Dynamical Study in Fuzzy Threshold Dynamics of a Cholera Epidemic Model

Hepatitis B epidemic was and is still a rich subject that sparks the interest of epidemiological researchers. The dynamics of this epidemic is often modeled by a system with constant parameters. In reality, the parameters associated with the Hepatitis B model are not certain, but the interval in which it belongs to can readily be determined. Our paper focuses on an imprecise Hepatitis B model perturbed by Lévy noise due to unexpected environmental disturbances. This model has a global positive solution. Under an appropriate assumption, we prove the existence of a unique ergodic stationary distribution by using the mutually exclusive possibilities lemma demonstrated by Stettner in 1986. Our main effort is to establish an almost perfect condition for the existence of the stationary distribution. Numerical simulations are introduced to illustrate the analytical results.

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“…e same logic was applied for epidemic models. In [20], the authors treated a cholera epidemic model with uncertain parameters.…”

Section: Introductionmentioning

confidence: 99%

Ergodic Stationary Distribution of a Stochastic Hepatitis B Epidemic Model with Interval-Valued Parameters and Compensated Poisson Process

Kiouach

Sabbar

2020

Computational and Mathematical Methods in Medicine

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“…Panja et al, , 2017P. Panja et al, , 2017aP. Panja et al, , 2017bMortoja Golam et al, 2018; related to ecological as well as epidemiological problems.…”

Section: Introductionmentioning

confidence: 99%

Is the forest biomass a key regulator of global warming?: A mathematical modelling study

Panja

2020

Geology, Ecology, and Landscapes

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In this article, a mathematical model has been formulated by considering forest biomass and global warming as a separate compartment. It is assumed that the forest biomass follow logistic growth in the absence of global warming. It is also assumed that the growth of forest biomass is affected by global warming. It is considered that the density of forest biomass decreases due to natural burning of forests, cut down of forest biomass by human beings and continuous harvesting of forest biomass by human being. It is found that if we can increase the area of forest biomass then the rate of increase of global warming will be reduced. It is also found that if the harvesting rate of forest biomass increases, then global warming will be gradually increased. Finally, some numerical simulation results have been presented.

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“…Mathematical modelling was started with the work of Volterra [32]. After Volterra, many researchers [5,13,17,18,19,23,24] have studied several mathematical models to understand predator-prey dynamics. Effects of seasonality on predator-prey dynamics has been investigated by Levy et al [16].…”

Section: Introductionmentioning

confidence: 99%

A Novel Prey-Predator Quadratic Harvesting Model via Optimal Control Theory and Hopf Bifurcation

Panja¹,

Jana²

2020

Nep J. Math. Sci.

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In this investigation, a predator-prey interaction model among Phytoplankton, Zooplankton and Fish has been developed. In the absence of Zooplankton and Fish, it is assumed that Phytoplankton grows logistically. It is assumed that Zooplankton consumes Phytoplankton and Fish consumes Phytoplankton as well as Zooplankton. Holling type I & II functional responses have been considered to formulate the our proposed model. It is considered that Phytoplankton releases some toxin in the aquatic environment which makes some death in Zooplankton population. Quadratic harvesting is considered on Fish species. Boundedness of the solution of our proposed model has also been studied. Local stability of the system around each equilibrium point has been investigated. Also, the global stability of the interior equilibrium point has been studied. Existence condition of Hopf bifurcation of our proposed system has been studied. It is found that half saturation constant (α) can change the system dynamics. It is also found that the harvesting rate of Fish (E) and consumption rate of Zooplankton (γ1) has a significant role in the stability of the system. Again, it is found that the harvesting of Fish species will be increased if the selling price of Fish (p) and the annual discount (δ1) of Fish production cost increases. It is also found that the optimal harvesting rate of Fish decreases due to the increase of cost (c) of harvesting of Fish. Finally, some numerical simulation results have been presented to verify our analytical findings.

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Dynamical Study in Fuzzy Threshold Dynamics of a Cholera Epidemic Model

Cited by 30 publications

References 25 publications

Ergodic Stationary Distribution of a Stochastic Hepatitis B Epidemic Model with Interval-Valued Parameters and Compensated Poisson Process

Ergodic Stationary Distribution of a Stochastic Hepatitis B Epidemic Model with Interval-Valued Parameters and Compensated Poisson Process

Is the forest biomass a key regulator of global warming?: A mathematical modelling study

A Novel Prey-Predator Quadratic Harvesting Model via Optimal Control Theory and Hopf Bifurcation

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