The paper establishes two stochastic SIRS models with jumps to describe the spread of network virus by cyber war, terrorism and others. First, adding random perturbations proportionally to each variable, we get the dy...The paper establishes two stochastic SIRS models with jumps to describe the spread of network virus by cyber war, terrorism and others. First, adding random perturbations proportionally to each variable, we get the dynamic properties around the positive equilibrium of the deterministic model and the conditions for persistence and extinction. Second, giving a random disturbance to endemic equilibrium, we get a stochastic system with jumps. By modifying the existing Lyapunov function, we prove the positive solution of the system is stochastically stable.展开更多
A stochastic susceptible-infective-recovered-susceptible( SIRS) model with non-linear incidence and Levy jumps was considered. Under certain conditions, the SIRS had a global positive solution. The stochastically ulti...A stochastic susceptible-infective-recovered-susceptible( SIRS) model with non-linear incidence and Levy jumps was considered. Under certain conditions, the SIRS had a global positive solution. The stochastically ultimate boundedness of the solution of the model was obtained by using the method of Lyapunov function and the generalized Ito's formula. At last,asymptotic behaviors of the solution were discussed according to the value of R0. If R0< 1,the solution of the model oscillates around a steady state, which is the diseases free equilibrium of the corresponding deterministic model,and if R0> 1,it fluctuates around the endemic equilibrium of the deterministic model.展开更多
In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start wi...In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R<sub>0</sub> ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.展开更多
It is of crucial significance to study the infectious disease phenomenon by using the SIRS model and thoughts of Julia set.In this paper,Julia set of the discrete version of the SIRS model is established to analyze th...It is of crucial significance to study the infectious disease phenomenon by using the SIRS model and thoughts of Julia set.In this paper,Julia set of the discrete version of the SIRS model is established to analyze the fractal dynamics of this model.Then,controller is designed to change the Julia set.Furthermore,the box-counting dimensions of the controlled Julia sets by selecting different appropriate parameters are computed to show the complexity of the model.Finally,a nonlinear coupling method is introduced to synchronize the Julia sets with different parameters of the same system.Simulation results show the efficacy of t hese met hods.展开更多
ln this paper,we propose and investigate an SlRS model with age structure and twodelays.Both the infected and the recovered individuals have age structure,the infectionrate(from the infective to the susceptible)and th...ln this paper,we propose and investigate an SlRS model with age structure and twodelays.Both the infected and the recovered individuals have age structure,the infectionrate(from the infective to the susceptible)and the immune loss rate(from the recoveredto the susceptible)are related to two independent time delays,respectively.We provethat the proposed age structured SIRS model is well-posed by using the Co-semigrouptheory.The basic reproduction number Ro is given,and the unique endemic equilib-rium exists when R_(0)>1,while the disease-free equilibrium always exists.A rigorousmathematical analysis for the stability of two equilibria is provided.The disease-freeequilibrium is local asymptotically stable if R_(0)<1,and the endemic equilibrium is localasymptotically stable if R_(0)>1 and τl=0.Finally,we give numerical simulations toverify our results.展开更多
This paper is concerned with a delayed SIRS epidemic model with a nonlinear incidence rate. The main results are given in terms of local stability and Hopf bifurcation. Sufficient conditions for the local stability of...This paper is concerned with a delayed SIRS epidemic model with a nonlinear incidence rate. The main results are given in terms of local stability and Hopf bifurcation. Sufficient conditions for the local stability of the positive equilibrium and existence of Hopf bifurcation are obtained by regarding the time delay as the bifurcation parameter. Further,the properties of Hopf bifurcation such as the direction and stability are investigated by using the normal form theory and center manifold argument. Finally,some numerical simulations are presented to verify the theoretical analysis.展开更多
In this article, an SIRS epidemic model spread by vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no end...In this article, an SIRS epidemic model spread by vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point (if it exists) is globally stable with a respect "weak delay". Some known results are generalized.展开更多
