ◽  
Asymptotic Stability ◽  
Stable Disease ◽  
Reproduction Number ◽  
Geometric Approach ◽  
Backward Bifurcation ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Bifurcation Phenomenon ◽  
Disease Free

In this paper, we propose a mathematical model of tuberculosis with two treatments and exogenous re-infection, in which the treatment is effective for a number of infectious individuals and it fails for some other infectious individuals who are being treated. We show that the model exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium coexists with a stable endemic equilibria when the related basic reproduction number is less than unity. Also, it is shown that under certain conditions the model cannot exhibit backward bifurcation. Furthermore, it is shown in the absence of re-infection, the backward bifurcation phenomenon does not exist, in which the disease-free equilibrium of the model is globally asymptotically stable when the associated reproduction number is less than unity. The global asymptotic stability of the endemic equilibrium, when the associated reproduction number is greater than unity, is established using the geometric approach. Numerical simulations are presented to illustrate our main results.

scholarly journals Modeling Transmission of Tuberculosis with MDR and Undetected Cases

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Yongqi Liu ◽  
Zhendong Sun ◽  
Guiquan Sun ◽  
Qiu Zhong ◽  
Li Jiang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Control Strategies ◽  
Multidrug Resistant ◽  
Vital Role ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Tb Control ◽  
Disease Free

This paper presents a novel mathematical model with multidrug-resistant (MDR) and undetected TB cases. The theoretical analysis indicates that the disease-free equilibrium is globally asymptotically stable ifR0<1; otherwise, the system may exist a locally asymptotically stable endemic equilibrium. The model is also used to simulate and predict TB epidemic in Guangdong. The results imply that our model is in agreement with actual data and the undetected rate plays vital role in the TB trend. Our model also implies that TB cannot be eradicated from population if it continues to implement current TB control strategies.

scholarly journals Stability Analysis of a Vector-Borne Disease with Variable Human Population

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Muhammad Ozair ◽  
Abid Ali Lashari ◽  
Il Hyo Jung ◽  
Young Il Seo ◽  
Byul Nim Kim
Keyword(s):  
Mathematical Model ◽  
Human Population ◽  
Feasible Region ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Vector Borne Disease ◽  
Vector Borne ◽  
Theoretical Results ◽  
Disease Free ◽  
Varying Population

A mathematical model of a vector-borne disease involving variable human population is analyzed. The varying population size includes a term for disease-related deaths. Equilibria and stability are determined for the system of ordinary differential equations. IfR0≤1, the disease-“free” equilibrium is globally asymptotically stable and the disease always dies out. IfR0>1, a unique “endemic” equilibrium is globally asymptotically stable in the interior of feasible region and the disease persists at the “endemic” level. Our theoretical results are sustained by numerical simulations.

scholarly journals A Mathematical Model of COVID-19 Pandemic: A Case Study of Bangkok, Thailand

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Pakwan Riyapan ◽  
Sherif Eneye Shuaib ◽  
Arthit Intarasit
Keyword(s):  
Mathematical Model ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Proposed Model ◽  
Next Generation Matrix ◽  
Disease Free ◽  
The Basic Reproduction Number

In this study, we propose a new mathematical model and analyze it to understand the transmission dynamics of the COVID-19 pandemic in Bangkok, Thailand. It is divided into seven compartmental classes, namely, susceptible S , exposed E , symptomatically infected I s , asymptomatically infected I a , quarantined Q , recovered R , and death D , respectively. The next-generation matrix approach was used to compute the basic reproduction number denoted as R cvd 19 of the proposed model. The results show that the disease-free equilibrium is globally asymptotically stable if R cvd 19 < 1 . On the other hand, the global asymptotic stability of the endemic equilibrium occurs if R cvd 19 > 1 . The mathematical analysis of the model is supported using numerical simulations. Moreover, the model’s analysis and numerical results prove that the consistent use of face masks would go on a long way in reducing the COVID-19 pandemic.

scholarly journals Stability of a Mathematical Model of Malaria Transmission with Relapse

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Hai-Feng Huo ◽  
Guang-Ming Qiu
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Recovery Rate ◽  
Reproduction Number ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Next Generation Matrix ◽  
The Government ◽  
Disease Free ◽  
The Basic Reproduction Number

A more realistic mathematical model of malaria is introduced, in which we not only consider the recovered humans return to the susceptible class, but also consider the recovered humans return to the infectious class. The basic reproduction numberR0is calculated by next generation matrix method. It is shown that the disease-free equilibrium is globally asymptotically stable ifR0≤1, and the system is uniformly persistence ifR0>1. Some numerical simulations are also given to explain our analytical results. Our results show that to control and eradicate the malaria, it is very necessary for the government to decrease the relapse rate and increase the recovery rate.

