A fractional-order delayed SEIR rumor spreading model with a nonlinear incidence function is established in this paper,and a novel strategy to control the bifurcation of this model is proposed.First,Hopf bifurcation i...A fractional-order delayed SEIR rumor spreading model with a nonlinear incidence function is established in this paper,and a novel strategy to control the bifurcation of this model is proposed.First,Hopf bifurcation is investigated by considering time delay as bifurcation parameter for the system without a feedback controller.Then,a state feedback controller is designed to control the occurrence of bifurcation in advance or to delay it by changing the parameters of the controller.Finally,in order to verify the theoretical results,some numerical simulations are given.展开更多
Upon infecting a host cell,the reticulate body(RB)form of the Chlamydia bacteria simply proliferates by binary fission for an extended period.Available data show only RB units in the infected cells 20 hours post infec...Upon infecting a host cell,the reticulate body(RB)form of the Chlamydia bacteria simply proliferates by binary fission for an extended period.Available data show only RB units in the infected cells 20 hours post infection(hpi),spanning nearly half way through the development cycle.With data collected every 4 hpi,conversion to the elementary body(EB)form begins abruptly at a rapid rate sometime around 24 hpi.By modeling proliferation and conversion as simple birth and death processes,it has been shown that the optimal strategy for maximizing the total(mean)EB population at host cell lysis time is a bang-bang control qualitatively replicating the observed conversion activities.However,the simple birth and death model for the RB proliferation and conversion to EB deviates in a significant way from the available data on the evolution of the RB population after the onset of RB-to-EB conversion.By working with a more refined model that takes into account a small size threshold eligibility requirement for conversion noted in the available data,we succeed in removing the deficiency of the previous models on the evolution of the RB population without affecting the optimal bang-bang conversion strategy.展开更多
The Internet era has brought great convenience to our life and communication.Meanwhile,it also makes a bunch of rumors propagate faster and causes even more harm to human life.Therefore,it is necessary to perform effe...The Internet era has brought great convenience to our life and communication.Meanwhile,it also makes a bunch of rumors propagate faster and causes even more harm to human life.Therefore,it is necessary to perform effective control mechanisms to minimize the negative social impact from rumors.Thereout,firstly,we formulate a rumor spreading model considering psychological factors and thinking time,then,we add white noise(i.e.,stochastic interference)and two pulse control strategies which denote education mechanism and refutation mechanism into the model.Secondly,we obtain the global positive solutions and demonstrate the global exponential stability of the unique positive periodic rumor-free solution.Thirdly,we discuss the extinction and persistence of rumor.Moreover,we use Pontriagin’s minimum principle to explore the optimal impulse control.Finally,several numerical simulations are carried out to verify the effectiveness and availability of the theoretical analysis.We conclude that the pulse control strategies have a great influence on controlling rumor spreading,and different control strategies should be adopted under different transmission scenarios.展开更多
In recent years,rumor spreading has caused widespread public panic and affected the whole social harmony and stability.Consequently,how to control the rumor spreading effectively and reduce its negative influence urge...In recent years,rumor spreading has caused widespread public panic and affected the whole social harmony and stability.Consequently,how to control the rumor spreading effectively and reduce its negative influence urgently needs people to pay much attention.In this paper,we mainly study the near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters.Firstly,the science knowledge propagation and the refutation mechanism as the control strategies are introduced into a stochastic rumor spreading model.Then,some sufficient and necessary conditions for the near-optimal control of the stochastic rumor spreading model are discussed respectively.Finally,through some numerical simulations,the validity and availability of theoretical analysis is verified.Meanwhile,it shows the significance and effectiveness of the proposed control strategies on controlling rumor spreading,and demonstrates the influence of stochastic disturbance and imprecise parameters on the process of rumor spreading.展开更多
In this paper, an extended version of standard susceptible-infected （SI） model is proposed to consider the influence of a medium access control mechanism on virus spreading in wireless sensor networks. Theoretical a...In this paper, an extended version of standard susceptible-infected （SI） model is proposed to consider the influence of a medium access control mechanism on virus spreading in wireless sensor networks. Theoretical analysis shows that the medium access control mechanism obviously reduces the density of infected nodes in the networks, which has been ignored in previous studies. It is also found that by increasing the network node density or node communication radius greatly increases the number of infected nodes. The theoretical results are confirmed by numerical simulations.展开更多
Research works on width compensation and correction were carried out in order to eliminate the effects of the PVPC( plan view pattern control) on width accuracy of plate mill. The thickness correction calculation form...Research works on width compensation and correction were carried out in order to eliminate the effects of the PVPC( plan view pattern control) on width accuracy of plate mill. The thickness correction calculation formula was derived for compensation the width deviation caused by PVPC function,and the formula is unified under the thinning and thickening conditions. In order to improve the width calculation accuracy, width spread calculation process was modified with dividing one large reduction pass to several small reduction calculation steps. The thickness wedge was simplified to rectangle based on the volume constant principle,and the width spread model for PVPC was constructed. The width compensation and correction for the PVPC functions are used for the online control process,and the Product dimension accuracy is improved. With the decrease of crop losses,the product yield was increased with 0. 2%.展开更多