In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By u...In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.展开更多
This paper presents a restricted SIRmathematicalmodel to analyze the evolution of a contagious infectious disease outbreak(COVID-19)using available data.The new model focuses on two main concepts:first,it can present ...This paper presents a restricted SIRmathematicalmodel to analyze the evolution of a contagious infectious disease outbreak(COVID-19)using available data.The new model focuses on two main concepts:first,it can present multiple waves of the disease,and second,it analyzes how far an infection can be eradicated with the help of vaccination.The stability analysis of the equilibrium points for the suggested model is initially investigated by identifying the matching equilibrium points and examining their stability.The basic reproduction number is calculated,and the positivity of the solutions is established.Numerical simulations are performed to determine if it is multipeak and evaluate vaccination’s effects.In addition,the proposed model is compared to the literature already published and the effectiveness of vaccination has been recorded.展开更多
Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and state-dependent control, where the fraction of susceptib...Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and state-dependent control, where the fraction of susceptible individuals in population is as the detection threshold value. By the Poincaré map, theory of differential inequalities and differential equation geometry, the existence and orbital stability of the disease-free periodic solution are discussed. Theoretical results show that by state-dependent pulse vaccination we can make the proportion of infected individuals tend to zero, and control the transmission of disease in population.展开更多
Typically,a computer has infectivity as soon as it is infected.It is a reality that no antivirus programming can identify and eliminate all kinds of viruses,suggesting that infections would persevere on the Internet.T...Typically,a computer has infectivity as soon as it is infected.It is a reality that no antivirus programming can identify and eliminate all kinds of viruses,suggesting that infections would persevere on the Internet.To understand the dynamics of the virus propagation in a better way,a computer virus spread model with fuzzy parameters is presented in this work.It is assumed that all infected computers do not have the same contribution to the virus transmission process and each computer has a different degree of infectivity,which depends on the quantity of virus.Considering this,the parametersβandγbeing functions of the computer virus load,are considered fuzzy numbers.Using fuzzy theory helps us understand the spread of computer viruses more realistically as these parameters have fixed values in classical models.The essential features of the model,like reproduction number and equilibrium analysis,are discussed in fuzzy senses.Moreover,with fuzziness,two numerical methods,the forward Euler technique,and a nonstandard finite difference(NSFD)scheme,respectively,are developed and analyzed.In the evidence of the numerical simulations,the proposed NSFD method preserves the main features of the dynamic system.It can be considered a reliable tool to predict such types of solutions.展开更多
In this paper we provide different types of approach in mathematical biology about infection disease and understanding the dynamic of epidemic mathematical models specially in COVID-19 disease which first outbroke in ...In this paper we provide different types of approach in mathematical biology about infection disease and understanding the dynamic of epidemic mathematical models specially in COVID-19 disease which first outbroke in China and fast spread around the world. We work in the connection between the mathematical models and the solution analytically and numerically. At first, we emphasize the Susceptible-Infectious-Recovered (SIR) models’ extension for policy significance. Then, we found the improved SIER model done by research. In third section, we examine the improved model when an appropriate vaccine has been found, we introduce the model of SIR with vaccine term which ends up with discussion and conclusion about the effect of vaccinate. The comprehension of COVID-19 transmission methods, structures, and characteristics is greatly aided by these mathematical models analytically and numerically.展开更多
