Prasenjit Das | China Medical University,Taiwan (original) (raw)
Papers by Prasenjit Das
ISRN Biomathematics, 2012
Cholera still remains as a severe global threat and is currently spreading in Africa and other pa... more Cholera still remains as a severe global threat and is currently spreading in Africa and other parts of the world. The role of lytic bacteriophage as an intervention of cholera outbreaks is investigated using a mathematical model. Dynamics of cholera is discussed on basis of the basic reproduction number . Conditions of Hopf bifurcation are also derived for a positive net growth rate of Vibrio cholerae. Stability analysis and numerical simulations suggest that bacteriophage may contribute to lessening the severity of cholera epidemics by reducing the number of Vibrio cholerae in the environment. Hence with the presence of phage virus, cholera is self-limiting in nature. By using phage as a biological control agent in endemic areas, one may also influence the temporal dynamics of cholera epidemics while reducing the excessive use of chemicals. We also performed stochastic analysis which suggests that the model system is globally asymptotically stable in probability when the strengths...
Nonlinear Dynamics and Systems Theory
We present an in-host HIV/AIDS model with saturation effect and a discrete time delay. It is show... more We present an in-host HIV/AIDS model with saturation effect and a discrete time delay. It is shown that infection is endemic when ℛ 0 >1 but dies out when ℛ 0 <1. The switching phenomenon for the stable equilibria is observed when a discrete time delay is incorporated. The parameters that can control the disease transmission are also discussed. Numerical simulations are carried out to verify and support the analytical results and illustrate possible behavior scenarios of the model.
International Journal of Modern Nonlinear Theory and Application, 2012
The article concentrates on the role of fluctuating parameters for removable population from the ... more The article concentrates on the role of fluctuating parameters for removable population from the incubated class in a susceptible-incubated-infected model. The discrete analogous of this model is also investigated. Conditions for local asymptotic stability are derived for both the disease free and endemic cases. Numerical simulations are performed to validate the theoretical results.
Journal of Mathematical Modelling and Algorithms, 2011
ABSTRACT We present a deterministic HIV/AIDS model with delay. We then extend the model by adjoin... more ABSTRACT We present a deterministic HIV/AIDS model with delay. We then extend the model by adjoining terms capturing stochastic effects. The intensity of the fluctuations in the stochastic system is analytically evaluated using Fourier transform methods. We carry out simulations to assess differences in the dynamical behavior of the deterministic and stochastic models. Simulation results show that they are no significant differences in the behavior of the two models. KeywordsHIV/AIDS model–Incubation–Delay–Stochasticity
Mathematical and Computer Modelling, 2011
Although cholera has existed for ages, it has continued to plague many parts of the world. In thi... more Although cholera has existed for ages, it has continued to plague many parts of the world. In this study, a deterministic model for cholera in a community is presented and rigorously analysed in order to determine the effects of malnutrition in the spread of the disease. The important mathematical features of the cholera model are thoroughly investigated. The epidemic threshold known as the basic reproductive number and equilibria for the model are determined, and stabilities are investigated. The disease-free equilibrium is shown to be globally asymptotically stable. Local stability of the endemic equilibrium is determined using centre manifold theory and conditions for its global stability are derived using a suitable Lyapunov function. Numerical simulations suggest that an increase in susceptibility to cholera due to malnutrition results in an increase in the number of cholera infected individuals in a community. The results suggest that nutritional issues should be addressed in impoverished communities affected by cholera in order to reduce the burden of the disease.
Journal of Theoretical Biology, 2010
A deterministic model for assessing the dynamics of mixed species malaria infections in a human p... more A deterministic model for assessing the dynamics of mixed species malaria infections in a human population is presented to investigate the effects of dual infection with Plasmodium malariae and Plasmodium falciparum. Qualitative analysis of the model including positivity and boundedness is performed. In addition to the disease free equilibrium, we show that there exists a boundary equilibrium corresponding to each species. The isolation reproductive number of each species is computed as well as the reproductive number of the full model. Conditions for global stability of the disease free equilibrium as well as local stability of the boundary equilibria are derived. The model has an interior equilibrium which exists if at least one of the isolation reproductive numbers is greater than unity. Among the interesting dynamical behaviours of the model, the phenomenon of backward bifurcation where a stable boundary equilibrium coexists with a stable interior equilibrium, for a certain range of the associated invasion reproductive number less than unity is observed. Results from analysis of the model show that, when cross-immunity between the two species is weak, there is a high probability of coexistence of the two species and when cross-immunity is strong, competitive exclusion is high. Further, an increase in the reproductive number of species i increases the stability of its boundary equilibrium and its ability to invade an equilibrium of species j. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.
