Hongbin Guo - Profile on Academia.edu (original) (raw)
Papers by Hongbin Guo
Mathematical biosciences and engineering : MBE, 2018
Hepatitis B virus (HBV) is responsible for an estimated 378 million infections worldwide and 620,... more Hepatitis B virus (HBV) is responsible for an estimated 378 million infections worldwide and 620, 000 deaths annually. Safe and effective vaccination programs have been available for decades, but coverage is limited due to economic and social factors. We investigate the effect of immigration and infection age on HBV transmission dynamics, incorporating age-dependent immigration flow and vertical transmission. The mathematical model can be used to describe HBV transmission in highly endemic regions with vertical transmission and migration of infected HBV individuals. Due to the effects of immigration, there is no disease-free equilibrium or reproduction number. We show that the unique endemic equilibrium exists only when immigration into the infective class is measurable. The smoothness and attractiveness of the solution semiflow are analyzed, and boundedness and uniform persistence are determined. Global stability of the unique endemic equilibrium is shown by a Lyapunov functional f...
Global stability of the endemic equilibrium of a tuberculosis model with immigration and treatment
Canadian Applied Mathematics Quarterly
A mathematical analysis is carried out for a tuberculosis (TB) model incorporating both latent an... more A mathematical analysis is carried out for a tuberculosis (TB) model incorporating both latent and clinical stages, immigration and treatment. With immigration into the latent classes, we show that the model always has a unique endemic equilibrium and it is globally asymptotically stable. The global stability of the endemic equilibrium is proved using a global Lyapunov function.
Applied Mathematics and Computation, 2018
We formulate a multi-stage SEIR model for infectious diseases with continuous age structure for e... more We formulate a multi-stage SEIR model for infectious diseases with continuous age structure for each successive infectious stage during a long infective period. The model can describe disease progression through multiple infectious stages as in the case of HIV, hepatitis B and hepatitis C. Mathematical analysis shows that the global dynamics are completely determined by the basic reproductive number R 0. If R 0 ≤ 1 , the disease-free equilibrium is globally asymptotically stable and the disease dies out. If R 0 > 1 , a unique endemic equilibrium is globally asymptotically stable, and the disease persists at the endemic equilibrium. The proof of global stability of endemic equilibria utilizes a Lyapunov functional. Numerical simulations are illustrated and model generalization is also discussed.
Dynamics in a vector disease model
This paper is concerned with the existence of entire solutions in a vector disease model with dif... more This paper is concerned with the existence of entire solutions in a vector disease model with diffusive and nonlocal delays. The entire solutions are meant by solutions defined for all t∈R. By considering the mixing of traveling wave solutions with heteroclinic orbits of spatially averaged ordinary differential equations, several new types of entire solutions are obtained.
Modelling Quality and Warranty Cost
SIAM Journal on Applied Mathematics, 2012
We propose a general class of multistage epidemiological models that allow possible deterioration... more We propose a general class of multistage epidemiological models that allow possible deterioration and amelioration between any two infected stages. The models can describe disease progression through multiple latent or infectious stages as in the case of HIV and tuberculosis. Amelioration is incorporated into the models to account for the effects of antiretroviral or antibiotic treatment. The models also incorporate general nonlinear incidences and general nonlinear forms of population transfer among stages. Under biologically motivated assumptions, we derive the basic reproduction number R 0 and show that the global dynamics are completely determined by R 0 : if R 0 ≤ 1, the disease-free equilibrium is globally asymptotically stable, and the disease dies out; if R 0 > 1, then the disease persists in all stages and a unique endemic equilibrium is globally asymptotically stable.
For a class of multigroup SIR epidemic models with varying subpopulation sizes, we establish that... more For a class of multigroup SIR epidemic models with varying subpopulation sizes, we establish that the global dynamics are completely determined by the basic reproduction number R 0 . More specifically, we prove that, if R 0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable; if R 0 > 1, then there exists a unique endemic equilibrium and it is globally asymptotically stable in the interior of the feasible region. Our proof of global stability utilizes the method of global Lyapunov functions and results from graph theory.
