An HIV model was considered. The parameters of the model are estimated by adjoint dada assimilation method. The results showed the method is valid. This method has potential application to a wide variety of models in ...An HIV model was considered. The parameters of the model are estimated by adjoint dada assimilation method. The results showed the method is valid. This method has potential application to a wide variety of models in biomathematics.展开更多
This paper shows how mathematical methods can be implemented to formulate guidelines for clinical testing and monitoring of HIV/AIDS disease. First, a mathematical model for HIV infection is presented which the measur...This paper shows how mathematical methods can be implemented to formulate guidelines for clinical testing and monitoring of HIV/AIDS disease. First, a mathematical model for HIV infection is presented which the measurement of the CD4+T cells and the viral load counts are needed to estimate all its parameters. Next, through an analysis of model properties, the minimal number of measurement samples is obtained. In the sequel, the effect of Reverse Transcriptase enzyme Inhibitor (RTI) on HIV progression is demonstrated by using a control function. Also the total cost of treatment by this kind of drugs has been minimized. The numerical results are obtained by a numerical method in discretization issue, called AVK.展开更多
HIV is a retrovirus that infects and impairs the cells and functions of the immune system. It has caused a great challenge to global public health systems and leads to Acquired Immunodeficiency Syndrome (AIDS), if not...HIV is a retrovirus that infects and impairs the cells and functions of the immune system. It has caused a great challenge to global public health systems and leads to Acquired Immunodeficiency Syndrome (AIDS), if not attended to in good time. Antiretroviral therapy is used for managing the virus in a patient’s lifetime. Some of the symptoms of the disease include lean body mass and many opportunistic infections. This study has developed a SIAT mathematical model to investigate the impact of inconsistency in treatment of the disease. The arising non-linear differential equations have been obtained and analyzed. The DFE and its stability have been obtained and the study found that it is locally asymptotically stable when the basic reproduction number is less than unity. The endemic equilibrium has been obtained and found to be globally asymptotically stable when the basic reproduction number is greater than unity. Numerical solutions have been obtained and analyzed to give the trends in the spread dynamics. The inconsistency in treatment uptake has been analyzed through the numerical solutions. The study found that when the treatment rate of those infected increases, it leads to an increase in treatment population, which slows down the spread of HIV and vice versa. An increase in the rate of treatment of those with AIDS leads to a decrease in the AIDS population, the reverse happens when this rate decreases. The study recommends that the community involvement in advocating for consistent treatment of HIV to curb the spread of the disease.展开更多
A non-linear HIV-TB co-infection has been formulated and analyzed. The positivity and invariant region has been established. The disease free equilibrium and its stability has been determined. The local stability was ...A non-linear HIV-TB co-infection has been formulated and analyzed. The positivity and invariant region has been established. The disease free equilibrium and its stability has been determined. The local stability was determined and found to be stable under given conditions. The basic reproduction number was obtained and according to findings, co-infection diminishes when this number is less than unity, and persists when the number is greater than unity. The global stability of the endemic equilibrium was calculated. The impact of HIV on TB was established as well as the impact of TB on HIV. Numerical solution was also done and the findings indicate that when the rate of HIV treatment increases the latent TB increases while the co-infected population decreases. When the rate of HIV treatment decreases the latent TB population decreases and the co-infected population increases. Encouraging communities to prioritize the consistent treatment of HIV infected individuals must be emphasized in order to reduce the scourge of HIV-TB co-infection.展开更多
The dynamics of a single strain HIV model is studied. The basic reproduction number R0 used as a bifurcation parameter shows that the system undergoes transcritical and saddle-node bifurcations. The usual threshold un...The dynamics of a single strain HIV model is studied. The basic reproduction number R0 used as a bifurcation parameter shows that the system undergoes transcritical and saddle-node bifurcations. The usual threshold unit value of R0 does not completely determine the eradication of the disease in an HIV infected person. In particular, a sub-threshold value Rc is established which determines the system's number of endemic states: multiple if Rc 〈 Ro 〈 1, only one if Rc=Ro = 1, and none if R0 〈 Rc 〈 1.展开更多