Mathematical model of forest fire was based on an analysis of known experimental data and using concept and methods from reactive media mechanics. In this paper the assignment and theoretical investigations of the pro...Mathematical model of forest fire was based on an analysis of known experimental data and using concept and methods from reactive media mechanics. In this paper the assignment and theoretical investigations of the problems of crown forest fire spread in windy condition were carried out. In this context, a study—mathematical modeling—of the conditions of forest fire spreading that would make it possible to obtain a detailed picture of the change in the temperature and component concentration fields with time, and determine as well as the limiting condition of fire propagation in forest with fire break.展开更多
In this paper we introduce a classical SI model to capture the spread of an infectious disease within a population. More precisely, the spatial diffusion of HIV/AIDS in a population is modeled. For that, we assume tha...In this paper we introduce a classical SI model to capture the spread of an infectious disease within a population. More precisely, the spatial diffusion of HIV/AIDS in a population is modeled. For that, we assume that the spread is due to the anarchical comportment of infected individuals along a road, especially, “lorry drivers”. The question which consists of the control of the infection is also addressed. Infected individuals moving from a town to another one, the diffusion is then anisotropic with a main direction of propagation, namely the road direction. Using a semi-group argument and a maximum principle, the uniqueness of a solution to the problem is established. This solution is also estimated. We end this paper by considering some numerical experiments in the case of HIV/AIDS spread in Mali along a road connecting two towns.展开更多
Mimosa diplotricha is an invasive perennial, scrambling, thorny, leguminous shrub of neotropical origin widely acknowledged as a major economic, agricultural and ecological burden in its introduced ranges. Although th...Mimosa diplotricha is an invasive perennial, scrambling, thorny, leguminous shrub of neotropical origin widely acknowledged as a major economic, agricultural and ecological burden in its introduced ranges. Although the plant is thought to have been present in Nigeria for well over two decades, its mode and time of introduction is uncertain. In spite of the continuing spread of, and the menace caused by M. diplotricha in Nigeria, no attempt has been made to map the distribution of the plant countrywide. Therefore, we conducted a countrywide survey between 2007 and 2009, sponsored by the Weed Science Society of Nigeria (WSSN) to determine the spread and status of Mimosa diplotricha in Nigeria. A further objective of this paper was to review literatures on Mimosa diplotricha in Nigeria and elsewhere to enable comparison. In this paper, we report on the spread, distribution and problems of Mimosa diplotricha in Nigeria based on the field monitoring surveys conducted. The distribution of this invasive plant in Nigeria has been mapped and is presented together with its ecology and problems being caused. Since the early 1990s, the weed has started to spread and invade many parts of the country causing significant damage to many natural and semi natural ecosystems. The different control options used by farmers to control Mimosa diplotricha in Nigeria are discussed. Based on the successful control of this invasive plant using the biocontrol agent, Heteropsylla spinulosa in countries such as Australia and Papua New Guinea (PNG), we discussed the biological control prospects for the management of Mimosa diplotricha in Nigeria. Such control attempts stands to benefit from international collaborations between Nigerian institutions and a host of others in Australia, PNG and/or Brazil. Finally three major causes for the massive and continuing spread of this weed in Nigeria are presented with recommendations for the Nigerian government and institutions to: 1) formulate policies and legislations regarding the control and management of invasive alien plant species which is currently nonexistent;2) enlighten the general public on the dangers of invasive alien plant species such as Mimosa diplotricha;and 3) initiate actions such as early detection and rapid response (EDRR) and biological control in order to prevent further spread of, and invasion by invasive plant species including Mimosa diplotricha.展开更多
Since the onset of the COVID-19 epidemic, the world has been impressed by two things: The number of people infected and the number of deaths. Here, we propose a mathematical model of the spread of this disease, analyz...Since the onset of the COVID-19 epidemic, the world has been impressed by two things: The number of people infected and the number of deaths. Here, we propose a mathematical model of the spread of this disease, analyze this model mathematically and determine one or more dominant factors in the propagation of the COVID-19 epidemic. We consider the S-E-I-R epidemic model in the form of ordinary differential equations, in a population structured in susceptibles S, exposed E as caregivers, travelers and assistants at public events, infected I and recovered R classes. Here we decompose the recovered class into two classes: The deaths class D and the class of those who are truly healed H. After the model construction, we have calculated the basic reproduction number R<sub>0</sub>, which is a function of certain number of parameters like the size of the exposed class E. In our paper, the mathematical analysis, which consists in searching the equilibrium points and studying their stability, is done. The work identifies some parameters on which one can act to control the spread of the disease. The numerical simulations are done and they illustrate our theoretical analysis.展开更多
基金supported by the National Natural Science Foundation of China (U1703262,62163035,61866036,62006196,61963033,62163035)the Tianshan Innovation Team Program (2020D14017)the Tianshan Xuesong Program (2018XS02).
