Stage structured models, by grouping individuals with similar demographic characteristics togethe... more Stage structured models, by grouping individuals with similar demographic characteristics together, have proven useful in describing population dynamics. This manuscript starts from reviewing two widely used modeling frameworks that are in the form of integral equations and age-structured partial differential equations. Both modeling frameworks can be reduced to the same differential equation structures with/without time delays by applying Dirac and gamma distributions for the stage durations. Each framework has its advantages and inherent limitations. The net reproduction number and initial growth rate can be easily defined from the integral equation. However, it becomes challenging to integrate the density-dependent regulations on the stage distribution and survival probabilities in an integral equation, which may be suitably incorporated into partial differential equations. Further recent modeling studies, in particular those by Stephen A. Gourley and collaborators, are reviewed ...
Some species may have totally different ages at successful reproduction (ages at maturity) in pop... more Some species may have totally different ages at successful reproduction (ages at maturity) in population growth. For example, Ixodes ticks, a vector species responsible for many tick-borne diseases, may suspend development and undergo diapause during maturation process, which naturally introduce distinct ages at reproduction. Although the age at reproduction is a key demographic trait that is probably under high selective pressure, it is highly variable and the effect of this variability on spatial establishment and invasion is not well understood. In this study, a spatial mechanistic model, in the form of reaction diffusion equations with nonlocal terms incorporating two different ages at reproduction, is formulated and mathematically analyzed from a dynamical system point of view. Specifically, the persistence of the species in a bounded domain can be predicted by the net reproduction number and the spreading property in an unbounded domain in terms of spreading speed and travelin...
This paper investigates the global stabilization problem of k-valued logical control networks (KV... more This paper investigates the global stabilization problem of k-valued logical control networks (KVLCNs) via event-triggered control (ETC), where the control inputs only work at several certain individual states. Compared with traditional state feedback control, the designed ETC approach not only shortens the transient period of logical networks but also decreases the number of controller executions. The content of this paper is divided into two parts. In the first part, a necessary and sufficient criterion is derived for the event-triggered stabilization of KVLCNs, and a construction procedure is developed to design all timeoptimal event-triggered stabilizers. In the second part, the switching-cost-optimal event-triggered stabilizer is designed to minimize the number of controller executions. A labeled digraph is obtained based on the dynamic of the overall system. Utilizing this digraph, we formulate a universal and unified procedure called the minimal spanning in-tree algorithm to minimize the triggering event set. Furthermore, we illustrate the effectiveness of obtained results through several numerical examples.
International Journal of Robust and Nonlinear Control, 2019
In this paper, the stability problems of a class of switched systems with limiting average dwell ... more In this paper, the stability problems of a class of switched systems with limiting average dwell time (ADT) are concerned. The common ADT is improved to a form of limit, and the limiting ADT even can be infinite. Different from previous results, in order to take full advantage of stabilizing switchings, switching-dependent switched parameters are first used to describe the relationship of two consecutive activated switchings. Then, stability criteria of switched systems with limiting ADT are established, which are less conservative comparing with the existing results. Additionally, some stability criteria of switched systems including continuous-time and discrete-time cases are derived. Finally, the validity and effectiveness of our results are elucidated by numerical examples.
Lyme disease, a typical tick-borne disease, imposes increasing global public health challenges. A... more Lyme disease, a typical tick-borne disease, imposes increasing global public health challenges. A growing body of theoretical models have been proposed to better understand various factors determining the disease risk, which not only enrich our understanding on the ecological cycle of disease transmission but also promote new theoretical developments on model formulation, analysis and simulation. In this paper, we provide a review about the models and results we have obtained recently on modeling and analyzing Lyme disease transmission, with the purpose to highlight various aspects in the ecological cycle of disease transmission to be incorporated, including the growth of ticks with different stages in the life cycle, the seasonality, host diversity, spatial disease pattern due to host short distance movement and bird migration, co-infection with other tick-borne pathogens, and climate change impact.