The HIV problem is studied by version of delay mathematical models which consider the apoptosis of uninfected CD4<sup>+</sup> T cells which cultured with infected T cells in big volume. The opportunistic i...The HIV problem is studied by version of delay mathematical models which consider the apoptosis of uninfected CD4<sup>+</sup> T cells which cultured with infected T cells in big volume. The opportunistic infection and the apoptosis of uninfected CD4<sup>+</sup> T cells are caused directly or indirectly by a toxic substance produced from HIV genes. Ubiquitously, the nonlinear incidence rate brings forth the increasing number of infected CD4<sup>+</sup> T cells with introduction of small time delay, and in addition, there also exists a natural time delay factor during the process of virus replication. With state feedback control of time delay, the bifurcating periodical oscillating phenomena is induced via Hopf bifurcation. Mathematically, with the geometrical criterion applied in the stability analysis of delay model, the critical threshold of Hopf bifurcation in multiple delay differential equations which satisfy the transversal condition is derived. By applying reduction dimensional method combined with the center manifold theory, the stability of the bifurcating periodical solution is analyzed by the perturbation near Hopf point.展开更多
In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of...In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of HIV infection of CD4<sup>+</sup>T cells with therapy effect. The fractional derivative in our approach is in the sense of Riemann-Liouville. To solve the problem, we reduce the system of FDE to a discrete optimization problem. By obtaining the optimal solutions of new problem by minimization the total errors, we obtain the approximate solution of the original problem. The numerical solutions obtained from the proposed approach indicate that our approximation is easy to implement and accurate when it is applied to a systems of FDEs.展开更多
This study explored a novel systemic community-based model for detecting and manag-ing people living with HIV/AIDS (PLWHA). Both quantitative and qualitative research methods were used in this study. A quantitative qu...This study explored a novel systemic community-based model for detecting and manag-ing people living with HIV/AIDS (PLWHA). Both quantitative and qualitative research methods were used in this study. A quantitative questionnaire investigation was conducted in a sample of 1192 subjects which were randomly selected from two areas with high HIV prevalence, Xiangfan City and Shiyan City of Hubei Province, China. Twenty-two medical and health service staffs were inter-viewed by semi-structured questionnaire focusing on awareness, status, problems, and suggestions about community-based Voluntary Counseling and Testing and Provider Initiated Testing and Coun-seling (VCT/PITC). And they were organized to discuss about the aforementioned issues in Xiangfan City and Shiyan City, respectively. Our results showed that the accessibility and availability of the general VCT/PITC were bad. About 28.3% had known and only 4.9% had made use of VCT/PITC. Developing community-based VCT/PITC had some special advantages that can overcome some ex-isting problems to remedy the aforementioned defects. We are led to conclude that, to maximize the availability and uptake rate of the VCT/PITC, we plan to detect PLWHA by developing the commu-nity-based VCT/PITC through 4 paths. Then we establish the community HIV health care center con-stituted of 8 sectors to provide an overall management. Thus, we can effectively detect and manage the PLWHA with a new systemic community-based model.展开更多
Objective This study was to investigate the HIV current situation in Liangshan prefecture, in order to predict prevalence and transmission trends. Methods Region-specific population, behavior, serosurveillence, and po...Objective This study was to investigate the HIV current situation in Liangshan prefecture, in order to predict prevalence and transmission trends. Methods Region-specific population, behavior, serosurveillence, and policy/program data (from 1995 to 2020) were gathered from various local and national organizations and applied to the Asian Epidemic Model (AEM) and used to derive estimates of future HIV prevalence, epidemic trends, and outcomes of intervention strategies. Results The AEM projections for 2020 included increased number of people living with HIV (PLHIV; to 136 617), increased HIV prevalence (2.51%), and 8037 deaths from acquired immunodeficiency syndrome (AIDS) in this region. However, the overall HIV incidence rate (per 10 000) was projected to decline from 27 in 2015 to 22 in 2020, largely due to a predicted decrease in HIV infection rate (per 10 000) from 658 in 2013 to 621 in 2020 among intravenous drug users. In contrast, the cases of HIV infection per i0 000 was projected to increase from 420 in 2010 to 503 in 2020 among men who have sex with men, and from 8 in 2010 to 15 in 2020 among the general population. The predominant risk factor for HIV transmission over the next decade in Liangshan was casual sex. Community-based outreach strategies to reduce injected drug use and casual sex, and to promote condom use, were predicted as effective interventions to decrease HIV transmission. Conclusion Implementation of a comprehensive public health program, with targeting to the region-specific at-risk populations, will help to mitigate HIV/AIDS spread in Liangshan.展开更多
A delayed HIV/AIDS epidemic model with treatment and vertical transmission is investigated. The model allows some infected individuals to move from the symptomatic phase to the asymptomatic phase;next generation of in...A delayed HIV/AIDS epidemic model with treatment and vertical transmission is investigated. The model allows some infected individuals to move from the symptomatic phase to the asymptomatic phase;next generation of infected individuals may be infected and it will take them some time to get maturity and infect others. Mathematical analysis shows that the global dynamics of the spread of the HIV/AIDS are completely determined by the basic reproduction number R0 for our model. If R0 R0 > 1.展开更多
