In this research,novel epidemic models based on fractional calculus are developed by utilizing the Caputo and Atangana-Baleanu(AB)derivatives.These models integrate vaccination effects,additional safety measures,home ...In this research,novel epidemic models based on fractional calculus are developed by utilizing the Caputo and Atangana-Baleanu(AB)derivatives.These models integrate vaccination effects,additional safety measures,home and hospital isolation,and treatment options.Fractional models are particularly significant as they provide a more comprehensive understanding of epidemic diseases and can account for non-locality and memory effects.Equilibrium points of the model are calculated,including the disease-free and endemic equilibrium points,and the basic reproduction number R0 is computed using the next-generation matrix approach.Results indicate that the epidemic becomes endemic when R0 is greater than unity,and it goes extinct when it is less than unity.The positiveness and boundedness of the solutions of model are verified.The Routh-Hurwitz technique is utilized to analyze the local stability of equilibrium points.The Lyapunov function and the LaSalle’s principle are used to demonstrate the global stability of equilibrium points.Numerical schemes are proposed,and their validity is established by comparing them to the fourth-order Runge-Kutta(RK4)method.Numerical simulations are performed using the Adams-Bashforth-Moulton predictor-corrector algorithm for the Caputo time-fractional derivative and the Toufik-Atangana numerical technique for the AB time-fractional derivative.The study looks at how the quarantine policy affected different human population groups.On the basis of these findings,a strict quarantine policy voluntarily implemented by an informed human population can help reduce the pandemic’s spread.Additionally,vaccination efforts become a crucial tool in the fight against diseases.We can greatly lower the number of susceptible people and develop a shield of immunity in the population by guaranteeing common access to vaccinations and boosting vaccination awareness.Moreover,the graphical representations of the fractional models are also developed.展开更多
A simulation model based on nonlinear ordinary differential equations to interpret the transmission dynamics of Zika Virus (ZIKV), is formulated and analyzed, integrating the asymptomatic human population and coupled ...A simulation model based on nonlinear ordinary differential equations to interpret the transmission dynamics of Zika Virus (ZIKV), is formulated and analyzed, integrating the asymptomatic human population and coupled to the Aedes aegypti dynamics, the epidemic threshold Basic Reproduction Number R0 is determined, as the spectral radius of Next-Generation Matrix and the system is simulated with MAPLE computing program taking the parameter values from literature.展开更多
The basic reproduction number,R_(0),is a well-known quantifier of epidemic spread.However,a class of existing methods for estimating R_(0)from incidence data early in the epidemic can lead to an over-estimation of thi...The basic reproduction number,R_(0),is a well-known quantifier of epidemic spread.However,a class of existing methods for estimating R_(0)from incidence data early in the epidemic can lead to an over-estimation of this quantity.In particular,when fitting deterministic models to estimate the rate of spread,we do not account for the stochastic nature of epidemics and that,given the same system,some outbreaks may lead to epidemics and some may not.Typically,an observed epidemic that we wish to control is a major outbreak.This amounts to implicit selection for major outbreaks which leads to the over-estimation problem.We formally characterised the split between major and minor outbreaks by using Otsu's method which provides us with a working definition.We show that by conditioning a‘deterministic’model on major outbreaks,we can more reliably estimate the basic reproduction number from an observed epidemic trajectory.展开更多
Even though vaccines against rabies are available,rabies still remains a burden killing a significant number of humans as well as domestic and wild animals in many parts of the world,including Nepal.In this study,we d...Even though vaccines against rabies are available,rabies still remains a burden killing a significant number of humans as well as domestic and wild animals in many parts of the world,including Nepal.In this study,we develop a mathematical model to describe transmission dynamics of rabies in Nepal.In particular,an indirect interspecies transmission from jackals to humans through dogs,which is relevant to the context of Nepal,is one of the novel features of our model.Our model utilizes annual dog-bite data collected from Nepal for a decade long period,allowing us to reasonably estimate parameters related to rabies transmission in Nepal.Using our model,we calculated the basic reproduction number(R_(0)=1:16)as well as intraspecies basic reproduction numbers of dogs(R_(0)^(D)=1:14)and jackals(R_(0)^(J)=0:07)for Nepal,and identified that the dog-related parameters are primary contributors to R0.Our results show that,along with dogs,jackals may also play an important role,albeit lesser extent,in the persistence of rabies in Nepal.Our model also suggests that control strategies may help reduce the prevalence significantly but the jackal vaccination may not be as effective as dog-related preventive strategies.To get deeper insight into the role of intraspecies and interspecies transmission between dog and jackal populations in the persistence of rabies,we also extended our model analysis into a wider parameter range.Interestingly,for some feasible parameters,even though rabies is theoretically controlled in each dog and jackal populations(R_(0)^(D)<1,R_(0)^(J)<1)if isolated,the rabies epidemic may still occur(R_(0)>1)due to interspecies transmission.These results may be useful to design effective prevention and control strategies for mitigating rabies burden in Nepal and other parts of the world.展开更多