We consider the Fisher-KPP equation in a wavelike shifting environment for which the wave profile... more We consider the Fisher-KPP equation in a wavelike shifting environment for which the wave profile of the environment is given by a monotonically decreasing function changing signs (shifting from favorable to unfavorable environment). This type of equation arises naturally from the consideration of pathogen spread in a classical susceptible-infected-susceptible epidemiological model of a host population where the disease impact on host mobility and mortality is negligible. We conclude that there are three different ranges of the disease transmission rate where the disease spread has distinguished spatiotemporal patterns: extinction; spread in pace with the host invasion; spread not in a wave format and slower than the host invasion. We calculate the disease propagation speed when disease does spread. Our analysis for a related elliptic operator provides closed form expressions for two generalized eigenvalues in an unbounded domain. The obtained closed forms yield unsolvability of the related elliptic equation in the critical case, which relates to the open problem 4.6 in [H.
There is a growing body of biological investigations to understand impacts of seasonally changing... more There is a growing body of biological investigations to understand impacts of seasonally changing environmental conditions on population dynamics in various research fields such as single population growth and disease transmission. On the other side, understanding the population dynamics subject to seasonally changing weather conditions plays a fundamental role in predicting the trends of population patterns and disease transmission risks under the scenarios of climate change. With the host-macroparasite interaction as a motivating example, we propose a synthesised approach for investigating the population dynamics subject to seasonal environmental variations from theoretical point of view, where the model development, basic reproduction ratio formulation and computation, and rigorous mathematical analysis are involved. The resultant model with periodic delay presents a novel term related to the rate of change of the developmental duration, bringing new challenges to dynamics analysis. By investigating a periodic semiflow on a suitably chosen phase space, the global dynamics of a threshold type is established: all solutions either go to zero when basic reproduction ratio is less than one, or stabilise at a positive periodic state when the reproduction ratio is greater than one. The synthesised approach developed here is applicable to broader contexts of investigating biological systems with seasonal developmental durations.
The immunization strategies through contact tracing on the susceptible-infected-recovered framewo... more The immunization strategies through contact tracing on the susceptible-infected-recovered framework in social networks are modelled to evaluate the cost-effectiveness of information-based vaccination programs with particular focus on the scenario where individuals belonging to a specific set can get vaccinated due to the vaccine shortages and other economic or humanity constraints. By using the block heterogeneous mean-field approach, a series of discrete-time dynamical models is formulated and the condition for epidemic outbreaks can be established which is shown to be not only dependent on the network structure but also closely related to the immunization control parameters. Results show that increasing the immunization strength can effectively raise the epidemic threshold, which is different from the predictions obtained through the susceptible-infected-susceptible network framework, where epidemic threshold is independent of the vaccination strength. Furthermore, a significant d...
With the aim of understanding epidemic spreading in a general multiplex network and designing opt... more With the aim of understanding epidemic spreading in a general multiplex network and designing optimal immunization strategies, a mathematical model based on multiple degree is built to analyze the threshold condition for epidemic outbreak. Two kinds of strategies, the multiplex node-based immunization and the layer node-based immunization, are examined. Theoretical results show that the general framework proposed here can illustrate the effect of diverse correlations and immunizations on the outbreak condition in multiplex networks. Under a set of conditions on uncorrelated coefficients, the specific epidemic thresholds are shown to be only dependent on the respective degree distribution in each layer.
A deterministic model proposed in previous literatures to approximate the well-known Richards mod... more A deterministic model proposed in previous literatures to approximate the well-known Richards model is investigated. However, the model assumption of small initial value for infection size is released in the current manuscript. Taking the advantage of the closed form of solutions, we establish the epidemic characteristics of disease transmission: the outbreak size, the peak size and the turning point for the cumulative infected cases. It is shown that the usual disease outbreak threshold condition (the basic reproduction number R0 is greater than unity) fails to fully guarantee the existence of peaking time and turning point when the initial infection size is not relatively small. The epidemic characteristics not only depend on R0 but also on another index, the net reproduction number R0*.
Theoretical biology & medical modelling, Jan 28, 2014
Lyme disease imposes increasing global public health challenges. To better understand the joint e... more Lyme disease imposes increasing global public health challenges. To better understand the joint effects of seasonal temperature variation and host community composition on the pathogen transmission, a stage-structured periodic model is proposed by integrating seasonal tick development and activity, multiple host species and complex pathogen transmission routes between ticks and reservoirs. Two thresholds, one for tick population dynamics and the other for Lyme-pathogen transmission dynamics, are identified and shown to fully classify the long-term outcomes of the tick invasion and disease persistence. Seeding with the realistic parameters, the tick reproduction threshold and Lyme disease spread threshold are estimated to illustrate the joint effects of the climate change and host community diversity on the pattern of Lyme disease risk. It is shown that climate warming can amplify the disease risk and slightly change the seasonality of disease risk. Both the "dilution effect&quo...