Journal of Biological Systems, 2005
This paper analyzes an epidemic model for carrier dependent infectious disease-cholera. Existence... more This paper analyzes an epidemic model for carrier dependent infectious disease-cholera. Existence criteria of carrier-free equilibrium point and endemic equilibrium point(unique or multiple) are discussed. Some threshold conditions are derived for which disease-free, carrier-free as ...
Journal of Biological Systems, 2004
Abstract: A Susceptible-Infective (SI) model is considered in this paper with time delay. The dea... more Abstract: A Susceptible-Infective (SI) model is considered in this paper with time delay. The death rate is assumed to be density dependent for this model. Conditions are derived under which there can be no change in stability. Using the discrete time delay as a bifurcation ...
Journal of Biological Systems, 2005
This study analyzes a model of hepatitis C with acute infectious, chronic infectious and the reco... more This study analyzes a model of hepatitis C with acute infectious, chronic infectious and the recovery or immune classes. Stability characters of disease-free and endemic proportionate equilibrium points are discussed. The role of immune system on the long-term survival of the ...
mail.cmu.edu.tw
Abstract. A discrete-time susceptible-infected model with saturation in inci-dence is investigate... more Abstract. A discrete-time susceptible-infected model with saturation in inci-dence is investigated.For this model, the existence and the stability of fixed points are analyzed.Stochastic analysis of the model suggests that it is asymptotically mean square stable for certain ...
Applied Mathematics and Computation, 2011
Discrete and stochastic version of a susceptible-infective model system with nonlinear incidence ... more Discrete and stochastic version of a susceptible-infective model system with nonlinear incidence rate is investigated. We observe that the discrete system converges to a unique equilibrium point for certain effective transmission rate of the disease and beyond which ...
Clinical and Experimental Nephrology, 2009
The hepatitis B virus (HBV) is estimated to have infected about 350 million people worldwide, mak... more The hepatitis B virus (HBV) is estimated to have infected about 350 million people worldwide, making it one of the most common human pathogens. Renal involvement is among its most common extra hepatic manifestations and usually manifests in the form of immune complex mediated glomerulopathy, such as membranous glomerulonephritis (MGN), membranoproliferative glomerulonephritis (MPGN), mesangioproliferative glomerulonephritis and immunoglobulin A (IgA) nephropathy. Occurrence of focal and segmental glomerular sclerosis (FSGS) with HBV infection is rare and only five cases have been reported earlier. We report two cases of hepatitis B associated FSGS. In both the cases, HBsAg was demonstrated in the renal tissue and both the cases showed response to treatment with lamivudine, thus indicating a possible causal association between the viral infection and occurrence of nephrotic syndrome.
The article concentrates on the study of delay and stochastic effect on a density dependent S-I e... more The article concentrates on the study of delay and stochastic effect on a
density dependent S-I epidemic model with randomly fluctuating environment. The
study shows the effect of noise on the size of epidemic is remarkable. The fluctuations
lead to noise contributions of additive character and additive noise of sufficient richness
reduces the random attractor to a single point. Numerical simulations are also
performed to validate the results.
In this article we concentrate on the analysis of a Swine Flu Transmission Model. The local and g... more In this article we concentrate on the analysis of a Swine Flu Transmission Model. The local and
global stability of the model suggest that although the disease is endemic in nature still the disease
is under control if we are enough cautious to control the contact rate. Numerical simulation
are also performed to validate the analytical results.
Journal of Biological Systems, 2006
This article concentrates on the study of delay effect on a model of schistosomiasis transmission... more This article concentrates on the study of delay effect on a model of schistosomiasis transmission with control measures such as predation or harvesting and chemotherapy. In the presence of predation or harvesting and chemotherapy, system admits multiple endemic equilibria. Mathematical analysis shows that they are opposite in nature regarding stability. One may observe switching phenomena for the unstable equilibrium by incorporating delay. The disease may be highly endemic if there is no control measure, which is obvious from the model analysis. Results obtained in this paper are also verified through numerical simulations.