HIV/AIDS is a public health problem especially in sub-Saharan Africa where majority of infections and deaths occur. Despite the large number of studies and efforts made in covering the data gap using mathematical mode...HIV/AIDS is a public health problem especially in sub-Saharan Africa where majority of infections and deaths occur. Despite the large number of studies and efforts made in covering the data gap using mathematical models, little is known on how model estimates are confounded by the transmission variabilities that exist in stages of HIV progression. This work investigates the impact of including stages of HIV transmission in HIV/AIDS models. A deterministic HIV/AIDS model is developed and extended to include stages of HIV progression of infected individuals. Theoretical investigation of the models and numerical analyses indicate that the two models produce different estimates, with the model without stages producing lower estimates than the staged model. These results call for a careful consideration in evaluating the efficiency of HIV/AIDS models that are used to estimate and project the burden of HIV/AIDS disease.展开更多
Mycobacterium tuberculosis(M.tb) and human immunodeficiency virus(HIV) co-infection has become a public health issue worldwide. Up to now, there have been many unresolved issues either in the clinical diagnosis and tr...Mycobacterium tuberculosis(M.tb) and human immunodeficiency virus(HIV) co-infection has become a public health issue worldwide. Up to now, there have been many unresolved issues either in the clinical diagnosis and treatment of M.tb/HIV coinfection or in the basic understanding of the mechanisms for the impairments to the immune system by interactions of these two pathogens. One important reason for these unsolved issues is the lack of appropriate animal models for the study of M.tb/HIV coinfection. This paper reviews the recent development of research on the animal models of M.tb/HIV co-infection, with a focus on the non-human primate models.展开更多
In this paper,an HIV dynamics model with the proliferation of CD4 T cells is proposed.The authors consider nonnegativity,boundedness,global asymptotic stability of the solutions and bifurcation properties of the stead...In this paper,an HIV dynamics model with the proliferation of CD4 T cells is proposed.The authors consider nonnegativity,boundedness,global asymptotic stability of the solutions and bifurcation properties of the steady states.It is proved that the virus is cleared from the host under some conditions if the basic reproduction number R0 is less than unity.Meanwhile,the model exhibits the phenomenon of backward bifurcation.We also obtain one equilibrium is semi-stable by using center manifold theory.It is proved that the endemic equilibrium is globally asymptotically stable under some conditions if R0 is greater than unity.It also is proved that the model undergoes Hopf bifurcation from the endemic equilibrium under some conditions.It is novelty that the model exhibits two famous bifurcations,backward bifurcation and Hopf bifurcation.The model is extended to incorporate the specific Cytotoxic T Lymphocytes(CTLs)immune response.Stabilities of equilibria and Hopf bifurcation are considered accordingly.In addition,some numerical simulations for justifying the theoretical analysis results are also given in paper.展开更多
文摘An HIV model was considered. The parameters of the model are estimated by adjoint dada assimilation method. The results showed the method is valid. This method has potential application to a wide variety of models in biomathematics.
文摘This paper shows how mathematical methods can be implemented to formulate guidelines for clinical testing and monitoring of HIV/AIDS disease. First, a mathematical model for HIV infection is presented which the measurement of the CD4+T cells and the viral load counts are needed to estimate all its parameters. Next, through an analysis of model properties, the minimal number of measurement samples is obtained. In the sequel, the effect of Reverse Transcriptase enzyme Inhibitor (RTI) on HIV progression is demonstrated by using a control function. Also the total cost of treatment by this kind of drugs has been minimized. The numerical results are obtained by a numerical method in discretization issue, called AVK.
文摘HIV is a retrovirus that infects and impairs the cells and functions of the immune system. It has caused a great challenge to global public health systems and leads to Acquired Immunodeficiency Syndrome (AIDS), if not attended to in good time. Antiretroviral therapy is used for managing the virus in a patient’s lifetime. Some of the symptoms of the disease include lean body mass and many opportunistic infections. This study has developed a SIAT mathematical model to investigate the impact of inconsistency in treatment of the disease. The arising non-linear differential equations have been obtained and analyzed. The DFE and its stability have been obtained and the study found that it is locally asymptotically stable when the basic reproduction number is less than unity. The endemic equilibrium has been obtained and found to be globally asymptotically stable when the basic reproduction number is greater than unity. Numerical solutions have been obtained and analyzed to give the trends in the spread dynamics. The inconsistency in treatment uptake has been analyzed through the numerical solutions. The study found that when the treatment rate of those infected increases, it leads to an increase in treatment population, which slows down the spread of HIV and vice versa. An increase in the rate of treatment of those with AIDS leads to a decrease in the AIDS population, the reverse happens when this rate decreases. The study recommends that the community involvement in advocating for consistent treatment of HIV to curb the spread of the disease.
