In this article, an infectious model with saturation effect is considered. By using compound matrix theory and a series of theorems associated to qualitative theory of differential equations which are introduced by Mu...In this article, an infectious model with saturation effect is considered. By using compound matrix theory and a series of theorems associated to qualitative theory of differential equations which are introduced by Muldowney and Micheal Li, we study globally stable problem of the model.展开更多
The SEIR epidemic model studied here includes constant inflows of new susceptibles, exposeds, infectives, and recovereds. This model also incorporates a population size dependent contact rate and a disease-related dea...The SEIR epidemic model studied here includes constant inflows of new susceptibles, exposeds, infectives, and recovereds. This model also incorporates a population size dependent contact rate and a disease-related death. As the infected fraction cannot be eliminated from the population, this kind of model has only the unique endemic equilibrium that is globally asymptotically stable. Under the special case where the new members of immigration are all susceptible, the model considered here shows a threshold phenomenon and a sharp threshold has been obtained. In order to prove the global asymptotical stability of the endemic equilibrium, the authors introduce the change of variable, which can reduce our four-dimensional system to a three-dimensional asymptotical autonomous system with limit equation.展开更多
Stochasticity is introduced into a susceptible-exposed but not infectious-infectious-removed （SEIR） model describing epidemics＇ transmission, via the technique of parameter perturbation which is standard in stochas...Stochasticity is introduced into a susceptible-exposed but not infectious-infectious-removed （SEIR） model describing epidemics＇ transmission, via the technique of parameter perturbation which is standard in stochastic population modeling. The existence and uniqueness of the model have been proved in this paper. And E detailed analysis on global asymptotic stability is also carried out.展开更多
In this paper, we investigate the global stability of an SEIR (Susceptible-Exposed-Infected-Remove) epidemic model with infectious force under intervention strategies. To address this issue, we prove that the basic re...In this paper, we investigate the global stability of an SEIR (Susceptible-Exposed-Infected-Remove) epidemic model with infectious force under intervention strategies. To address this issue, we prove that the basic reproduction number R0 plays an essential role in determining whether the disease extincts or persists. If , there is a unique disease-free equilibrium point of the model which is globally asymptotically stable and the disease dies out, and if , there exists a unique endemic equilibrium point which is globally asymptotically stable and the disease persists.展开更多
Malaria,a devastating disease caused by the Plasmodium parasite and transmitted through the bites of female Anopheles mosquitoes,remains a significant public health concern,claiming over 600,000 lives annually,predomi...Malaria,a devastating disease caused by the Plasmodium parasite and transmitted through the bites of female Anopheles mosquitoes,remains a significant public health concern,claiming over 600,000 lives annually,predominantly among children.Novel tools,including the application of Wolbachia,are being developed to combat malaria-transmitting mosquitoes.This study presents a modified susceptible-exposed-infectious-recovered-susceptible(SEIRS)compartmental mathematical model to evaluate the impact of awareness-based control measures on malaria transmission dynamics,incorporating mosquito interactions and seasonality.Employing the next-generation matrix approach,we calculated a basic reproduction number(R0)of 2.4537,indicating that without robust control measures,the disease will persist in the human population.The model equations were solved numerically using fourth and fifth-order Runge-Kutta methods.The model was fitted to malaria incidence data from Kenya spanning 2000 to 2021 using least squares curve fitting.The fitting algorithm yielded a mean absolute error(MAE)of 2.6463 when comparing the actual data points to the simulated values of infectious human population(Ih).This finding indicates that the proposed mathematical model closely aligns with the recorded malaria incidence data.The optimal values of the model parameters were estimated from the fitting algorithm,and future malaria dynamics were projected for the next decade.The research findings suggest that social media-based awareness campaigns,coupled with specific optimization control measures and effective management methods,offer the most cost-effective approach to managing malaria.展开更多