Proceedings of the American Mathematical Society, 2008
A class of global Lyapunov functions is revisited and used to resolve a long-standing open proble... more A class of global Lyapunov functions is revisited and used to resolve a long-standing open problem on the uniqueness and global stability of the endemic equilibrium of a class of multi-group models in mathematical epidemiology. We show how the group structure of the models, as manifested in the derivatives of the Lyapunov function, can be completely described using graph theory.
Mathematical Biosciences and Engineering, 2011
Spread of tuberculosis (TB) due to the immigration from some developing countries with high TB in... more Spread of tuberculosis (TB) due to the immigration from some developing countries with high TB incidence to developed countries poses an increasing challenge in the global TB control. Here a simple compartmental TB model with constant immigration, early and late latency is developed in order to investigate the impact of new immigrants with latent TB on the overall TB incidence, and to compare the difference contributed by different proportions of latently-infected new immigrants with high or low risk to develop active TB shortly after arrival. The global dynamics of the system is completely classified, numerical simulations are carried out for different scenarios, and potential applications to public health policy are discussed.
Global dynamics of a mathematical model of tuberculosis
Mathematical studies of the transmission dynamics of infectious diseases in heterogeneous populations--PhD Thesis
The impact of HIV treatment as prevention in the presence of other prevention strategies: Lessons learned from a review of mathematical models set in resource-rich countries
We aimed to assess the potential prevention benefits of HIV treatment as prevention (TasP) in res... more We aimed to assess the potential prevention benefits of HIV treatment as prevention (TasP) in resource-rich countries and examine the potential interactions between TasP and other prevention strategies by reviewing mathematical models of TasP. Multiple databases were searched for mathematical models published in the previous 5 years (from July 2007 to July 2012). The nine models located were set in Canada, Australia and the United States. These models' predictions suggested that the impact of expanding treatment rates on expected new infections could range widely, from no decrease to a decrease of 76%, depending on the time horizon, assumptions and the form of TasP modeled. Increased testing, reducing sexually transmitted infections and reducing risky practices were also predicted to be important strategies for decreasing expected new infections. Sensitivity analysis suggests that current uncertainties such as the effectiveness of highly active antiretroviral therapy outside of heterosexual transmission, less than ideal adherence, and risk compensation, could impact on the success of TasP at the population level. The results from large scale pilots and community randomized controlled trials will be useful in demonstrating how well this prevention approach works in real world settings, and in identifying the factors that are needed to support its effectiveness.
BMC Infectious Diseases, 2012
Background: Pre-existing cellular immunity has been recognized as one of the key factors in deter... more Background: Pre-existing cellular immunity has been recognized as one of the key factors in determining the outcome of influenza infection by reducing the likelihood of clinical disease and mitigates illness. Whether, and to what extent, the effect of this self-protective mechanism can be captured in the population dynamics of an influenza epidemic has not been addressed. Methods: We applied previous findings regarding T-cell cross-reactivity between the 2009 pandemic H1N1 strain and seasonal H1N1 strains to investigate the possible changes in the magnitude and peak time of the epidemic. Continuous Monte-Carlo Markov Chain (MCMC) model was employed to simulate the role of pre-existing immunity on the dynamical behavior of epidemic peak. Results: From the MCMC model simulations, we observed that, as the size of subpopulation with partially effective pre-existing immunity increases, the mean magnitude of the epidemic peak decreases, while the mean time to reach the peak increases. However, the corresponding ranges of these variations are relatively small. Conclusions: Our study concludes that the effective role of pre-existing immunity in alleviating disease outcomes (e.g., hospitalization) of novel influenza virus remains largely undetectable in population dynamics of an epidemic. The model outcome suggests that rapid clinical investigations on T-cell assays remain crucial for determining the protection level conferred by pre-existing cellular responses in the face of an emerging influenza virus.