Hepatitis B is an infectious disease worthy of attention.Considering the incubation period,psychological inhibition factor,vaccine,limited medical resources and horizontal transmission,an SIRS model is proposed to des...Hepatitis B is an infectious disease worthy of attention.Considering the incubation period,psychological inhibition factor,vaccine,limited medical resources and horizontal transmission,an SIRS model is proposed to describe hepatitis B transmission dynamics.In order to describe the behavior changes caused by people's psychological changes,the non-monotonic incidence rate is adopted in the model.We use the saturated treatment rate to describe the limited medical resources.Mathematical analysis shows the existence conditions of the equilibria,forward or backward bifurcation,Hopf bifurcation and the Bogdanov-Takens bifurcation.During the observation of the case data of hepatitis B in China,it is found that there are mainly three features,periodic outbreaks,aperiodic outbreaks,and periodic outbreaks turns to aperiodic outbreaks.According to the above features,we select three different representative regions,Jiangxi,Zhejiang province and Beijing,and then use our model to fit the actual monthly hepatitis B case data.The basic reproduction numbers that we estimated are 1.7712,1.4805 and 1.4132,respectively.The results of data fitting are consistent with those of theoretical analysis.According to the sensitivity analysis of Ro,we conclude that reducing contact,increasing treatment rate,strengthening vaccination and revaccinating can effectively prevent and control the prevalence of hepatitis B.展开更多
In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch in...In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].展开更多
In this paper we present a model with spatial heterogeneity based on cellular automata (CA). In the model we consider the relevant heterogeneity of host (susceptible) mixing and the natural birth rate. We divide t...In this paper we present a model with spatial heterogeneity based on cellular automata (CA). In the model we consider the relevant heterogeneity of host (susceptible) mixing and the natural birth rate. We divide the susceptible population into three groups according to the immunity of each individual based on the classical susceptible-infectedremoved (SIR) epidemic models, and consider the spread of an infectious disease transmitted by direct contact among humans and vectors that have not an incubation period to become infectious. We test the local stability and instability of the disease-free equilibrium by the spectrum radii of Jacobian. The simulation shows that the structure of the nearest neighbour size of the cell (or the degree of the scale-free networks) plays a very important role in the spread properties of infectious disease. The positive equilibrium of the infections versus the neighbour size follows the third power law if an endemic equilibrium point exists. Finally, we analyse the feature of the infection waves for the homogeneity and heterogeneous cases respectively.展开更多
In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.T...In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.展开更多
This paper is concerned with the spatial propagation of an SIR epidemic model with nonlocal diffusion and free boundaries describing the evolution of a disease.This model can be viewed as a nonlocal version of the fre...This paper is concerned with the spatial propagation of an SIR epidemic model with nonlocal diffusion and free boundaries describing the evolution of a disease.This model can be viewed as a nonlocal version of the free boundary problem studied by Kim et al.(An SIR epidemic model with free boundary.Nonlinear Anal RWA,2013,14:1992-2001).We first prove that this problem has a unique solution defined for all time,and then we give sufficient conditions for the disease vanishing and spreading.Our result shows that the disease will not spread if the basic reproduction number R_(0)<1,or the initial infected area h_(0),expanding ability μ and the initial datum S_(0) are all small enough when 1<R_(0)<1+d/μ_(2)+α.Furthermore,we show that if 1<R_(0)<1+d/μ_(2)+α,the disease will spread when h_(0) is large enough or h_(0) is small but μ is large enough.It is expected that the disease will always spread when R_(0)≥1+d/μ_(2)+α which is different from the local model.展开更多
During the late months of last year,a novel coronavirus was detected in Hubei,China.The virus,since then,has spread all across the globe forcing Word Health Organization(WHO)to declare COVID-19 outbreak a pandemic.In ...During the late months of last year,a novel coronavirus was detected in Hubei,China.The virus,since then,has spread all across the globe forcing Word Health Organization(WHO)to declare COVID-19 outbreak a pandemic.In Spain,the virus started infecting the country slowly until rapid growth of infected people occurred in Madrid,Barcelona and other major cities.The government in an attempt to stop the rapssid spread of the virus and ensure that health system will not reach its capacity,implement strict measures by putting the entire country in quarantine.The duration of these measures,depends on the evolution of the virus in Spain.In this study,a Deep Neural Network approach using Monte Carlo is proposed for generating a database to train networks for estimating the optimal parameters of a SIR epidemiology model.The number of total infected people as of April 7 in Spain is considered as input to the Deep Neural Network.The adaptability of the model was evaluated using the latest data upon completion of this paper,i.e.,April 14.The date range for the peak of infected people(i.e.,active cases)based on the new information is estimated to be within 74 to 109 days after the first recorded case of COVID-19 in Spain.In addition,a curve fitting measure based on the squared Euclidean distance indicates that according to the current data the peak might occur before the 86th day.Collectively,Deep Neural Networks have proven accurate and useful tools in handling big epidemiological data and for peak prediction estimates.展开更多