文摘A non-linear HIV-TB co-infection has been formulated and analyzed. The positivity and invariant region has been established. The disease free equilibrium and its stability has been determined. The local stability was determined and found to be stable under given conditions. The basic reproduction number was obtained and according to findings, co-infection diminishes when this number is less than unity, and persists when the number is greater than unity. The global stability of the endemic equilibrium was calculated. The impact of HIV on TB was established as well as the impact of TB on HIV. Numerical solution was also done and the findings indicate that when the rate of HIV treatment increases the latent TB increases while the co-infected population decreases. When the rate of HIV treatment decreases the latent TB population decreases and the co-infected population increases. Encouraging communities to prioritize the consistent treatment of HIV infected individuals must be emphasized in order to reduce the scourge of HIV-TB co-infection.
文摘The dynamics of a single strain HIV model is studied. The basic reproduction number R0 used as a bifurcation parameter shows that the system undergoes transcritical and saddle-node bifurcations. The usual threshold unit value of R0 does not completely determine the eradication of the disease in an HIV infected person. In particular, a sub-threshold value Rc is established which determines the system's number of endemic states: multiple if Rc 〈 Ro 〈 1, only one if Rc=Ro = 1, and none if R0 〈 Rc 〈 1.
文摘The HIV problem is studied by version of delay mathematical models which consider the apoptosis of uninfected CD4<sup>+</sup> T cells which cultured with infected T cells in big volume. The opportunistic infection and the apoptosis of uninfected CD4<sup>+</sup> T cells are caused directly or indirectly by a toxic substance produced from HIV genes. Ubiquitously, the nonlinear incidence rate brings forth the increasing number of infected CD4<sup>+</sup> T cells with introduction of small time delay, and in addition, there also exists a natural time delay factor during the process of virus replication. With state feedback control of time delay, the bifurcating periodical oscillating phenomena is induced via Hopf bifurcation. Mathematically, with the geometrical criterion applied in the stability analysis of delay model, the critical threshold of Hopf bifurcation in multiple delay differential equations which satisfy the transversal condition is derived. By applying reduction dimensional method combined with the center manifold theory, the stability of the bifurcating periodical solution is analyzed by the perturbation near Hopf point.
文摘In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of HIV infection of CD4<sup>+</sup>T cells with therapy effect. The fractional derivative in our approach is in the sense of Riemann-Liouville. To solve the problem, we reduce the system of FDE to a discrete optimization problem. By obtaining the optimal solutions of new problem by minimization the total errors, we obtain the approximate solution of the original problem. The numerical solutions obtained from the proposed approach indicate that our approximation is easy to implement and accurate when it is applied to a systems of FDEs.
基金supported by a grant from the Global Fund(No. 2008-NGS-26)
文摘This study explored a novel systemic community-based model for detecting and manag-ing people living with HIV/AIDS (PLWHA). Both quantitative and qualitative research methods were used in this study. A quantitative questionnaire investigation was conducted in a sample of 1192 subjects which were randomly selected from two areas with high HIV prevalence, Xiangfan City and Shiyan City of Hubei Province, China. Twenty-two medical and health service staffs were inter-viewed by semi-structured questionnaire focusing on awareness, status, problems, and suggestions about community-based Voluntary Counseling and Testing and Provider Initiated Testing and Coun-seling (VCT/PITC). And they were organized to discuss about the aforementioned issues in Xiangfan City and Shiyan City, respectively. Our results showed that the accessibility and availability of the general VCT/PITC were bad. About 28.3% had known and only 4.9% had made use of VCT/PITC. Developing community-based VCT/PITC had some special advantages that can overcome some ex-isting problems to remedy the aforementioned defects. We are led to conclude that, to maximize the availability and uptake rate of the VCT/PITC, we plan to detect PLWHA by developing the commu-nity-based VCT/PITC through 4 paths. Then we establish the community HIV health care center con-stituted of 8 sectors to provide an overall management. Thus, we can effectively detect and manage the PLWHA with a new systemic community-based model.