Influenza and Other Respiratory Viruses, 2010
Discrete and Continuous Dynamical Systems - Series B, 2012
Population migration and immigration have greatly increased the spread and transmission of many i... more Population migration and immigration have greatly increased the spread and transmission of many infectious diseases at a regional, national and global scale. To investigate quantitatively and qualitatively the impact of migration and immigration on the transmission dynamics of infectious diseases, especially in heterogeneous host populations, we incorporate immigration/migration terms into all sub-population compartments, susceptible and infected, of two types of well-known heterogeneous epidemic models: multistage models and multi-group models for HIV/AIDS and other STDs. We show that, when migration or immigration into infected sub-population is present, the disease always becomes endemic in the population and tends to a unique asymptotically stable endemic equilibrium P ⇤ . The global stability of P ⇤ is established under general and biological meaningful conditions, and the proof utilizes a global Lyapunov function and the graph-theoretic techniques developed in .
Nonlinear Analysis: Real World Applications, 2011
Global stability in a mathematical model of tuberculosis
Mathematical analysis is carried out for a mathematical model of Tuberculosis (TB) that incorpora... more Mathematical analysis is carried out for a mathematical model of Tuberculosis (TB) that incorporates both latent and clinical stages. Our analysis establishes that the global dynamics of the model are completely determined by a basic reproduction number R0. If R0 1, the TB always dies out. If R0 > 1, the TB becomes endemic, and a unique endemic equilibrium is
Global Stability in Multigroup Epidemic Models
Modeling and Dynamics of Infectious Diseases, 2009
Mathematical Biosciences and Engineering, 2006
We analyze a mathematical model for infectious diseases that progress through distinct stages wit... more We analyze a mathematical model for infectious diseases that progress through distinct stages within infected hosts. An example of such a disease is AIDS, which results from HIV infection. For a general n-stage stage-progression (SP) model with bilinear incidences, we prove that the global dynamics are completely determined by the basic reproduction number R 0 . If R 0 ≤ 1, then the disease-free equilibrium P 0 is globally asymptotically stable and the disease always dies out. If R 0 > 1, P 0 is unstable, and a unique endemic equilibrium P * is globally asymptotically stable, and the disease persists at the endemic equilibrium. The basic reproduction numbers for the SP model with density dependent incidence forms are also discussed.
Journal of Biological Dynamics, 2008
Mathematical biosciences and engineering : MBE, 2018
Hepatitis B virus (HBV) is responsible for an estimated 378 million infections worldwide and 620,... more Hepatitis B virus (HBV) is responsible for an estimated 378 million infections worldwide and 620, 000 deaths annually. Safe and effective vaccination programs have been available for decades, but coverage is limited due to economic and social factors. We investigate the effect of immigration and infection age on HBV transmission dynamics, incorporating age-dependent immigration flow and vertical transmission. The mathematical model can be used to describe HBV transmission in highly endemic regions with vertical transmission and migration of infected HBV individuals. Due to the effects of immigration, there is no disease-free equilibrium or reproduction number. We show that the unique endemic equilibrium exists only when immigration into the infective class is measurable. The smoothness and attractiveness of the solution semiflow are analyzed, and boundedness and uniform persistence are determined. Global stability of the unique endemic equilibrium is shown by a Lyapunov functional f...
Global stability of the endemic equilibrium of a tuberculosis model with immigration and treatment
Canadian Applied Mathematics Quarterly
A mathematical analysis is carried out for a tuberculosis (TB) model incorporating both latent an... more A mathematical analysis is carried out for a tuberculosis (TB) model incorporating both latent and clinical stages, immigration and treatment. With immigration into the latent classes, we show that the model always has a unique endemic equilibrium and it is globally asymptotically stable. The global stability of the endemic equilibrium is proved using a global Lyapunov function.
Applied Mathematics and Computation, 2018
We formulate a multi-stage SEIR model for infectious diseases with continuous age structure for e... more We formulate a multi-stage SEIR model for infectious diseases with continuous age structure for each successive infectious stage during a long infective period. The model can describe disease progression through multiple infectious stages as in the case of HIV, hepatitis B and hepatitis C. Mathematical analysis shows that the global dynamics are completely determined by the basic reproductive number R 0. If R 0 ≤ 1 , the disease-free equilibrium is globally asymptotically stable and the disease dies out. If R 0 > 1 , a unique endemic equilibrium is globally asymptotically stable, and the disease persists at the endemic equilibrium. The proof of global stability of endemic equilibria utilizes a Lyapunov functional. Numerical simulations are illustrated and model generalization is also discussed.