文摘A fractional-order delayed SEIR rumor spreading model with a nonlinear incidence function is established in this paper,and a novel strategy to control the bifurcation of this model is proposed.First,Hopf bifurcation is investigated by considering time delay as bifurcation parameter for the system without a feedback controller.Then,a state feedback controller is designed to control the occurrence of bifurcation in advance or to delay it by changing the parameters of the controller.Finally,in order to verify the theoretical results,some numerical simulations are given.
文摘Upon infecting a host cell,the reticulate body(RB)form of the Chlamydia bacteria simply proliferates by binary fission for an extended period.Available data show only RB units in the infected cells 20 hours post infection(hpi),spanning nearly half way through the development cycle.With data collected every 4 hpi,conversion to the elementary body(EB)form begins abruptly at a rapid rate sometime around 24 hpi.By modeling proliferation and conversion as simple birth and death processes,it has been shown that the optimal strategy for maximizing the total(mean)EB population at host cell lysis time is a bang-bang control qualitatively replicating the observed conversion activities.However,the simple birth and death model for the RB proliferation and conversion to EB deviates in a significant way from the available data on the evolution of the RB population after the onset of RB-to-EB conversion.By working with a more refined model that takes into account a small size threshold eligibility requirement for conversion noted in the available data,we succeed in removing the deficiency of the previous models on the evolution of the RB population without affecting the optimal bang-bang conversion strategy.
基金partially supported by the Project for the National Natural Science Foundation of China(Grant Nos.72174121 and 71774111)the Program for Professor of Special Appointment(Eastern Scholar)at Shanghai Institutions of Higher Learning+1 种基金the Project for the Natural Science Foundation of Shanghai(Grant No.21ZR1444100)Project Soft Science Research of Shanghai(Grant No.22692112600)。
文摘The Internet era has brought great convenience to our life and communication.Meanwhile,it also makes a bunch of rumors propagate faster and causes even more harm to human life.Therefore,it is necessary to perform effective control mechanisms to minimize the negative social impact from rumors.Thereout,firstly,we formulate a rumor spreading model considering psychological factors and thinking time,then,we add white noise(i.e.,stochastic interference)and two pulse control strategies which denote education mechanism and refutation mechanism into the model.Secondly,we obtain the global positive solutions and demonstrate the global exponential stability of the unique positive periodic rumor-free solution.Thirdly,we discuss the extinction and persistence of rumor.Moreover,we use Pontriagin’s minimum principle to explore the optimal impulse control.Finally,several numerical simulations are carried out to verify the effectiveness and availability of the theoretical analysis.We conclude that the pulse control strategies have a great influence on controlling rumor spreading,and different control strategies should be adopted under different transmission scenarios.
基金Project supported by the Program for Professor of Special Appointment(Eastern Scholar)at Shanghai Institutions of Higher Learningthe Project for the Natural Science Foundation of Shanghai,China(Grant No.21ZR1444100)the Project for the National Natural Science Foundation of China(Grant Nos.72174121,71774111,71871144,and 71804047)。
文摘In recent years,rumor spreading has caused widespread public panic and affected the whole social harmony and stability.Consequently,how to control the rumor spreading effectively and reduce its negative influence urgently needs people to pay much attention.In this paper,we mainly study the near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters.Firstly,the science knowledge propagation and the refutation mechanism as the control strategies are introduced into a stochastic rumor spreading model.Then,some sufficient and necessary conditions for the near-optimal control of the stochastic rumor spreading model are discussed respectively.Finally,through some numerical simulations,the validity and availability of theoretical analysis is verified.Meanwhile,it shows the significance and effectiveness of the proposed control strategies on controlling rumor spreading,and demonstrates the influence of stochastic disturbance and imprecise parameters on the process of rumor spreading.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61103231 and 61103230)the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2012082)+2 种基金the Innovation Program of Graduate Scientific Research in Institution of Higher Education of Jiangsu Province,China (Grant No. CXZZ11 0401)the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2011JM8012)the Basic Research Foundation of Engineering University of the Chinese People’s Armed Police Force (Grant No. WJY201218)
文摘In this paper, an extended version of standard susceptible-infected （SI） model is proposed to consider the influence of a medium access control mechanism on virus spreading in wireless sensor networks. Theoretical analysis shows that the medium access control mechanism obviously reduces the density of infected nodes in the networks, which has been ignored in previous studies. It is also found that by increasing the network node density or node communication radius greatly increases the number of infected nodes. The theoretical results are confirmed by numerical simulations.