A mechanistic model of the tick vector of Lyme disease, Ixodes scapularis, was adapted to a deter... more A mechanistic model of the tick vector of Lyme disease, Ixodes scapularis, was adapted to a deterministic structure. Using temperature normals smoothed by Fourier analysis to generate seasonal temperature-driven development rates and host biting rates, and a next generation matrix approach, the model was used to obtain values for the basic reproduction number (R(0)) for I. scapularis at locations in southern Canada where the tick is established and emerging. The R(0) at Long Point, Point Pelee and Chatham sites where I. scapularis are established, was estimated at 1.5, 3.19 and 3.65, respectively. The threshold temperature conditions for tick population survival (R(0)=1) were shown to be the same as those identified using the mechanistic model (2800-3100 cumulative annual degree days >0°C), and a map of R(0) for I. scapularis, the first such map for an arthropod vector, was drawn for Canada east of the Rocky Mountains. This map supports current risk assessments for Lyme disease risk emergence in Canada. Sensitivity analysis identified host abundance, tick development rates and summer temperatures as highly influential variables in the model, which is consistent with our current knowledge of the biology of this tick. The development of a deterministic model for I. scapularis that is capable of providing values for R(0) is a key step in our evolving ability to develop tools for assessment of Lyme disease risk emergence and for development of public health policies on surveillance, prevention and control.
Malaria is one of the most important parasitic infections in humans and more than two billion peo... more Malaria is one of the most important parasitic infections in humans and more than two billion people are at risk every year. There were an estimated 247 million malaria cases in 2006, causing nearly a million deaths. Currently, malaria is still endemic in 109 countries. Human malaria is caused by protozoan parasites of the genus Plasmodium, transmitted from human-to-human by the female Anopheles mosquito. Over the past century, considerable work has .been invested in the study of malaria transmission. However, only a few studies with malaria consider the spatial and temporal heterogeneities of this disease. Hence, there is an essential need for more informa-First and foremost, I would like to express my deepest appreciation to my supervisor, Professor Xiaoqiang Zhao, whose encouragement, guidance and support from the initial to the final level enabled me to develop an understanding of the amazing area of dynamical systems and mathematical biology. Without his contributions of time, ideas and funding, this thesis would not have been possible. I truly respect him for the excellent example he has provided as a great scholar: brilliant insight and enthusiasm in mathematical research, and great effort of guiding students to grow into mathematical researchers. My thanks also go to Mrs. Zhao. Her kind help made my life in St. John's much more enjoyable. I warmly thank Professor Jie Xiao for teaching me functional analysis and giving me frequent encouragement. In addition, I am also indebted to Professor Chris Radford for taking time out of his busy schedule to serve as my teaching supervisor in the Graduate Program of Teaching, to Professor Marco Merkli and Professor Ivan Booth for serving on the supervisor committee for my PhD program. I greatfully acknowledge the NSERC of Canada, MITACS of Canada, AARMS, the School of Graduate Studies for providing financial supports. I am also grateful to the Department of Mathematics and Statistics headed by Professor Chris Radford, for providing me teaching assistant fellowship and convenient facilities. Thanks also v go to all staff members at the department for their help.
Annali di Matematica Pura ed Applicata (1923 -), 2021
By employing a novel perturbation approach and the method of invariant sets of descending flow, t... more By employing a novel perturbation approach and the method of invariant sets of descending flow, this manuscript investigates the existence and multiplicity of sign-changing solutions to a class of semilinear Kirchhoff equations in the following form − a + b R 3 |∇u| 2 △u + V (x)u = f (u), x ∈ R 3. The methodology proposed in the current paper is robust, in the sense that, the monotonicity condition for the nonlinearity is not required. As an example, the nonlinear term including the power-type nonlinearity f (u) = |u| p−2 u for p ∈ (2, 4) is presented, which remains unsolved in the existing literature. Moreover, energy doubling is established, i.e., the energy of sign-changing solutions is strictly large than two times that of the ground state solutions for small b > 0.