Dynamics in a vector disease model
This paper is concerned with the existence of entire solutions in a vector disease model with dif... more This paper is concerned with the existence of entire solutions in a vector disease model with diffusive and nonlocal delays. The entire solutions are meant by solutions defined for all t∈R. By considering the mixing of traveling wave solutions with heteroclinic orbits of spatially averaged ordinary differential equations, several new types of entire solutions are obtained.
Modelling Quality and Warranty Cost
SIAM Journal on Applied Mathematics, 2012
We propose a general class of multistage epidemiological models that allow possible deterioration... more We propose a general class of multistage epidemiological models that allow possible deterioration and amelioration between any two infected stages. The models can describe disease progression through multiple latent or infectious stages as in the case of HIV and tuberculosis. Amelioration is incorporated into the models to account for the effects of antiretroviral or antibiotic treatment. The models also incorporate general nonlinear incidences and general nonlinear forms of population transfer among stages. Under biologically motivated assumptions, we derive the basic reproduction number R 0 and show that the global dynamics are completely determined by R 0 : if R 0 ≤ 1, the disease-free equilibrium is globally asymptotically stable, and the disease dies out; if R 0 > 1, then the disease persists in all stages and a unique endemic equilibrium is globally asymptotically stable.
For a class of multigroup SIR epidemic models with varying subpopulation sizes, we establish that... more For a class of multigroup SIR epidemic models with varying subpopulation sizes, we establish that the global dynamics are completely determined by the basic reproduction number R 0 . More specifically, we prove that, if R 0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable; if R 0 > 1, then there exists a unique endemic equilibrium and it is globally asymptotically stable in the interior of the feasible region. Our proof of global stability utilizes the method of global Lyapunov functions and results from graph theory.
Proceedings of the American Mathematical Society, 2008
A class of global Lyapunov functions is revisited and used to resolve a long-standing open proble... more A class of global Lyapunov functions is revisited and used to resolve a long-standing open problem on the uniqueness and global stability of the endemic equilibrium of a class of multi-group models in mathematical epidemiology. We show how the group structure of the models, as manifested in the derivatives of the Lyapunov function, can be completely described using graph theory.
Mathematical Biosciences and Engineering, 2011
Spread of tuberculosis (TB) due to the immigration from some developing countries with high TB in... more Spread of tuberculosis (TB) due to the immigration from some developing countries with high TB incidence to developed countries poses an increasing challenge in the global TB control. Here a simple compartmental TB model with constant immigration, early and late latency is developed in order to investigate the impact of new immigrants with latent TB on the overall TB incidence, and to compare the difference contributed by different proportions of latently-infected new immigrants with high or low risk to develop active TB shortly after arrival. The global dynamics of the system is completely classified, numerical simulations are carried out for different scenarios, and potential applications to public health policy are discussed.
Global dynamics of a mathematical model of tuberculosis
Mathematical studies of the transmission dynamics of infectious diseases in heterogeneous populations--PhD Thesis
The impact of HIV treatment as prevention in the presence of other prevention strategies: Lessons learned from a review of mathematical models set in resource-rich countries
We aimed to assess the potential prevention benefits of HIV treatment as prevention (TasP) in res... more We aimed to assess the potential prevention benefits of HIV treatment as prevention (TasP) in resource-rich countries and examine the potential interactions between TasP and other prevention strategies by reviewing mathematical models of TasP. Multiple databases were searched for mathematical models published in the previous 5 years (from July 2007 to July 2012). The nine models located were set in Canada, Australia and the United States. These models' predictions suggested that the impact of expanding treatment rates on expected new infections could range widely, from no decrease to a decrease of 76%, depending on the time horizon, assumptions and the form of TasP modeled. Increased testing, reducing sexually transmitted infections and reducing risky practices were also predicted to be important strategies for decreasing expected new infections. Sensitivity analysis suggests that current uncertainties such as the effectiveness of highly active antiretroviral therapy outside of heterosexual transmission, less than ideal adherence, and risk compensation, could impact on the success of TasP at the population level. The results from large scale pilots and community randomized controlled trials will be useful in demonstrating how well this prevention approach works in real world settings, and in identifying the factors that are needed to support its effectiveness.
