Souvik Bhattacharya | University of Trento (original) (raw)
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Papers by Souvik Bhattacharya
This article introduces a novel model that studies the major factors jeopardizing the TB control ... more This article introduces a novel model that studies the major factors jeopardizing the TB control programme in China. A previously developed two strain TB model is augmented with a class of individuals not registered under the TB control programme. The paper investigates the basic reproduction number and proves the global stability of the disease free equilibrium. The presence of three endemic equilibria is established in the model. With the help of numerical simulations a comparative study has been performed to test the validity of the model presented here to the real data available from the Ministry of Health of the People’s Republic of China. Sensitivity and elasticity analysis gives the key parameters that would govern the successful tuberculosis control in China.
Journal of pharmacology & clinical research, Mar 9, 2017
Item-Response Theory (IRT) has recently gain importance in evaluation of diseases like Alzheimer ... more Item-Response Theory (IRT) has recently gain importance in evaluation of diseases like Alzheimer and Parkinson. It turns out to be an efficient way of evaluating the overall disease progression in these score based disease evaluation. This short review discusses the major aspects of IRT which is responsible in improving the standard of evaluation of a score based disease progression.
International Journal of Cloud Applications and Computing
In a cloud computing environment, effective scheduling policies and load balancing have always be... more In a cloud computing environment, effective scheduling policies and load balancing have always been the aim. An efficient task scheduler must be proficient in a dynamically distributed environment and to the policy of efficient scheduling of jobs based upon the workload. In this research, a novel hybrid heuristic algorithm is developed for balancing the load among cloud nodes. This is achieved by hybridizing the existing ant colony optimization (ACO), artificial bee colony algorithm (ABC), and AHP (analytical hierarchy process) algorithm. The AHP algorithm and the artificial bee colony (ABC) algorithm is used for figuring out the best servers suitable for a particular job, and the ant colony algorithm is used to find the most efficient path to that particular server. The proposed algorithm is better in resource utilization. It also performs better load balancing, which keeps on improving with time. The result analysis shows better average response time and better average makespan ti...
International Journal of Biomathematics
In this paper, an epidemic model of a vector-borne disease, namely, malaria, is considered. The e... more In this paper, an epidemic model of a vector-borne disease, namely, malaria, is considered. The explicit expression of the basic reproduction number is obtained, the local and global asymptotical stability of the disease-free equilibrium is proved under certain conditions. It is shown that the model exhibits the phenomenon of backward bifurcation where the stable disease-free equilibrium coexists with a stable endemic equilibrium. Further, it is proved that the unique endemic equilibrium is globally asymptotically stable under certain conditions.
ACS Applied Energy Materials
Journal of biological dynamics, 2016
This paper introduces a novel immuno-eco-epidemiological model of competition in which one of the... more This paper introduces a novel immuno-eco-epidemiological model of competition in which one of the species is affected by a pathogen. The infected individuals from species one are structured by time-since-infection and the within-host dynamics of the pathogen and the immune response is also modelled. A novel feature of the model is the impact of the species two numbers on the ability of species one to mount an immune response. The within-host model has three equilibria: an extinction equilibrium, pathogen-only equilibrium and pathogen and immune response equilibrium which exists if the immune response reproduction number R0 > 1. The extinction equilibrium is always unstable, the pathogen-only equilibrium is stable if R0 < 1, and the coexistence equilibrium is stable whenever it exists. The between-host competition model has six equilibria: an extinction equilibrium, three disease-free equilibria: species one-only equilibrium, species two-only equilibrium and a disease-free spec...
Theoretical Population Biology
Briggs et al. (1993) introduced a host-parasitoid model for the dynamics of a system with two par... more Briggs et al. (1993) introduced a host-parasitoid model for the dynamics of a system with two parasitoids that attack different juvenile stages of a common host. Their main result was that coexistence of the parasitoids is only possible when there is sufficient variability in the maturation delays of the host juvenile stages. Here we analyse the phenomenon of coexistence in that model more deeply. We show that with some distribution families for the maturation delays, the coexistence equilibrium is unique, while with other distributions multiple coexistence equilibria can be found. In particular we find that stable coexistence does not necessarily require mutual invasibility.
This article introduces a predator-prey model with the prey structured by body size, based on rep... more This article introduces a predator-prey model with the prey structured by body size, based on reports in the literature that predation rates are prey-size specific. The model is built on the foundation of the onespecies physiologically structured models studied earlier. Three types of equilibria are found: extinction, multiple prey-only equilibria and possibly multiple predator-prey coexistence equilibria. The stabilities of the equilibria are investigated. Comparison is made with the underlying ODE Lotka-Volterra model. It turns out that the ODE model can exhibit sustain oscillations if there is an Allee effect in the net reproduction rate, that is the net reproduction rate grows for some range of the prey's population size. In contrast, it is shown that the structured PDE model can exhibit sustain oscillations even if the net reproductive rate is strictly declining with prey population size. We find that predation, even size-non-specific linear predation can destabilize a stable prey-only equilibrium, if reproduction is size specific and limited to individuals of large enough size. Furthermore, we show that size-specific predation can also destabilize the predatorprey equilibrium in the PDE model. We surmise that size-specific predation allows for temporary prey escape which is responsible for destabilization in the predator-prey dynamics.