International Journal of Infectious Diseases, 2020
The emerging virus, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), caused a large ... more The emerging virus, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), caused a large outbreak of coronavirus disease, COVID-19, in Wuhan, China, since December 2019. COVID-19 soon spread to other regions of China and overseas. In Hong Kong, local mitigation measures were implemented since the first imported case was confirmed on January 23, 2020. Here we evaluated the temporal variation of detection delay from symptoms onset to laboratory confirmation of SARS-CoV-2 in Hong Kong. Methods: A regression model is adopted to quantify the association between the SARS-CoV-2 detection delay and calendar time. The association is tested and further validated by a Cox proportional hazard model. Findings: The estimated median detection delay was 9.5 days (95%CI: 6.5 À 11.5) in the second half of January, reduced to 6.0 days (95%CI: 5.5 À 9.5) in the first half of February 2020. We estimate that SARS-CoV-2 detection efficiency improved at a daily rate of 5.40% (95%CI: 2.54 À 8.33) in Hong Kong. Conclusions: The detection efficiency of SARS-CoV-2 was likely being improved substantially in Hong Kong since the first imported case was detected. Sustaining enforcement in timely detection and other effective control measures are recommended to prevent the SARS-CoV-2 infection.
1 JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China ... more 1 JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China 2 Shenzhen Research Institute of Chinese University of Hong Kong, Shenzhen, China 3 Clinical Research Centre, Zhujiang Hospital, Southern Medical University, Guangzhou, Guangdong, China 4 Department of Mathematics, Shanghai Normal University, Shanghai, China 5 Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China 6 School of Mathematics and Statistics, Huaiyin Normal University, Huaian, China 7 School of Public Health, Li Ka Shing Faculty of Medicine, University of Hong Kong, Hong Kong, China 8 Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi, 830011, China 9 School of Nursing, Hong Kong Polytechnic University, Hong Kong, China * Correspondence to: [email protected] (SZ), [email protected] (WW), and [email protected] (DH)
Stage structured models, by grouping individuals with similar demographic characteristics togethe... more Stage structured models, by grouping individuals with similar demographic characteristics together, have proven useful in describing population dynamics. This manuscript starts from reviewing two widely used modeling frameworks that are in the form of integral equations and age-structured partial differential equations. Both modeling frameworks can be reduced to the same differential equation structures with/without time delays by applying Dirac and gamma distributions for the stage durations. Each framework has its advantages and inherent limitations. The net reproduction number and initial growth rate can be easily defined from the integral equation. However, it becomes challenging to integrate the density-dependent regulations on the stage distribution and survival probabilities in an integral equation, which may be suitably incorporated into partial differential equations. Further recent modeling studies, in particular those by Stephen A. Gourley and collaborators, are reviewed ...
Some species may have totally different ages at successful reproduction (ages at maturity) in pop... more Some species may have totally different ages at successful reproduction (ages at maturity) in population growth. For example, Ixodes ticks, a vector species responsible for many tick-borne diseases, may suspend development and undergo diapause during maturation process, which naturally introduce distinct ages at reproduction. Although the age at reproduction is a key demographic trait that is probably under high selective pressure, it is highly variable and the effect of this variability on spatial establishment and invasion is not well understood. In this study, a spatial mechanistic model, in the form of reaction diffusion equations with nonlocal terms incorporating two different ages at reproduction, is formulated and mathematically analyzed from a dynamical system point of view. Specifically, the persistence of the species in a bounded domain can be predicted by the net reproduction number and the spreading property in an unbounded domain in terms of spreading speed and travelin...
This paper investigates the global stabilization problem of k-valued logical control networks (KV... more This paper investigates the global stabilization problem of k-valued logical control networks (KVLCNs) via event-triggered control (ETC), where the control inputs only work at several certain individual states. Compared with traditional state feedback control, the designed ETC approach not only shortens the transient period of logical networks but also decreases the number of controller executions. The content of this paper is divided into two parts. In the first part, a necessary and sufficient criterion is derived for the event-triggered stabilization of KVLCNs, and a construction procedure is developed to design all timeoptimal event-triggered stabilizers. In the second part, the switching-cost-optimal event-triggered stabilizer is designed to minimize the number of controller executions. A labeled digraph is obtained based on the dynamic of the overall system. Utilizing this digraph, we formulate a universal and unified procedure called the minimal spanning in-tree algorithm to minimize the triggering event set. Furthermore, we illustrate the effectiveness of obtained results through several numerical examples.