ISRN Biomathematics, 2012
Cholera still remains as a severe global threat and is currently spreading in Africa and other pa... more Cholera still remains as a severe global threat and is currently spreading in Africa and other parts of the world. The role of lytic bacteriophage as an intervention of cholera outbreaks is investigated using a mathematical model. Dynamics of cholera is discussed on basis of the basic reproduction number R 0 . Conditions of Hopf bifurcation are also derived for a positive net growth rate of Vibrio cholerae. Stability analysis and numerical simulations suggest that bacteriophage may contribute to lessening the severity of cholera epidemics by reducing the number of Vibrio cholerae in the environment. Hence with the presence of phage virus, cholera is self-limiting in nature. By using phage as a biological control agent in endemic areas, one may also influence the temporal dynamics of cholera epidemics while reducing the excessive use of chemicals. We also performed stochastic analysis which suggests that the model system is globally asymptotically stable in probability when the strengths of white noise are less than some specific quantities.
Differential Equations and Dynamical Systems, 2009
We present a Susceptible-Infective-Susceptible (S-I-S) model with two distinct discrete time dela... more We present a Susceptible-Infective-Susceptible (S-I-S) model with two distinct discrete time delays representing a period of temporary immunity of newborns and a disease incubation period with randomly fluctuating environment. The stability of the equilibria is robustly investigated for the case with and without delay. Conditions for supercritical and subcritical Hopf bifurcation are derived. Comprehensive numerical simulations show that adding delay to an epidemic model could change the asymptotic stability of the system, altering the location of (stable or unstable) endemic equilibrium, or even leading to chaotic behavior. Further, simulation results illustrate that, in some cases where the disease becomes endemic in the model system without delay, addition of delays for temporary immunity and incubation period facilitates smaller final infective population sizes, even if endemicity is still maintained. Effects of randomness of the environment in terms of white noise are thoroughly investigated jointly with delay. The results demonstrate that there are no significant differences in dynamical behaviour of the system when considering delay solely or jointly with stochasticity.
Mathematical and Computer Modelling, 2006
This paper deals with the analysis of a Chagas' disease model consisting of acute and chronic, re... more This paper deals with the analysis of a Chagas' disease model consisting of acute and chronic, resistance classes along with vector population. Local as well as global analyses have been carried out for the model with or without resistance class. We identify the parameter that controls the dynamics of the system. The results are also verified through numerical simulation.
ISRN Biomathematics, 2012
Cholera still remains as a severe global threat and is currently spreading in Africa and other pa... more Cholera still remains as a severe global threat and is currently spreading in Africa and other parts of the world. The role of lytic bacteriophage as an intervention of cholera outbreaks is investigated using a mathematical model. Dynamics of cholera is discussed on basis of the basic reproduction number . Conditions of Hopf bifurcation are also derived for a positive net growth rate of Vibrio cholerae. Stability analysis and numerical simulations suggest that bacteriophage may contribute to lessening the severity of cholera epidemics by reducing the number of Vibrio cholerae in the environment. Hence with the presence of phage virus, cholera is self-limiting in nature. By using phage as a biological control agent in endemic areas, one may also influence the temporal dynamics of cholera epidemics while reducing the excessive use of chemicals. We also performed stochastic analysis which suggests that the model system is globally asymptotically stable in probability when the strengths...
Nonlinear Dynamics and Systems Theory
We present an in-host HIV/AIDS model with saturation effect and a discrete time delay. It is show... more We present an in-host HIV/AIDS model with saturation effect and a discrete time delay. It is shown that infection is endemic when ℛ 0 >1 but dies out when ℛ 0 <1. The switching phenomenon for the stable equilibria is observed when a discrete time delay is incorporated. The parameters that can control the disease transmission are also discussed. Numerical simulations are carried out to verify and support the analytical results and illustrate possible behavior scenarios of the model.
International Journal of Modern Nonlinear Theory and Application, 2012
The article concentrates on the role of fluctuating parameters for removable population from the ... more The article concentrates on the role of fluctuating parameters for removable population from the incubated class in a susceptible-incubated-infected model. The discrete analogous of this model is also investigated. Conditions for local asymptotic stability are derived for both the disease free and endemic cases. Numerical simulations are performed to validate the theoretical results.