BMC Infectious Diseases, 2012
Background: Pre-existing cellular immunity has been recognized as one of the key factors in deter... more Background: Pre-existing cellular immunity has been recognized as one of the key factors in determining the outcome of influenza infection by reducing the likelihood of clinical disease and mitigates illness. Whether, and to what extent, the effect of this self-protective mechanism can be captured in the population dynamics of an influenza epidemic has not been addressed. Methods: We applied previous findings regarding T-cell cross-reactivity between the 2009 pandemic H1N1 strain and seasonal H1N1 strains to investigate the possible changes in the magnitude and peak time of the epidemic. Continuous Monte-Carlo Markov Chain (MCMC) model was employed to simulate the role of pre-existing immunity on the dynamical behavior of epidemic peak. Results: From the MCMC model simulations, we observed that, as the size of subpopulation with partially effective pre-existing immunity increases, the mean magnitude of the epidemic peak decreases, while the mean time to reach the peak increases. However, the corresponding ranges of these variations are relatively small. Conclusions: Our study concludes that the effective role of pre-existing immunity in alleviating disease outcomes (e.g., hospitalization) of novel influenza virus remains largely undetectable in population dynamics of an epidemic. The model outcome suggests that rapid clinical investigations on T-cell assays remain crucial for determining the protection level conferred by pre-existing cellular responses in the face of an emerging influenza virus.
Influenza and Other Respiratory Viruses, 2010
Discrete and Continuous Dynamical Systems - Series B, 2012
Population migration and immigration have greatly increased the spread and transmission of many i... more Population migration and immigration have greatly increased the spread and transmission of many infectious diseases at a regional, national and global scale. To investigate quantitatively and qualitatively the impact of migration and immigration on the transmission dynamics of infectious diseases, especially in heterogeneous host populations, we incorporate immigration/migration terms into all sub-population compartments, susceptible and infected, of two types of well-known heterogeneous epidemic models: multistage models and multi-group models for HIV/AIDS and other STDs. We show that, when migration or immigration into infected sub-population is present, the disease always becomes endemic in the population and tends to a unique asymptotically stable endemic equilibrium P ⇤ . The global stability of P ⇤ is established under general and biological meaningful conditions, and the proof utilizes a global Lyapunov function and the graph-theoretic techniques developed in .
Nonlinear Analysis: Real World Applications, 2011
Global stability in a mathematical model of tuberculosis
Mathematical analysis is carried out for a mathematical model of Tuberculosis (TB) that incorpora... more Mathematical analysis is carried out for a mathematical model of Tuberculosis (TB) that incorporates both latent and clinical stages. Our analysis establishes that the global dynamics of the model are completely determined by a basic reproduction number R0. If R0 1, the TB always dies out. If R0 > 1, the TB becomes endemic, and a unique endemic equilibrium is
Global Stability in Multigroup Epidemic Models
Modeling and Dynamics of Infectious Diseases, 2009
Mathematical Biosciences and Engineering, 2006
We analyze a mathematical model for infectious diseases that progress through distinct stages wit... more We analyze a mathematical model for infectious diseases that progress through distinct stages within infected hosts. An example of such a disease is AIDS, which results from HIV infection. For a general n-stage stage-progression (SP) model with bilinear incidences, we prove that the global dynamics are completely determined by the basic reproduction number R 0 . If R 0 ≤ 1, then the disease-free equilibrium P 0 is globally asymptotically stable and the disease always dies out. If R 0 > 1, P 0 is unstable, and a unique endemic equilibrium P * is globally asymptotically stable, and the disease persists at the endemic equilibrium. The basic reproduction numbers for the SP model with density dependent incidence forms are also discussed.
Journal of Biological Dynamics, 2008