In this paper,an SEIR model with nonlinear incidence rates are studied.The basic reproduction number R_0 characterizes the disease transmission dynamics: if R_0≤ 1,the disease-free equilibrium is globally asymptotica...In this paper,an SEIR model with nonlinear incidence rates are studied.The basic reproduction number R_0 characterizes the disease transmission dynamics: if R_0≤ 1,the disease-free equilibrium is globally asymptotically stable and the disease always dies out,if R_0> 1 then there is a unique endemic equilibrium which is globally asymptotically stable and the disease persists.展开更多
The microscopic global nucleon–nucleus optical model potential(OMP)proposed by Whitehead,Lim,and Holt,the WLH potential(Whitehead et al.,Phys Rev Lett 127:182502,2021),which was constructed in the framework of many-b...The microscopic global nucleon–nucleus optical model potential(OMP)proposed by Whitehead,Lim,and Holt,the WLH potential(Whitehead et al.,Phys Rev Lett 127:182502,2021),which was constructed in the framework of many-body per-turbation theory with state-of-the-art nuclear interactions from chiral effective field theory(EFT),was tested with(p,d)transfer reactions calculated using adiabatic wave approximation.The target nuclei included both stable and unstable nuclei,and the incident energies reached 200 MeV.The results were compared with experimental data and predictions using the phenomenological global optical potential of Koning and Delaroche,the KD02 potential.Overall,we found that the micro-scopic WLH potential described the(p,d)reaction angular distributions similarly to the phenomenological KD02 potential;however,the former was slightly better than the latter for radioactive targets.On average,the obtained spectroscopic factors(SFs)using both microscopic and phenomenological potentials were similar when the incident energies were below approxi-mately 120 MeV.However,their difference tended to increase at higher incident energies,which was particularly apparent for the doubly magic target nucleus 40Ca.展开更多
In this paper, a SEIR model with ratio-dependent transmission rate in the form ?is studied and the basic reproduction number which determines the disease’s extinction or continued existence is obtained. By constructi...In this paper, a SEIR model with ratio-dependent transmission rate in the form ?is studied and the basic reproduction number which determines the disease’s extinction or continued existence is obtained. By constructing the proper Lyapunov function, we prove that if R0 ≤ 1, the disease-free equilibrium point of the model is globally asymptotically stable and the disease always dies out;if R0 > 1, the endemic equilibrium point is globally asymptotically stable and the disease persists.展开更多
基金The NNSF (10171010) of China Major Project of Education Ministry (01061) of China, Key Library for Vegetation Ecology, Education Ministry of China.
文摘In this article, an infectious model with saturation effect is considered. By using compound matrix theory and a series of theorems associated to qualitative theory of differential equations which are introduced by Muldowney and Micheal Li, we study globally stable problem of the model.
基金This research is supported by the NNSF of China (19971066)
文摘The SEIR epidemic model studied here includes constant inflows of new susceptibles, exposeds, infectives, and recovereds. This model also incorporates a population size dependent contact rate and a disease-related death. As the infected fraction cannot be eliminated from the population, this kind of model has only the unique endemic equilibrium that is globally asymptotically stable. Under the special case where the new members of immigration are all susceptible, the model considered here shows a threshold phenomenon and a sharp threshold has been obtained. In order to prove the global asymptotical stability of the endemic equilibrium, the authors introduce the change of variable, which can reduce our four-dimensional system to a three-dimensional asymptotical autonomous system with limit equation.
基金the International Economics and Foreign Trade Subject Group Research Projects on the Special Development Fund(2013-2014) for Higher Education from the Central to Support the Local,China(No.Y13022)
文摘Stochasticity is introduced into a susceptible-exposed but not infectious-infectious-removed （SEIR） model describing epidemics＇ transmission, via the technique of parameter perturbation which is standard in stochastic population modeling. The existence and uniqueness of the model have been proved in this paper. And E detailed analysis on global asymptotic stability is also carried out.