基金Sponsored by the Fundamental Research Funds for the Central Universities(Grant No.N120407007)
文摘Research works on width compensation and correction were carried out in order to eliminate the effects of the PVPC( plan view pattern control) on width accuracy of plate mill. The thickness correction calculation formula was derived for compensation the width deviation caused by PVPC function,and the formula is unified under the thinning and thickening conditions. In order to improve the width calculation accuracy, width spread calculation process was modified with dividing one large reduction pass to several small reduction calculation steps. The thickness wedge was simplified to rectangle based on the volume constant principle,and the width spread model for PVPC was constructed. The width compensation and correction for the PVPC functions are used for the online control process,and the Product dimension accuracy is improved. With the decrease of crop losses,the product yield was increased with 0. 2%.
文摘Mathematical model of forest fire was based on an analysis of known experimental data and using concept and methods from reactive media mechanics. In this paper the assignment and theoretical investigations of the problems of crown forest fire spread in windy condition were carried out. In this context, a study—mathematical modeling—of the conditions of forest fire spreading that would make it possible to obtain a detailed picture of the change in the temperature and component concentration fields with time, and determine as well as the limiting condition of fire propagation in forest with fire break.
文摘In this paper we introduce a classical SI model to capture the spread of an infectious disease within a population. More precisely, the spatial diffusion of HIV/AIDS in a population is modeled. For that, we assume that the spread is due to the anarchical comportment of infected individuals along a road, especially, “lorry drivers”. The question which consists of the control of the infection is also addressed. Infected individuals moving from a town to another one, the diffusion is then anisotropic with a main direction of propagation, namely the road direction. Using a semi-group argument and a maximum principle, the uniqueness of a solution to the problem is established. This solution is also estimated. We end this paper by considering some numerical experiments in the case of HIV/AIDS spread in Mali along a road connecting two towns.
文摘Mimosa diplotricha is an invasive perennial, scrambling, thorny, leguminous shrub of neotropical origin widely acknowledged as a major economic, agricultural and ecological burden in its introduced ranges. Although the plant is thought to have been present in Nigeria for well over two decades, its mode and time of introduction is uncertain. In spite of the continuing spread of, and the menace caused by M. diplotricha in Nigeria, no attempt has been made to map the distribution of the plant countrywide. Therefore, we conducted a countrywide survey between 2007 and 2009, sponsored by the Weed Science Society of Nigeria (WSSN) to determine the spread and status of Mimosa diplotricha in Nigeria. A further objective of this paper was to review literatures on Mimosa diplotricha in Nigeria and elsewhere to enable comparison. In this paper, we report on the spread, distribution and problems of Mimosa diplotricha in Nigeria based on the field monitoring surveys conducted. The distribution of this invasive plant in Nigeria has been mapped and is presented together with its ecology and problems being caused. Since the early 1990s, the weed has started to spread and invade many parts of the country causing significant damage to many natural and semi natural ecosystems. The different control options used by farmers to control Mimosa diplotricha in Nigeria are discussed. Based on the successful control of this invasive plant using the biocontrol agent, Heteropsylla spinulosa in countries such as Australia and Papua New Guinea (PNG), we discussed the biological control prospects for the management of Mimosa diplotricha in Nigeria. Such control attempts stands to benefit from international collaborations between Nigerian institutions and a host of others in Australia, PNG and/or Brazil. Finally three major causes for the massive and continuing spread of this weed in Nigeria are presented with recommendations for the Nigerian government and institutions to: 1) formulate policies and legislations regarding the control and management of invasive alien plant species which is currently nonexistent;2) enlighten the general public on the dangers of invasive alien plant species such as Mimosa diplotricha;and 3) initiate actions such as early detection and rapid response (EDRR) and biological control in order to prevent further spread of, and invasion by invasive plant species including Mimosa diplotricha.
文摘Since the onset of the COVID-19 epidemic, the world has been impressed by two things: The number of people infected and the number of deaths. Here, we propose a mathematical model of the spread of this disease, analyze this model mathematically and determine one or more dominant factors in the propagation of the COVID-19 epidemic. We consider the S-E-I-R epidemic model in the form of ordinary differential equations, in a population structured in susceptibles S, exposed E as caregivers, travelers and assistants at public events, infected I and recovered R classes. Here we decompose the recovered class into two classes: The deaths class D and the class of those who are truly healed H. After the model construction, we have calculated the basic reproduction number R<sub>0</sub>, which is a function of certain number of parameters like the size of the exposed class E. In our paper, the mathematical analysis, which consists in searching the equilibrium points and studying their stability, is done. The work identifies some parameters on which one can act to control the spread of the disease. The numerical simulations are done and they illustrate our theoretical analysis.