International Journal of Robust and Nonlinear Control, 2019
In this paper, the stability problems of a class of switched systems with limiting average dwell ... more In this paper, the stability problems of a class of switched systems with limiting average dwell time (ADT) are concerned. The common ADT is improved to a form of limit, and the limiting ADT even can be infinite. Different from previous results, in order to take full advantage of stabilizing switchings, switching-dependent switched parameters are first used to describe the relationship of two consecutive activated switchings. Then, stability criteria of switched systems with limiting ADT are established, which are less conservative comparing with the existing results. Additionally, some stability criteria of switched systems including continuous-time and discrete-time cases are derived. Finally, the validity and effectiveness of our results are elucidated by numerical examples.
Lyme disease, a typical tick-borne disease, imposes increasing global public health challenges. A... more Lyme disease, a typical tick-borne disease, imposes increasing global public health challenges. A growing body of theoretical models have been proposed to better understand various factors determining the disease risk, which not only enrich our understanding on the ecological cycle of disease transmission but also promote new theoretical developments on model formulation, analysis and simulation. In this paper, we provide a review about the models and results we have obtained recently on modeling and analyzing Lyme disease transmission, with the purpose to highlight various aspects in the ecological cycle of disease transmission to be incorporated, including the growth of ticks with different stages in the life cycle, the seasonality, host diversity, spatial disease pattern due to host short distance movement and bird migration, co-infection with other tick-borne pathogens, and climate change impact.
We consider the Fisher-KPP equation in a wavelike shifting environment for which the wave profile... more We consider the Fisher-KPP equation in a wavelike shifting environment for which the wave profile of the environment is given by a monotonically decreasing function changing signs (shifting from favorable to unfavorable environment). This type of equation arises naturally from the consideration of pathogen spread in a classical susceptible-infected-susceptible epidemiological model of a host population where the disease impact on host mobility and mortality is negligible. We conclude that there are three different ranges of the disease transmission rate where the disease spread has distinguished spatiotemporal patterns: extinction; spread in pace with the host invasion; spread not in a wave format and slower than the host invasion. We calculate the disease propagation speed when disease does spread. Our analysis for a related elliptic operator provides closed form expressions for two generalized eigenvalues in an unbounded domain. The obtained closed forms yield unsolvability of the related elliptic equation in the critical case, which relates to the open problem 4.6 in [H.
There is a growing body of biological investigations to understand impacts of seasonally changing... more There is a growing body of biological investigations to understand impacts of seasonally changing environmental conditions on population dynamics in various research fields such as single population growth and disease transmission. On the other side, understanding the population dynamics subject to seasonally changing weather conditions plays a fundamental role in predicting the trends of population patterns and disease transmission risks under the scenarios of climate change. With the host-macroparasite interaction as a motivating example, we propose a synthesised approach for investigating the population dynamics subject to seasonal environmental variations from theoretical point of view, where the model development, basic reproduction ratio formulation and computation, and rigorous mathematical analysis are involved. The resultant model with periodic delay presents a novel term related to the rate of change of the developmental duration, bringing new challenges to dynamics analysis. By investigating a periodic semiflow on a suitably chosen phase space, the global dynamics of a threshold type is established: all solutions either go to zero when basic reproduction ratio is less than one, or stabilise at a positive periodic state when the reproduction ratio is greater than one. The synthesised approach developed here is applicable to broader contexts of investigating biological systems with seasonal developmental durations.
The immunization strategies through contact tracing on the susceptible-infected-recovered framewo... more The immunization strategies through contact tracing on the susceptible-infected-recovered framework in social networks are modelled to evaluate the cost-effectiveness of information-based vaccination programs with particular focus on the scenario where individuals belonging to a specific set can get vaccinated due to the vaccine shortages and other economic or humanity constraints. By using the block heterogeneous mean-field approach, a series of discrete-time dynamical models is formulated and the condition for epidemic outbreaks can be established which is shown to be not only dependent on the network structure but also closely related to the immunization control parameters. Results show that increasing the immunization strength can effectively raise the epidemic threshold, which is different from the predictions obtained through the susceptible-infected-susceptible network framework, where epidemic threshold is independent of the vaccination strength. Furthermore, a significant d...