In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive relea...In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive release and general nonlinear incidence rate and investigate dynamical behaviors of the model. Under the reasonable assumptions, the sufficient conditions which guarantee the globally attractive of the disease-free periodic solution and the permanence of the infected fish are established, that is, the infected fish dies out if , whereas the disease persists if . To substantiate our theoretical results, extensive numerical simulations are performed for a hypothetical set of parameter values.展开更多
The COVID-19 pandemic is a curse and a threat to global health, development, the economy, and peaceful society because of its massive transmission and high rates of mutation. More than 220 countries have been affected...The COVID-19 pandemic is a curse and a threat to global health, development, the economy, and peaceful society because of its massive transmission and high rates of mutation. More than 220 countries have been affected by COVID-19. The world is now facing a drastic situation because of this ongoing virus. Bangladesh is also dealing with this issue, and due to its dense population, it is particularly vulnerable to the spread of COVID-19. Recently, many non-linear systems have been proposed to solve the SIR (Susceptible, Infected, and Recovered) model for predicting Coronavirus cases. In this paper, we have discussed the fractional order SIR epidemic model of a non-fatal disease in a population of a constant size. Using the Laplace Adomian Decomposition method, we get an approximate solution to the model. To predict the dynamic transmission of COVID-19 in Bangladesh, we provide a numerical argument based on real data. We also conducted a comparative analysis among susceptible, infected, and recovered people. Furthermore, the most sensitive parameters for the Basic Reproduction Number (<em>R</em><sub>0</sub>) are graphically presented, and the impact of the compartments on the transmission dynamics of the COVID-19 pandemic is thoroughly investigated.展开更多
基金partially supported by the Natural Science Foundation of Heilongjiang Province(A201420)Educational Reform Project of Heilongjiang Province(JG2013010482)+1 种基金Foundation of Heilongjiang Province Educational Committee(12541696)the Natural Science Foundation of China(11401136,11301112,11301207,11501148)
文摘The paper establishes two stochastic SIRS models with jumps to describe the spread of network virus by cyber war, terrorism and others. First, adding random perturbations proportionally to each variable, we get the dynamic properties around the positive equilibrium of the deterministic model and the conditions for persistence and extinction. Second, giving a random disturbance to endemic equilibrium, we get a stochastic system with jumps. By modifying the existing Lyapunov function, we prove the positive solution of the system is stochastically stable.
基金National Natural Science Foundations of China(No.11071259,No.11371374)Research Fund for the Doctoral Program of Higher Education of China(No.20110162110060)
文摘A stochastic susceptible-infective-recovered-susceptible( SIRS) model with non-linear incidence and Levy jumps was considered. Under certain conditions, the SIRS had a global positive solution. The stochastically ultimate boundedness of the solution of the model was obtained by using the method of Lyapunov function and the generalized Ito's formula. At last,asymptotic behaviors of the solution were discussed according to the value of R0. If R0< 1,the solution of the model oscillates around a steady state, which is the diseases free equilibrium of the corresponding deterministic model,and if R0> 1,it fluctuates around the endemic equilibrium of the deterministic model.
文摘In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R<sub>0</sub> ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.
基金The authors are grateful to the anonymous referee for his helpful comments and valuable suggestions.This work was supported by the National Natural Science Foundation of China-Shandong joint fund(No.U1806203)Natural Science Foundation of Shandong Province(No.ZR2019MA051)+1 种基金the Fundamental Research Funds for the Central Universities(No.2019ZRJC005)National Nat-ural Science Foundation of China key fund(No.61533011).