文摘In this research,novel epidemic models based on fractional calculus are developed by utilizing the Caputo and Atangana-Baleanu(AB)derivatives.These models integrate vaccination effects,additional safety measures,home and hospital isolation,and treatment options.Fractional models are particularly significant as they provide a more comprehensive understanding of epidemic diseases and can account for non-locality and memory effects.Equilibrium points of the model are calculated,including the disease-free and endemic equilibrium points,and the basic reproduction number R0 is computed using the next-generation matrix approach.Results indicate that the epidemic becomes endemic when R0 is greater than unity,and it goes extinct when it is less than unity.The positiveness and boundedness of the solutions of model are verified.The Routh-Hurwitz technique is utilized to analyze the local stability of equilibrium points.The Lyapunov function and the LaSalle’s principle are used to demonstrate the global stability of equilibrium points.Numerical schemes are proposed,and their validity is established by comparing them to the fourth-order Runge-Kutta(RK4)method.Numerical simulations are performed using the Adams-Bashforth-Moulton predictor-corrector algorithm for the Caputo time-fractional derivative and the Toufik-Atangana numerical technique for the AB time-fractional derivative.The study looks at how the quarantine policy affected different human population groups.On the basis of these findings,a strict quarantine policy voluntarily implemented by an informed human population can help reduce the pandemic’s spread.Additionally,vaccination efforts become a crucial tool in the fight against diseases.We can greatly lower the number of susceptible people and develop a shield of immunity in the population by guaranteeing common access to vaccinations and boosting vaccination awareness.Moreover,the graphical representations of the fractional models are also developed.
文摘A simulation model based on nonlinear ordinary differential equations to interpret the transmission dynamics of Zika Virus (ZIKV), is formulated and analyzed, integrating the asymptomatic human population and coupled to the Aedes aegypti dynamics, the epidemic threshold Basic Reproduction Number R0 is determined, as the spectral radius of Next-Generation Matrix and the system is simulated with MAPLE computing program taking the parameter values from literature.
基金This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 955708.
文摘The basic reproduction number,R_(0),is a well-known quantifier of epidemic spread.However,a class of existing methods for estimating R_(0)from incidence data early in the epidemic can lead to an over-estimation of this quantity.In particular,when fitting deterministic models to estimate the rate of spread,we do not account for the stochastic nature of epidemics and that,given the same system,some outbreaks may lead to epidemics and some may not.Typically,an observed epidemic that we wish to control is a major outbreak.This amounts to implicit selection for major outbreaks which leads to the over-estimation problem.We formally characterised the split between major and minor outbreaks by using Otsu's method which provides us with a working definition.We show that by conditioning a‘deterministic’model on major outbreaks,we can more reliably estimate the basic reproduction number from an observed epidemic trajectory.
基金The work of NKV was partially supported by NSF grants DMS-1951793,DMS-1616299,DMS-1836647,and DEB-2030479 from the National Science Foundation of USA,and the UGP award and the start-up fund from San Diego State University.
文摘Even though vaccines against rabies are available,rabies still remains a burden killing a significant number of humans as well as domestic and wild animals in many parts of the world,including Nepal.In this study,we develop a mathematical model to describe transmission dynamics of rabies in Nepal.In particular,an indirect interspecies transmission from jackals to humans through dogs,which is relevant to the context of Nepal,is one of the novel features of our model.Our model utilizes annual dog-bite data collected from Nepal for a decade long period,allowing us to reasonably estimate parameters related to rabies transmission in Nepal.Using our model,we calculated the basic reproduction number(R_(0)=1:16)as well as intraspecies basic reproduction numbers of dogs(R_(0)^(D)=1:14)and jackals(R_(0)^(J)=0:07)for Nepal,and identified that the dog-related parameters are primary contributors to R0.Our results show that,along with dogs,jackals may also play an important role,albeit lesser extent,in the persistence of rabies in Nepal.Our model also suggests that control strategies may help reduce the prevalence significantly but the jackal vaccination may not be as effective as dog-related preventive strategies.To get deeper insight into the role of intraspecies and interspecies transmission between dog and jackal populations in the persistence of rabies,we also extended our model analysis into a wider parameter range.Interestingly,for some feasible parameters,even though rabies is theoretically controlled in each dog and jackal populations(R_(0)^(D)<1,R_(0)^(J)<1)if isolated,the rabies epidemic may still occur(R_(0)>1)due to interspecies transmission.These results may be useful to design effective prevention and control strategies for mitigating rabies burden in Nepal and other parts of the world.