Journal of Mathematical Modelling and Algorithms, 2011
ABSTRACT We present a deterministic HIV/AIDS model with delay. We then extend the model by adjoin... more ABSTRACT We present a deterministic HIV/AIDS model with delay. We then extend the model by adjoining terms capturing stochastic effects. The intensity of the fluctuations in the stochastic system is analytically evaluated using Fourier transform methods. We carry out simulations to assess differences in the dynamical behavior of the deterministic and stochastic models. Simulation results show that they are no significant differences in the behavior of the two models. KeywordsHIV/AIDS model–Incubation–Delay–Stochasticity
Mathematical and Computer Modelling, 2011
Although cholera has existed for ages, it has continued to plague many parts of the world. In thi... more Although cholera has existed for ages, it has continued to plague many parts of the world. In this study, a deterministic model for cholera in a community is presented and rigorously analysed in order to determine the effects of malnutrition in the spread of the disease. The important mathematical features of the cholera model are thoroughly investigated. The epidemic threshold known as the basic reproductive number and equilibria for the model are determined, and stabilities are investigated. The disease-free equilibrium is shown to be globally asymptotically stable. Local stability of the endemic equilibrium is determined using centre manifold theory and conditions for its global stability are derived using a suitable Lyapunov function. Numerical simulations suggest that an increase in susceptibility to cholera due to malnutrition results in an increase in the number of cholera infected individuals in a community. The results suggest that nutritional issues should be addressed in impoverished communities affected by cholera in order to reduce the burden of the disease.
Journal of Theoretical Biology, 2010
A deterministic model for assessing the dynamics of mixed species malaria infections in a human p... more A deterministic model for assessing the dynamics of mixed species malaria infections in a human population is presented to investigate the effects of dual infection with Plasmodium malariae and Plasmodium falciparum. Qualitative analysis of the model including positivity and boundedness is performed. In addition to the disease free equilibrium, we show that there exists a boundary equilibrium corresponding to each species. The isolation reproductive number of each species is computed as well as the reproductive number of the full model. Conditions for global stability of the disease free equilibrium as well as local stability of the boundary equilibria are derived. The model has an interior equilibrium which exists if at least one of the isolation reproductive numbers is greater than unity. Among the interesting dynamical behaviours of the model, the phenomenon of backward bifurcation where a stable boundary equilibrium coexists with a stable interior equilibrium, for a certain range of the associated invasion reproductive number less than unity is observed. Results from analysis of the model show that, when cross-immunity between the two species is weak, there is a high probability of coexistence of the two species and when cross-immunity is strong, competitive exclusion is high. Further, an increase in the reproductive number of species i increases the stability of its boundary equilibrium and its ability to invade an equilibrium of species j. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.
Journal of Biological Systems, 2005
This paper analyzes an epidemic model for carrier dependent infectious disease-cholera. Existence... more This paper analyzes an epidemic model for carrier dependent infectious disease-cholera. Existence criteria of carrier-free equilibrium point and endemic equilibrium point(unique or multiple) are discussed. Some threshold conditions are derived for which disease-free, carrier-free as ...
Journal of Biological Systems, 2004
Abstract: A Susceptible-Infective (SI) model is considered in this paper with time delay. The dea... more Abstract: A Susceptible-Infective (SI) model is considered in this paper with time delay. The death rate is assumed to be density dependent for this model. Conditions are derived under which there can be no change in stability. Using the discrete time delay as a bifurcation ...
Journal of Biological Systems, 2005
This study analyzes a model of hepatitis C with acute infectious, chronic infectious and the reco... more This study analyzes a model of hepatitis C with acute infectious, chronic infectious and the recovery or immune classes. Stability characters of disease-free and endemic proportionate equilibrium points are discussed. The role of immune system on the long-term survival of the ...
mail.cmu.edu.tw
Abstract. A discrete-time susceptible-infected model with saturation in inci-dence is investigate... more Abstract. A discrete-time susceptible-infected model with saturation in inci-dence is investigated.For this model, the existence and the stability of fixed points are analyzed.Stochastic analysis of the model suggests that it is asymptotically mean square stable for certain ...
Applied Mathematics and Computation, 2011
Discrete and stochastic version of a susceptible-infective model system with nonlinear incidence ... more Discrete and stochastic version of a susceptible-infective model system with nonlinear incidence rate is investigated. We observe that the discrete system converges to a unique equilibrium point for certain effective transmission rate of the disease and beyond which ...