With the aim of understanding epidemic spreading in a general multiplex network and designing opt... more With the aim of understanding epidemic spreading in a general multiplex network and designing optimal immunization strategies, a mathematical model based on multiple degree is built to analyze the threshold condition for epidemic outbreak. Two kinds of strategies, the multiplex node-based immunization and the layer node-based immunization, are examined. Theoretical results show that the general framework proposed here can illustrate the effect of diverse correlations and immunizations on the outbreak condition in multiplex networks. Under a set of conditions on uncorrelated coefficients, the specific epidemic thresholds are shown to be only dependent on the respective degree distribution in each layer.
A deterministic model proposed in previous literatures to approximate the well-known Richards mod... more A deterministic model proposed in previous literatures to approximate the well-known Richards model is investigated. However, the model assumption of small initial value for infection size is released in the current manuscript. Taking the advantage of the closed form of solutions, we establish the epidemic characteristics of disease transmission: the outbreak size, the peak size and the turning point for the cumulative infected cases. It is shown that the usual disease outbreak threshold condition (the basic reproduction number R0 is greater than unity) fails to fully guarantee the existence of peaking time and turning point when the initial infection size is not relatively small. The epidemic characteristics not only depend on R0 but also on another index, the net reproduction number R0*.
Theoretical biology & medical modelling, Jan 28, 2014
Lyme disease imposes increasing global public health challenges. To better understand the joint e... more Lyme disease imposes increasing global public health challenges. To better understand the joint effects of seasonal temperature variation and host community composition on the pathogen transmission, a stage-structured periodic model is proposed by integrating seasonal tick development and activity, multiple host species and complex pathogen transmission routes between ticks and reservoirs. Two thresholds, one for tick population dynamics and the other for Lyme-pathogen transmission dynamics, are identified and shown to fully classify the long-term outcomes of the tick invasion and disease persistence. Seeding with the realistic parameters, the tick reproduction threshold and Lyme disease spread threshold are estimated to illustrate the joint effects of the climate change and host community diversity on the pattern of Lyme disease risk. It is shown that climate warming can amplify the disease risk and slightly change the seasonality of disease risk. Both the "dilution effect&quo...
A mechanistic model of the tick vector of Lyme disease, Ixodes scapularis, was adapted to a deter... more A mechanistic model of the tick vector of Lyme disease, Ixodes scapularis, was adapted to a deterministic structure. Using temperature normals smoothed by Fourier analysis to generate seasonal temperature-driven development rates and host biting rates, and a next generation matrix approach, the model was used to obtain values for the basic reproduction number (R(0)) for I. scapularis at locations in southern Canada where the tick is established and emerging. The R(0) at Long Point, Point Pelee and Chatham sites where I. scapularis are established, was estimated at 1.5, 3.19 and 3.65, respectively. The threshold temperature conditions for tick population survival (R(0)=1) were shown to be the same as those identified using the mechanistic model (2800-3100 cumulative annual degree days >0°C), and a map of R(0) for I. scapularis, the first such map for an arthropod vector, was drawn for Canada east of the Rocky Mountains. This map supports current risk assessments for Lyme disease risk emergence in Canada. Sensitivity analysis identified host abundance, tick development rates and summer temperatures as highly influential variables in the model, which is consistent with our current knowledge of the biology of this tick. The development of a deterministic model for I. scapularis that is capable of providing values for R(0) is a key step in our evolving ability to develop tools for assessment of Lyme disease risk emergence and for development of public health policies on surveillance, prevention and control.