9Th European Conference on Mathematical and Theoretical Biology, Jun 9, 2014
... Debesh Chakraborty, Department of Economics, and Prof. ... Authors greatfully acknowledgeDr.S... more ... Debesh Chakraborty, Department of Economics, and Prof. ... Authors greatfully acknowledgeDr.SKSarkar (Member Secretary, WBPCB) and Mr.Debashish Sarkar (Regional Officer ... Bhaskar Shrachi, Srinivas & Haldia Steel), and three sponge iron plants (Adhunik, SPS & Ritesh). ...
Mathematical Modelling of Natural Phenomena, 2014
We formulate an immuno-epidemiological model of coupled "within-host" model of ODEs and "between-... more We formulate an immuno-epidemiological model of coupled "within-host" model of ODEs and "between-host" model of ODE and PDE, using the Human Immunodeficiency Virus (HIV) for illustration. Existence and uniqueness of solution to the "between-host" model is established, and an explicit expression for the basic reproduction number of the "between-host" model derived. Stability of disease-free and endemic equilibria is investigated. An optimal control problem with drug-treatment control on the within-host system is formulated and analyzed; these results are novel for optimal control of ODEs linked with such first order PDEs. Numerical simulations based on the forward-backward sweep method are obtained.
Journal of Nonlinear Dynamics, 2014
Depression is one of the major concerns of the present generation. A Markov chain model has been ... more Depression is one of the major concerns of the present generation. A Markov chain model has been used to portray and investigate this curse. Long-term behaviour of the model has been discussed. Different types of treatment strategies have been considered in this paper to identify the most powerful measure of keeping this disease from its spread in the society. This paper also focuses on the usefulness of the drugs available at present for the treatment of this disease.
Journal of Biological Systems, 2013
A two-strain epidemic model with differential susceptibility and mutation is formulated and analy... more A two-strain epidemic model with differential susceptibility and mutation is formulated and analyzed in this paper. The susceptible population is divided into two subgroups according to the vaccine that provides complete protection against one of the strains (strain two) but only partial against the other (strain one). The explicit formulae for the basic reproduction number and invasion reproduction number corresponding to each strain with and without mutation are derived, respectively. It is shown that there exist exclusive equilibria and coexistence equilibria, even if the reproduction number is below one. The stability of the disease-free equilibrium, strain dominance with or without mutation are investigated. The persistence of the disease is also briefly discussed. Numerical simulations are presented to illustrate the results.
This article introduces a novel model that studies the major factors jeopardizing the TB control ... more This article introduces a novel model that studies the major factors jeopardizing the TB control programme in China. A previously developed two strain TB model is augmented with a class of individuals not registered under the TB control programme. The paper investigates the basic reproduction number and proves the global stability of the disease free equilibrium. The presence of three endemic equilibria is established in the model. With the help of numerical simulations a comparative study has been performed to test the validity of the model presented here to the real data available from the Ministry of Health of the People’s Republic of China. Sensitivity and elasticity analysis gives the key parameters that would govern the successful tuberculosis control in China.
Journal of pharmacology & clinical research, Mar 9, 2017
Item-Response Theory (IRT) has recently gain importance in evaluation of diseases like Alzheimer ... more Item-Response Theory (IRT) has recently gain importance in evaluation of diseases like Alzheimer and Parkinson. It turns out to be an efficient way of evaluating the overall disease progression in these score based disease evaluation. This short review discusses the major aspects of IRT which is responsible in improving the standard of evaluation of a score based disease progression.
International Journal of Cloud Applications and Computing
In a cloud computing environment, effective scheduling policies and load balancing have always be... more In a cloud computing environment, effective scheduling policies and load balancing have always been the aim. An efficient task scheduler must be proficient in a dynamically distributed environment and to the policy of efficient scheduling of jobs based upon the workload. In this research, a novel hybrid heuristic algorithm is developed for balancing the load among cloud nodes. This is achieved by hybridizing the existing ant colony optimization (ACO), artificial bee colony algorithm (ABC), and AHP (analytical hierarchy process) algorithm. The AHP algorithm and the artificial bee colony (ABC) algorithm is used for figuring out the best servers suitable for a particular job, and the ant colony algorithm is used to find the most efficient path to that particular server. The proposed algorithm is better in resource utilization. It also performs better load balancing, which keeps on improving with time. The result analysis shows better average response time and better average makespan ti...
International Journal of Biomathematics
In this paper, an epidemic model of a vector-borne disease, namely, malaria, is considered. The e... more In this paper, an epidemic model of a vector-borne disease, namely, malaria, is considered. The explicit expression of the basic reproduction number is obtained, the local and global asymptotical stability of the disease-free equilibrium is proved under certain conditions. It is shown that the model exhibits the phenomenon of backward bifurcation where the stable disease-free equilibrium coexists with a stable endemic equilibrium. Further, it is proved that the unique endemic equilibrium is globally asymptotically stable under certain conditions.
