Construction of Equivalent Stochastic Differential Equation Models

Allen, E.J.; Allen, Linda J. S.; Arciniega, Armando; Greenwood, Priscilla E.

doi:10.1080/07362990701857129

Cited by 153 publications

(144 citation statements)

References 21 publications

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“…We have identified the different possible changes in population density that may take place within a small time interval and then constructed the stochastic differential system following the modeling approach proposed in [5]. The constructed stochastic model is capable to capture the demographic fluctuation in all three populations involved with the model.…”

Section: Discussionmentioning

confidence: 99%

“…To formulate the stochastic model we need a square matrix 'B' such that B 2 = Σ, but there is no unified way to do this for models involving three or more species. In [1,5], authors have discussed in detail how this difficulty can be tackled and provided an unified way to proceed further. Adapting the said approach discussed, we can define a matrix G as follows,…”

Section: Ps Mandal M Banerjee Deterministic Chaos Vs Stochastic mentioning

confidence: 99%

“…The third approach is the most well-known procedure adopted for the formulation of stochastic differential equation models. In this approach, specific functional forms are chosen for drift and diffusion matrix for the dynamical system under consideration [5]. Due to limitations of mathematical machineries to analyze these stochastic models, most of the investigations in this direction are based upon exhaustive numerical simulations and interpretation of the results obtained through numerical simulations for suitable range of parameter values.…”

Section: Introductionmentioning

confidence: 99%

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Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model

Mandal

Banerjee

2012

Math. Model. Nat. Phenom.

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Abstract. An eco-epidemiological model of susceptible Tilapia fish, infected Tilapia fish and Pelicans is investigated by several author based upon the work initiated by Chattopadhyay and Bairagi (Ecol. Model., 136, 103 -112, 2001). In this paper, we investigate the dynamics of the same model by considering different parameters involved with the model as bifurcation parameters in details. Considering the intrinsic growth rate of susceptible Tilapia fish as bifurcation parameter, we demonstrate the period doubling route to chaos. Next we consider the force of infection as bifurcation parameter and demonstrate the occurrence of two successive Hopfbifurcations. We identify the existence of backward Hopf-bifurcation when the death rate of predators is considered as bifurcation parameter. Finally we construct a stochastic differential equation model corresponding to the deterministic model to understand the role of demographic stochasticity. Exhaustive numerical simulation of the stochastic model reveals the large amplitude fluctuation in the population of fish and Pelicans for certain parameter values. Extinction scenario for Pelicans is also captured from the stochastic model.

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Section: Discussionmentioning

confidence: 99%

Section: Ps Mandal M Banerjee Deterministic Chaos Vs Stochastic mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model

Mandal

Banerjee

2012

Math. Model. Nat. Phenom.

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“…The diagram of the stochastic model of the TB infection is given by Fig 1. The mathematical stochastic model of TB infection in the presence of treatment is written under the compact form by the following equation (1) (its formulation uses [1], [5], [6], [7], and [22])…”

Section: Controlmentioning

confidence: 99%

“…In epidemiology and others domain as biology, demography, economy..., many stochastic models deriving from their deterministic formulation. The reference of the literature for a variety of wellknown stochastic models deriving from their deterministic counterparts include the books [1], [5], [6], [7], and [22]. Our contribution is first in Sub Section II.A, the formulation of a stochastic model of TB with treatment from a deterministic model of TB-only (Sharomi [18]) which is formulated along the lines of the model in Feng and al.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of the treatment frequency in a stochastic model of tuberculosis

Sébastien

Danhree

Rodoumta

2017

BIOMATH

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Abstract-This paper presents a stochastic model of the Tuberculosis(TB) infection with treatment in a population composed of four individuals compartments: susceptible individuals, latent infected individuals, active infected individuals and recovered individuals after the therapy. A preliminary survey of the model is performed on the stability before approaching the crucial left of the topic. The aim in this paper is to control the treatment frequency in a stochastic model of the TB infection while minimizing the cost of the measures. Then, we formulate an optimal control problem that consists in minimizing the relative cost of the dynamics of TB-model in order to reduce the prevalence and the mortality due to this infection. The optimal problem is solved by applying the Projection Stochastic Gradient Method in order to find the optimal numerical solution. Finally, we provide some numerical simulations of the controlled model.

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Modeling 2018 Ebola virus disease outbreak with Cholesky decomposition

Mouanguissa

Kamara

Wang

2021

Math Methods in App Sciences

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In this paper, we analyze a modified Susceptible‐Exposed‐Infectious‐Dead‐Recovered (SEIDR) model in the literature of the Ebola disease with uncertainties. The model is constructed using a van Kampen expansion method to have an Ebola SEIDR stochastic Fokker–Planck equation model. This model has a deterministic equation and noise covariance matrix. The basic reproduction number of the deterministic equation is calculated using the next‐generation matrix method. We prove the uniqueness and existence of the deterministic model using Lipschitz conditions and also show that it is locally asymptotically stable at it endemic equilibrium states. We constructed two equivalent stochastic differential equations (SDEs) models, whereas the Weiner process is equal to (i) the number of model equations and (ii) the number of independent changes in the model. Our aim is to solve (i) computationally using Cholesky decomposition technique with the variance–covariance matrix. Our proposed Cholesky decomposition SEIRD‐SDEs model is compared with (ii) and also with the epidemic data of the 2018 Ebola outbreak in the Democratic Republic of Congo. We also use numerical analyses to show that the importance of post‐death transmission is difficult to identify with noise terms supported by statistical hypothesis testing.

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Construction of Equivalent Stochastic Differential Equation Models

Cited by 153 publications

References 21 publications

Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model

Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model

Optimal control of the treatment frequency in a stochastic model of tuberculosis

Modeling 2018 Ebola virus disease outbreak with Cholesky decomposition

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