Malaria is one of the most important parasitic infections in humans and more than two billion peo... more Malaria is one of the most important parasitic infections in humans and more than two billion people are at risk every year. There were an estimated 247 million malaria cases in 2006, causing nearly a million deaths. Currently, malaria is still endemic in 109 countries. Human malaria is caused by protozoan parasites of the genus Plasmodium, transmitted from human-to-human by the female Anopheles mosquito. Over the past century, considerable work has .been invested in the study of malaria transmission. However, only a few studies with malaria consider the spatial and temporal heterogeneities of this disease. Hence, there is an essential need for more informa-First and foremost, I would like to express my deepest appreciation to my supervisor, Professor Xiaoqiang Zhao, whose encouragement, guidance and support from the initial to the final level enabled me to develop an understanding of the amazing area of dynamical systems and mathematical biology. Without his contributions of time, ideas and funding, this thesis would not have been possible. I truly respect him for the excellent example he has provided as a great scholar: brilliant insight and enthusiasm in mathematical research, and great effort of guiding students to grow into mathematical researchers. My thanks also go to Mrs. Zhao. Her kind help made my life in St. John's much more enjoyable. I warmly thank Professor Jie Xiao for teaching me functional analysis and giving me frequent encouragement. In addition, I am also indebted to Professor Chris Radford for taking time out of his busy schedule to serve as my teaching supervisor in the Graduate Program of Teaching, to Professor Marco Merkli and Professor Ivan Booth for serving on the supervisor committee for my PhD program. I greatfully acknowledge the NSERC of Canada, MITACS of Canada, AARMS, the School of Graduate Studies for providing financial supports. I am also grateful to the Department of Mathematics and Statistics headed by Professor Chris Radford, for providing me teaching assistant fellowship and convenient facilities. Thanks also v go to all staff members at the department for their help.
Annali di Matematica Pura ed Applicata (1923 -), 2021
By employing a novel perturbation approach and the method of invariant sets of descending flow, t... more By employing a novel perturbation approach and the method of invariant sets of descending flow, this manuscript investigates the existence and multiplicity of sign-changing solutions to a class of semilinear Kirchhoff equations in the following form − a + b R 3 |∇u| 2 △u + V (x)u = f (u), x ∈ R 3. The methodology proposed in the current paper is robust, in the sense that, the monotonicity condition for the nonlinearity is not required. As an example, the nonlinear term including the power-type nonlinearity f (u) = |u| p−2 u for p ∈ (2, 4) is presented, which remains unsolved in the existing literature. Moreover, energy doubling is established, i.e., the energy of sign-changing solutions is strictly large than two times that of the ground state solutions for small b > 0.
International Journal of Infectious Diseases, 2020
The emerging virus, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), caused a large ... more The emerging virus, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), caused a large outbreak of coronavirus disease, COVID-19, in Wuhan, China, since December 2019. COVID-19 soon spread to other regions of China and overseas. In Hong Kong, local mitigation measures were implemented since the first imported case was confirmed on January 23, 2020. Here we evaluated the temporal variation of detection delay from symptoms onset to laboratory confirmation of SARS-CoV-2 in Hong Kong. Methods: A regression model is adopted to quantify the association between the SARS-CoV-2 detection delay and calendar time. The association is tested and further validated by a Cox proportional hazard model. Findings: The estimated median detection delay was 9.5 days (95%CI: 6.5 À 11.5) in the second half of January, reduced to 6.0 days (95%CI: 5.5 À 9.5) in the first half of February 2020. We estimate that SARS-CoV-2 detection efficiency improved at a daily rate of 5.40% (95%CI: 2.54 À 8.33) in Hong Kong. Conclusions: The detection efficiency of SARS-CoV-2 was likely being improved substantially in Hong Kong since the first imported case was detected. Sustaining enforcement in timely detection and other effective control measures are recommended to prevent the SARS-CoV-2 infection.
1 JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China ... more 1 JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China 2 Shenzhen Research Institute of Chinese University of Hong Kong, Shenzhen, China 3 Clinical Research Centre, Zhujiang Hospital, Southern Medical University, Guangzhou, Guangdong, China 4 Department of Mathematics, Shanghai Normal University, Shanghai, China 5 Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China 6 School of Mathematics and Statistics, Huaiyin Normal University, Huaian, China 7 School of Public Health, Li Ka Shing Faculty of Medicine, University of Hong Kong, Hong Kong, China 8 Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi, 830011, China 9 School of Nursing, Hong Kong Polytechnic University, Hong Kong, China * Correspondence to: [email protected] (SZ), [email protected] (WW), and [email protected] (DH)
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