文摘It is of crucial significance to study the infectious disease phenomenon by using the SIRS model and thoughts of Julia set.In this paper,Julia set of the discrete version of the SIRS model is established to analyze the fractal dynamics of this model.Then,controller is designed to change the Julia set.Furthermore,the box-counting dimensions of the controlled Julia sets by selecting different appropriate parameters are computed to show the complexity of the model.Finally,a nonlinear coupling method is introduced to synchronize the Julia sets with different parameters of the same system.Simulation results show the efficacy of t hese met hods.
基金This work is supported by the National Natural Science Foundation of China(Nos.11871179,11861040 and 11961037)Science and technology project of Jiangxi Provincial Department of Education(G.J.J190923 and GJ.J170951).
文摘ln this paper,we propose and investigate an SlRS model with age structure and twodelays.Both the infected and the recovered individuals have age structure,the infectionrate(from the infective to the susceptible)and the immune loss rate(from the recoveredto the susceptible)are related to two independent time delays,respectively.We provethat the proposed age structured SIRS model is well-posed by using the Co-semigrouptheory.The basic reproduction number Ro is given,and the unique endemic equilib-rium exists when R_(0)>1,while the disease-free equilibrium always exists.A rigorousmathematical analysis for the stability of two equilibria is provided.The disease-freeequilibrium is local asymptotically stable if R_(0)<1,and the endemic equilibrium is localasymptotically stable if R_(0)>1 and τl=0.Finally,we give numerical simulations toverify our results.
基金National Natural Science Foundation of China(No.61273070)the Priority Academic Program Development of Jiangsu Higher Education Institutions,China
文摘This paper is concerned with a delayed SIRS epidemic model with a nonlinear incidence rate. The main results are given in terms of local stability and Hopf bifurcation. Sufficient conditions for the local stability of the positive equilibrium and existence of Hopf bifurcation are obtained by regarding the time delay as the bifurcation parameter. Further,the properties of Hopf bifurcation such as the direction and stability are investigated by using the normal form theory and center manifold argument. Finally,some numerical simulations are presented to verify the theoretical analysis.
基金This work is supported by the National Sciences Foundation of China (10471040)the Youth Science Foundations of Shanxi Province (20021003).
文摘In this article, an SIRS epidemic model spread by vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point (if it exists) is globally stable with a respect "weak delay". Some known results are generalized.
基金supported in part by JSPS Fellows,No.237213 of Japan Society for the Promotion of Science to the first authorthe Grant MTM2010-18318 of the MICINN,Spanish Ministry of Science and Innovation to the second authorScientific Research (c),No.21540230 of Japan Society for the Promotion of Science to the third author
文摘In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.
基金Research Partnership Program no.RP-21-09-06 from the Deanship of Scientific Research of Imam Mohammad Ibn Saud Islamic University(IMSIU).
文摘This paper presents a restricted SIRmathematicalmodel to analyze the evolution of a contagious infectious disease outbreak(COVID-19)using available data.The new model focuses on two main concepts:first,it can present multiple waves of the disease,and second,it analyzes how far an infection can be eradicated with the help of vaccination.The stability analysis of the equilibrium points for the suggested model is initially investigated by identifying the matching equilibrium points and examining their stability.The basic reproduction number is calculated,and the positivity of the solutions is established.Numerical simulations are performed to determine if it is multipeak and evaluate vaccination’s effects.In addition,the proposed model is compared to the literature already published and the effectiveness of vaccination has been recorded.
文摘Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and state-dependent control, where the fraction of susceptible individuals in population is as the detection threshold value. By the Poincaré map, theory of differential inequalities and differential equation geometry, the existence and orbital stability of the disease-free periodic solution are discussed. Theoretical results show that by state-dependent pulse vaccination we can make the proportion of infected individuals tend to zero, and control the transmission of disease in population.