Clinical and Experimental Nephrology, 2009
The hepatitis B virus (HBV) is estimated to have infected about 350 million people worldwide, mak... more The hepatitis B virus (HBV) is estimated to have infected about 350 million people worldwide, making it one of the most common human pathogens. Renal involvement is among its most common extra hepatic manifestations and usually manifests in the form of immune complex mediated glomerulopathy, such as membranous glomerulonephritis (MGN), membranoproliferative glomerulonephritis (MPGN), mesangioproliferative glomerulonephritis and immunoglobulin A (IgA) nephropathy. Occurrence of focal and segmental glomerular sclerosis (FSGS) with HBV infection is rare and only five cases have been reported earlier. We report two cases of hepatitis B associated FSGS. In both the cases, HBsAg was demonstrated in the renal tissue and both the cases showed response to treatment with lamivudine, thus indicating a possible causal association between the viral infection and occurrence of nephrotic syndrome.
The article concentrates on the study of delay and stochastic effect on a density dependent S-I e... more The article concentrates on the study of delay and stochastic effect on a
density dependent S-I epidemic model with randomly fluctuating environment. The
study shows the effect of noise on the size of epidemic is remarkable. The fluctuations
lead to noise contributions of additive character and additive noise of sufficient richness
reduces the random attractor to a single point. Numerical simulations are also
performed to validate the results.
In this article we concentrate on the analysis of a Swine Flu Transmission Model. The local and g... more In this article we concentrate on the analysis of a Swine Flu Transmission Model. The local and
global stability of the model suggest that although the disease is endemic in nature still the disease
is under control if we are enough cautious to control the contact rate. Numerical simulation
are also performed to validate the analytical results.
Journal of Biological Systems, 2006
This article concentrates on the study of delay effect on a model of schistosomiasis transmission... more This article concentrates on the study of delay effect on a model of schistosomiasis transmission with control measures such as predation or harvesting and chemotherapy. In the presence of predation or harvesting and chemotherapy, system admits multiple endemic equilibria. Mathematical analysis shows that they are opposite in nature regarding stability. One may observe switching phenomena for the unstable equilibrium by incorporating delay. The disease may be highly endemic if there is no control measure, which is obvious from the model analysis. Results obtained in this paper are also verified through numerical simulations.
ISRN Biomathematics, 2012
Cholera still remains as a severe global threat and is currently spreading in Africa and other pa... more Cholera still remains as a severe global threat and is currently spreading in Africa and other parts of the world. The role of lytic bacteriophage as an intervention of cholera outbreaks is investigated using a mathematical model. Dynamics of cholera is discussed on basis of the basic reproduction number R 0 . Conditions of Hopf bifurcation are also derived for a positive net growth rate of Vibrio cholerae. Stability analysis and numerical simulations suggest that bacteriophage may contribute to lessening the severity of cholera epidemics by reducing the number of Vibrio cholerae in the environment. Hence with the presence of phage virus, cholera is self-limiting in nature. By using phage as a biological control agent in endemic areas, one may also influence the temporal dynamics of cholera epidemics while reducing the excessive use of chemicals. We also performed stochastic analysis which suggests that the model system is globally asymptotically stable in probability when the strengths of white noise are less than some specific quantities.
Differential Equations and Dynamical Systems, 2009
We present a Susceptible-Infective-Susceptible (S-I-S) model with two distinct discrete time dela... more We present a Susceptible-Infective-Susceptible (S-I-S) model with two distinct discrete time delays representing a period of temporary immunity of newborns and a disease incubation period with randomly fluctuating environment. The stability of the equilibria is robustly investigated for the case with and without delay. Conditions for supercritical and subcritical Hopf bifurcation are derived. Comprehensive numerical simulations show that adding delay to an epidemic model could change the asymptotic stability of the system, altering the location of (stable or unstable) endemic equilibrium, or even leading to chaotic behavior. Further, simulation results illustrate that, in some cases where the disease becomes endemic in the model system without delay, addition of delays for temporary immunity and incubation period facilitates smaller final infective population sizes, even if endemicity is still maintained. Effects of randomness of the environment in terms of white noise are thoroughly investigated jointly with delay. The results demonstrate that there are no significant differences in dynamical behaviour of the system when considering delay solely or jointly with stochasticity.
Mathematical and Computer Modelling, 2006
This paper deals with the analysis of a Chagas' disease model consisting of acute and chronic, re... more This paper deals with the analysis of a Chagas' disease model consisting of acute and chronic, resistance classes along with vector population. Local as well as global analyses have been carried out for the model with or without resistance class. We identify the parameter that controls the dynamics of the system. The results are also verified through numerical simulation.