ACS Applied Energy Materials
Journal of biological dynamics, 2016
This paper introduces a novel immuno-eco-epidemiological model of competition in which one of the... more This paper introduces a novel immuno-eco-epidemiological model of competition in which one of the species is affected by a pathogen. The infected individuals from species one are structured by time-since-infection and the within-host dynamics of the pathogen and the immune response is also modelled. A novel feature of the model is the impact of the species two numbers on the ability of species one to mount an immune response. The within-host model has three equilibria: an extinction equilibrium, pathogen-only equilibrium and pathogen and immune response equilibrium which exists if the immune response reproduction number R0 > 1. The extinction equilibrium is always unstable, the pathogen-only equilibrium is stable if R0 < 1, and the coexistence equilibrium is stable whenever it exists. The between-host competition model has six equilibria: an extinction equilibrium, three disease-free equilibria: species one-only equilibrium, species two-only equilibrium and a disease-free spec...
Theoretical Population Biology
Briggs et al. (1993) introduced a host-parasitoid model for the dynamics of a system with two par... more Briggs et al. (1993) introduced a host-parasitoid model for the dynamics of a system with two parasitoids that attack different juvenile stages of a common host. Their main result was that coexistence of the parasitoids is only possible when there is sufficient variability in the maturation delays of the host juvenile stages. Here we analyse the phenomenon of coexistence in that model more deeply. We show that with some distribution families for the maturation delays, the coexistence equilibrium is unique, while with other distributions multiple coexistence equilibria can be found. In particular we find that stable coexistence does not necessarily require mutual invasibility.
This article introduces a predator-prey model with the prey structured by body size, based on rep... more This article introduces a predator-prey model with the prey structured by body size, based on reports in the literature that predation rates are prey-size specific. The model is built on the foundation of the onespecies physiologically structured models studied earlier. Three types of equilibria are found: extinction, multiple prey-only equilibria and possibly multiple predator-prey coexistence equilibria. The stabilities of the equilibria are investigated. Comparison is made with the underlying ODE Lotka-Volterra model. It turns out that the ODE model can exhibit sustain oscillations if there is an Allee effect in the net reproduction rate, that is the net reproduction rate grows for some range of the prey's population size. In contrast, it is shown that the structured PDE model can exhibit sustain oscillations even if the net reproductive rate is strictly declining with prey population size. We find that predation, even size-non-specific linear predation can destabilize a stable prey-only equilibrium, if reproduction is size specific and limited to individuals of large enough size. Furthermore, we show that size-specific predation can also destabilize the predatorprey equilibrium in the PDE model. We surmise that size-specific predation allows for temporary prey escape which is responsible for destabilization in the predator-prey dynamics.
9Th European Conference on Mathematical and Theoretical Biology, Jun 9, 2014
... Debesh Chakraborty, Department of Economics, and Prof. ... Authors greatfully acknowledgeDr.S... more ... Debesh Chakraborty, Department of Economics, and Prof. ... Authors greatfully acknowledgeDr.SKSarkar (Member Secretary, WBPCB) and Mr.Debashish Sarkar (Regional Officer ... Bhaskar Shrachi, Srinivas & Haldia Steel), and three sponge iron plants (Adhunik, SPS & Ritesh). ...
Mathematical Modelling of Natural Phenomena, 2014
We formulate an immuno-epidemiological model of coupled "within-host" model of ODEs and "between-... more We formulate an immuno-epidemiological model of coupled "within-host" model of ODEs and "between-host" model of ODE and PDE, using the Human Immunodeficiency Virus (HIV) for illustration. Existence and uniqueness of solution to the "between-host" model is established, and an explicit expression for the basic reproduction number of the "between-host" model derived. Stability of disease-free and endemic equilibria is investigated. An optimal control problem with drug-treatment control on the within-host system is formulated and analyzed; these results are novel for optimal control of ODEs linked with such first order PDEs. Numerical simulations based on the forward-backward sweep method are obtained.
Journal of Nonlinear Dynamics, 2014
Depression is one of the major concerns of the present generation. A Markov chain model has been ... more Depression is one of the major concerns of the present generation. A Markov chain model has been used to portray and investigate this curse. Long-term behaviour of the model has been discussed. Different types of treatment strategies have been considered in this paper to identify the most powerful measure of keeping this disease from its spread in the society. This paper also focuses on the usefulness of the drugs available at present for the treatment of this disease.
Journal of Biological Systems, 2013
A two-strain epidemic model with differential susceptibility and mutation is formulated and analy... more A two-strain epidemic model with differential susceptibility and mutation is formulated and analyzed in this paper. The susceptible population is divided into two subgroups according to the vaccine that provides complete protection against one of the strains (strain two) but only partial against the other (strain one). The explicit formulae for the basic reproduction number and invasion reproduction number corresponding to each strain with and without mutation are derived, respectively. It is shown that there exist exclusive equilibria and coexistence equilibria, even if the reproduction number is below one. The stability of the disease-free equilibrium, strain dominance with or without mutation are investigated. The persistence of the disease is also briefly discussed. Numerical simulations are presented to illustrate the results.