基金funded by China-MSD HIV/AIDS Partnership Project(2012-83)Comprehensive Assessment for HIV/AIDS Control and Prevention in Sichuan Province Project(2006-2010)
文摘Objective This study was to investigate the HIV current situation in Liangshan prefecture, in order to predict prevalence and transmission trends. Methods Region-specific population, behavior, serosurveillence, and policy/program data (from 1995 to 2020) were gathered from various local and national organizations and applied to the Asian Epidemic Model (AEM) and used to derive estimates of future HIV prevalence, epidemic trends, and outcomes of intervention strategies. Results The AEM projections for 2020 included increased number of people living with HIV (PLHIV; to 136 617), increased HIV prevalence (2.51%), and 8037 deaths from acquired immunodeficiency syndrome (AIDS) in this region. However, the overall HIV incidence rate (per 10 000) was projected to decline from 27 in 2015 to 22 in 2020, largely due to a predicted decrease in HIV infection rate (per 10 000) from 658 in 2013 to 621 in 2020 among intravenous drug users. In contrast, the cases of HIV infection per i0 000 was projected to increase from 420 in 2010 to 503 in 2020 among men who have sex with men, and from 8 in 2010 to 15 in 2020 among the general population. The predominant risk factor for HIV transmission over the next decade in Liangshan was casual sex. Community-based outreach strategies to reduce injected drug use and casual sex, and to promote condom use, were predicted as effective interventions to decrease HIV transmission. Conclusion Implementation of a comprehensive public health program, with targeting to the region-specific at-risk populations, will help to mitigate HIV/AIDS spread in Liangshan.
文摘A delayed HIV/AIDS epidemic model with treatment and vertical transmission is investigated. The model allows some infected individuals to move from the symptomatic phase to the asymptomatic phase;next generation of infected individuals may be infected and it will take them some time to get maturity and infect others. Mathematical analysis shows that the global dynamics of the spread of the HIV/AIDS are completely determined by the basic reproduction number R0 for our model. If R0 R0 > 1.
文摘HIV/AIDS is a public health problem especially in sub-Saharan Africa where majority of infections and deaths occur. Despite the large number of studies and efforts made in covering the data gap using mathematical models, little is known on how model estimates are confounded by the transmission variabilities that exist in stages of HIV progression. This work investigates the impact of including stages of HIV transmission in HIV/AIDS models. A deterministic HIV/AIDS model is developed and extended to include stages of HIV progression of infected individuals. Theoretical investigation of the models and numerical analyses indicate that the two models produce different estimates, with the model without stages producing lower estimates than the staged model. These results call for a careful consideration in evaluating the efficiency of HIV/AIDS models that are used to estimate and project the burden of HIV/AIDS disease.
基金supported by grants from the National Natural Sciences Foundation of China(81201261,81301428)the National Science Foundation for Post-doctoral Scientists of China(2013M5317456)the National Science and Technology Major Project of the Ministry of Science and Technology of China(2012ZX10004501-001-004)
文摘Mycobacterium tuberculosis(M.tb) and human immunodeficiency virus(HIV) co-infection has become a public health issue worldwide. Up to now, there have been many unresolved issues either in the clinical diagnosis and treatment of M.tb/HIV coinfection or in the basic understanding of the mechanisms for the impairments to the immune system by interactions of these two pathogens. One important reason for these unsolved issues is the lack of appropriate animal models for the study of M.tb/HIV coinfection. This paper reviews the recent development of research on the animal models of M.tb/HIV co-infection, with a focus on the non-human primate models.
基金The Teacher Research Capacity Promotion Program of Beijing Normal University Zhuhaithe NSF(11871108)of China
文摘In this paper,an HIV dynamics model with the proliferation of CD4 T cells is proposed.The authors consider nonnegativity,boundedness,global asymptotic stability of the solutions and bifurcation properties of the steady states.It is proved that the virus is cleared from the host under some conditions if the basic reproduction number R0 is less than unity.Meanwhile,the model exhibits the phenomenon of backward bifurcation.We also obtain one equilibrium is semi-stable by using center manifold theory.It is proved that the endemic equilibrium is globally asymptotically stable under some conditions if R0 is greater than unity.It also is proved that the model undergoes Hopf bifurcation from the endemic equilibrium under some conditions.It is novelty that the model exhibits two famous bifurcations,backward bifurcation and Hopf bifurcation.The model is extended to incorporate the specific Cytotoxic T Lymphocytes(CTLs)immune response.Stabilities of equilibria and Hopf bifurcation are considered accordingly.In addition,some numerical simulations for justifying the theoretical analysis results are also given in paper.