文摘In this paper, we investigate the global stability of an SEIR (Susceptible-Exposed-Infected-Remove) epidemic model with infectious force under intervention strategies. To address this issue, we prove that the basic reproduction number R0 plays an essential role in determining whether the disease extincts or persists. If , there is a unique disease-free equilibrium point of the model which is globally asymptotically stable and the disease dies out, and if , there exists a unique endemic equilibrium point which is globally asymptotically stable and the disease persists.
文摘Malaria,a devastating disease caused by the Plasmodium parasite and transmitted through the bites of female Anopheles mosquitoes,remains a significant public health concern,claiming over 600,000 lives annually,predominantly among children.Novel tools,including the application of Wolbachia,are being developed to combat malaria-transmitting mosquitoes.This study presents a modified susceptible-exposed-infectious-recovered-susceptible(SEIRS)compartmental mathematical model to evaluate the impact of awareness-based control measures on malaria transmission dynamics,incorporating mosquito interactions and seasonality.Employing the next-generation matrix approach,we calculated a basic reproduction number(R0)of 2.4537,indicating that without robust control measures,the disease will persist in the human population.The model equations were solved numerically using fourth and fifth-order Runge-Kutta methods.The model was fitted to malaria incidence data from Kenya spanning 2000 to 2021 using least squares curve fitting.The fitting algorithm yielded a mean absolute error(MAE)of 2.6463 when comparing the actual data points to the simulated values of infectious human population(Ih).This finding indicates that the proposed mathematical model closely aligns with the recorded malaria incidence data.The optimal values of the model parameters were estimated from the fitting algorithm,and future malaria dynamics were projected for the next decade.The research findings suggest that social media-based awareness campaigns,coupled with specific optimization control measures and effective management methods,offer the most cost-effective approach to managing malaria.
基金Supported by the National Natural Science Foundation of China(11101323)Supported by the Natural Science Basic Research Plan in Shaanxi Province of China(2014JQ1038)Supported by the Xi’an Polytechnic University Innovation Fund for Graduate Students(CX201608)
文摘In this paper,an SEIR model with nonlinear incidence rates are studied.The basic reproduction number R_0 characterizes the disease transmission dynamics: if R_0≤ 1,the disease-free equilibrium is globally asymptotically stable and the disease always dies out,if R_0> 1 then there is a unique endemic equilibrium which is globally asymptotically stable and the disease persists.
基金Supported by National Natural Science Foundation of China(Nos.U2067205 and 12205098)National Key Laboratory of Computational Physics(HX02021-35).
文摘The microscopic global nucleon–nucleus optical model potential(OMP)proposed by Whitehead,Lim,and Holt,the WLH potential(Whitehead et al.,Phys Rev Lett 127:182502,2021),which was constructed in the framework of many-body per-turbation theory with state-of-the-art nuclear interactions from chiral effective field theory(EFT),was tested with(p,d)transfer reactions calculated using adiabatic wave approximation.The target nuclei included both stable and unstable nuclei,and the incident energies reached 200 MeV.The results were compared with experimental data and predictions using the phenomenological global optical potential of Koning and Delaroche,the KD02 potential.Overall,we found that the micro-scopic WLH potential described the(p,d)reaction angular distributions similarly to the phenomenological KD02 potential;however,the former was slightly better than the latter for radioactive targets.On average,the obtained spectroscopic factors(SFs)using both microscopic and phenomenological potentials were similar when the incident energies were below approxi-mately 120 MeV.However,their difference tended to increase at higher incident energies,which was particularly apparent for the doubly magic target nucleus 40Ca.
文摘In this paper, a SEIR model with ratio-dependent transmission rate in the form ?is studied and the basic reproduction number which determines the disease’s extinction or continued existence is obtained. By constructing the proper Lyapunov function, we prove that if R0 ≤ 1, the disease-free equilibrium point of the model is globally asymptotically stable and the disease always dies out;if R0 > 1, the endemic equilibrium point is globally asymptotically stable and the disease persists.