文摘Typically,a computer has infectivity as soon as it is infected.It is a reality that no antivirus programming can identify and eliminate all kinds of viruses,suggesting that infections would persevere on the Internet.To understand the dynamics of the virus propagation in a better way,a computer virus spread model with fuzzy parameters is presented in this work.It is assumed that all infected computers do not have the same contribution to the virus transmission process and each computer has a different degree of infectivity,which depends on the quantity of virus.Considering this,the parametersβandγbeing functions of the computer virus load,are considered fuzzy numbers.Using fuzzy theory helps us understand the spread of computer viruses more realistically as these parameters have fixed values in classical models.The essential features of the model,like reproduction number and equilibrium analysis,are discussed in fuzzy senses.Moreover,with fuzziness,two numerical methods,the forward Euler technique,and a nonstandard finite difference(NSFD)scheme,respectively,are developed and analyzed.In the evidence of the numerical simulations,the proposed NSFD method preserves the main features of the dynamic system.It can be considered a reliable tool to predict such types of solutions.
文摘In this paper we provide different types of approach in mathematical biology about infection disease and understanding the dynamic of epidemic mathematical models specially in COVID-19 disease which first outbroke in China and fast spread around the world. We work in the connection between the mathematical models and the solution analytically and numerically. At first, we emphasize the Susceptible-Infectious-Recovered (SIR) models’ extension for policy significance. Then, we found the improved SIER model done by research. In third section, we examine the improved model when an appropriate vaccine has been found, we introduce the model of SIR with vaccine term which ends up with discussion and conclusion about the effect of vaccinate. The comprehension of COVID-19 transmission methods, structures, and characteristics is greatly aided by these mathematical models analytically and numerically.
文摘Hepatitis B is an infectious disease worthy of attention.Considering the incubation period,psychological inhibition factor,vaccine,limited medical resources and horizontal transmission,an SIRS model is proposed to describe hepatitis B transmission dynamics.In order to describe the behavior changes caused by people's psychological changes,the non-monotonic incidence rate is adopted in the model.We use the saturated treatment rate to describe the limited medical resources.Mathematical analysis shows the existence conditions of the equilibria,forward or backward bifurcation,Hopf bifurcation and the Bogdanov-Takens bifurcation.During the observation of the case data of hepatitis B in China,it is found that there are mainly three features,periodic outbreaks,aperiodic outbreaks,and periodic outbreaks turns to aperiodic outbreaks.According to the above features,we select three different representative regions,Jiangxi,Zhejiang province and Beijing,and then use our model to fit the actual monthly hepatitis B case data.The basic reproduction numbers that we estimated are 1.7712,1.4805 and 1.4132,respectively.The results of data fitting are consistent with those of theoretical analysis.According to the sensitivity analysis of Ro,we conclude that reducing contact,increasing treatment rate,strengthening vaccination and revaccinating can effectively prevent and control the prevalence of hepatitis B.
基金supported by Japan Society for the Promotion of Science (Grant Scientific Research (c), No. 24540219 to the first author, JSPS Fellows, No.237213 to the second author, and No. 222176 to the third author)
文摘In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].
基金Project supported by the National Natural Science Foundation of China (Grant No 10471040).
文摘In this paper we present a model with spatial heterogeneity based on cellular automata (CA). In the model we consider the relevant heterogeneity of host (susceptible) mixing and the natural birth rate. We divide the susceptible population into three groups according to the immunity of each individual based on the classical susceptible-infectedremoved (SIR) epidemic models, and consider the spread of an infectious disease transmitted by direct contact among humans and vectors that have not an incubation period to become infectious. We test the local stability and instability of the disease-free equilibrium by the spectrum radii of Jacobian. The simulation shows that the structure of the nearest neighbour size of the cell (or the degree of the scale-free networks) plays a very important role in the spread properties of infectious disease. The positive equilibrium of the infections versus the neighbour size follows the third power law if an endemic equilibrium point exists. Finally, we analyse the feature of the infection waves for the homogeneity and heterogeneous cases respectively.
文摘In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.