Analysis of a sex-structured HIV/AIDS model with the effect of screening of infectives

2014 ◽  
Vol 07 (05) ◽  
pp. 1450054 ◽  
Author(s):  
S. Athithan ◽  
Mini Ghosh
Keyword(s):  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Asymptotically Stable ◽  
Epidemic Threshold ◽  
Heterosexual Contact ◽  
Globally Asymptotically Stable ◽  
Transmission Of Disease ◽  
Globally Stable ◽  
Disease Free ◽  
Hiv Aids

This paper presents a nonlinear sex-structured mathematical model to study the spread of HIV/AIDS by considering transmission of disease by heterosexual contact. The epidemic threshold and equilibria for the model are determined, local stability and global stability of both the "Disease-Free Equilibrium" (DFE) and "Endemic Equilibrium" (EE) are discussed in detail. The DFE is shown to be locally and globally stable when the basic reproductive number ℛ0 is less than unity. We also prove that the EE is locally and globally asymptotically stable under some conditions. Finally, numerical simulations are reported to support the analytical findings.

scholarly journals Stability Analysis of an HIV/AIDS Dynamics Model with Drug Resistance

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Qianqian Li ◽  
Shengshan Cao ◽  
Xiao Chen ◽  
Guiquan Sun ◽  
Yunxi Liu ◽  
...  
Keyword(s):  
Drug Resistance ◽  
Threshold Value ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Asymptotically Stable ◽  
Dynamics Model ◽  
Globally Asymptotically Stable ◽  
Antiretroviral Drug ◽  
Disease Free ◽  
Hiv Aids

A mathematical model of HIV/AIDS transmission incorporating treatment and drug resistance was built in this study. We firstly calculated the threshold value of the basic reproductive number (R0) by the next generation matrix and then analyzed stability of two equilibriums by constructing Lyapunov function. WhenR0<1, the system was globally asymptotically stable and converged to the disease-free equilibrium. Otherwise, the system had a unique endemic equilibrium which was also globally asymptotically stable. While an antiretroviral drug tried to reduce the infection rate and prolong the patients’ survival, drug resistance was neutralizing the effects of treatment in fact.

scholarly journals A Mathematical Model for the Prediction of the Impact of Coronavirus(COVID­19) and Social Distancing Effect

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Mathematical Model ◽  
Data Fitting ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Social Distancing ◽  
The World ◽  
Unique Style ◽  
The Right ◽  
The Impact ◽  
Disease Free

The spread of coronavirus across the world has become a major pandemic following the Spanishflu of 1918. A mathematical model of the spread of the coronavirus with social distancing effect is studied. Amathematical model of the spread of the virus form Wuhan in China to the rest of the world is suggested andanalyzed. Another mathematical model with quarantine and social distancing factors is proposed and analyzed.Stability analysis for both models were carried out and data fitting was performed to predict the possible extinctionof the disease. The disease free equilibria of both models were locally and globally asymptotically stable. Themodels suggest that with interventions such as lock downs and social distancing the extinction of the coronaviruscan be achieved. Increasing social distancing could reduce the number of new cases by up to 30%. The paperpresents a unique style of considering both theoretical and data analysis which is rarely studied in the literature.Questions arising from this study for further research include the right time to apply interventions and the state ofpreparedness in case of similar pandemics.

scholarly journals Mathematical Analysis of Rabies Infection

2020 ◽  
Vol 2020 ◽  
pp. 1-17 ◽  
Author(s):  
C. S. Bornaa ◽  
Baba Seidu ◽  
M. I. Daabo
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Mathematical Analysis ◽  
Asymptotically Stable ◽  
Local Sensitivity ◽  
Globally Asymptotically Stable ◽  
Local Sensitivity Analysis ◽  
Disease Free

A mathematical model is proposed to study the dynamics of the transmission of rabies, incorporating predation of dogs by humans. The model is shown to have a unique disease-free equilibrium which is globally asymptotically stable whenever ℛ0≤1. Local sensitivity analysis suggests that the disease can be controlled through reducing contact with infected dogs, increasing immunization of dogs, screening recruited dogs, culling of infected dogs, and use of dog meat as a delicacy.

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.

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