基金Zhao was supported by a scholarship from the China Scholarship Council,Li was partially supported by NSF of China(11731005)Cao was partially supported by NSF of China(11901264).
文摘This paper is concerned with the spatial propagation of an SIR epidemic model with nonlocal diffusion and free boundaries describing the evolution of a disease.This model can be viewed as a nonlocal version of the free boundary problem studied by Kim et al.(An SIR epidemic model with free boundary.Nonlinear Anal RWA,2013,14:1992-2001).We first prove that this problem has a unique solution defined for all time,and then we give sufficient conditions for the disease vanishing and spreading.Our result shows that the disease will not spread if the basic reproduction number R_(0)<1,or the initial infected area h_(0),expanding ability μ and the initial datum S_(0) are all small enough when 1<R_(0)<1+d/μ_(2)+α.Furthermore,we show that if 1<R_(0)<1+d/μ_(2)+α,the disease will spread when h_(0) is large enough or h_(0) is small but μ is large enough.It is expected that the disease will always spread when R_(0)≥1+d/μ_(2)+α which is different from the local model.
基金This work was supported by the European Commission under project FLEXITRANSTORE-H2020-LCE-2016-2017-SGS-774407by the Spanish Ministry of Science under project ENE2017-88889-C2-1-RAny opinions,findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the host institutions or funders.
文摘During the late months of last year,a novel coronavirus was detected in Hubei,China.The virus,since then,has spread all across the globe forcing Word Health Organization(WHO)to declare COVID-19 outbreak a pandemic.In Spain,the virus started infecting the country slowly until rapid growth of infected people occurred in Madrid,Barcelona and other major cities.The government in an attempt to stop the rapssid spread of the virus and ensure that health system will not reach its capacity,implement strict measures by putting the entire country in quarantine.The duration of these measures,depends on the evolution of the virus in Spain.In this study,a Deep Neural Network approach using Monte Carlo is proposed for generating a database to train networks for estimating the optimal parameters of a SIR epidemiology model.The number of total infected people as of April 7 in Spain is considered as input to the Deep Neural Network.The adaptability of the model was evaluated using the latest data upon completion of this paper,i.e.,April 14.The date range for the peak of infected people(i.e.,active cases)based on the new information is estimated to be within 74 to 109 days after the first recorded case of COVID-19 in Spain.In addition,a curve fitting measure based on the squared Euclidean distance indicates that according to the current data the peak might occur before the 86th day.Collectively,Deep Neural Networks have proven accurate and useful tools in handling big epidemiological data and for peak prediction estimates.
文摘In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive release and general nonlinear incidence rate and investigate dynamical behaviors of the model. Under the reasonable assumptions, the sufficient conditions which guarantee the globally attractive of the disease-free periodic solution and the permanence of the infected fish are established, that is, the infected fish dies out if , whereas the disease persists if . To substantiate our theoretical results, extensive numerical simulations are performed for a hypothetical set of parameter values.
文摘The COVID-19 pandemic is a curse and a threat to global health, development, the economy, and peaceful society because of its massive transmission and high rates of mutation. More than 220 countries have been affected by COVID-19. The world is now facing a drastic situation because of this ongoing virus. Bangladesh is also dealing with this issue, and due to its dense population, it is particularly vulnerable to the spread of COVID-19. Recently, many non-linear systems have been proposed to solve the SIR (Susceptible, Infected, and Recovered) model for predicting Coronavirus cases. In this paper, we have discussed the fractional order SIR epidemic model of a non-fatal disease in a population of a constant size. Using the Laplace Adomian Decomposition method, we get an approximate solution to the model. To predict the dynamic transmission of COVID-19 in Bangladesh, we provide a numerical argument based on real data. We also conducted a comparative analysis among susceptible, infected, and recovered people. Furthermore, the most sensitive parameters for the Basic Reproduction Number (<em>R</em><sub>0</sub>) are graphically presented, and the impact of the compartments on the transmission dynamics of the COVID-19 pandemic is thoroughly investigated.