A comprehensive probabilistic solution of random SIS-type epidemiological models using the random variable transformation technique

Casabán, M.-C.; López, Juan Carlos Cortés; Navarro‐Quiles, A.; Romero, J.-V.; Roselló, M.-D.; Villanueva, Rafael

doi:10.1016/j.cnsns.2015.08.009

Cited by 50 publications

(29 citation statements)

References 23 publications

(37 reference statements)

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“…In this context, many authors have introduced stochastic population models to investigate the effect of environmental variability and perturbation [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. Here, we explore uncertainties present in the logistic model, which is commonly applied in the studies of human, plants and bacterial populations, as well as to evaluate economic growth.…”

Section: Introductionmentioning

confidence: 98%

“…Nevertheless, to design meaningful and realistic models, it is crucial to take into account that they are imprecise due to both the implicit lack of information and the A C C E P T E D M A N U S C R I P T mistakes in the measurement process present in related problems. Several approaches are considered, including the use of random variables to represent such parameters [1,2,3,9,11,12]. In [12], for instance, the authors analyze the logistic equation (1) with noise fluctuations in the carrying capacity.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density

Dorini

Cecconello

Dorini

2016

Communications in Nonlinear Science and Numerical Simulation

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density

Dorini

Cecconello

Dorini

2016

Communications in Nonlinear Science and Numerical Simulation

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“…via RVT method within the context of r.d.e. 's, it is worth pointing out that some significant contributions are [8][9][10][11][12][13][14]. Most of these contributions usually assume that uncertainty enters via a single r.v.…”

Section: Motivationmentioning

confidence: 99%

“…

Roselló, M. (2016). Solving random homogeneous linear second-order differential equations: a full probabilistic description.

…”

mentioning

confidence: 99%

Solving Random Homogeneous Linear Second-Order Differential Equations: A Full Probabilistic Description

et al. 2016

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Roselló, M. (2016). Solving random homogeneous linear second-order differential equations: a full probabilistic description. Mediterranean Journal of Mathematics. 13(6): 3817-3836. doi:10.1007/s00009-016-0716-6 Solving random homogeneous linear secondorder differential equations: A full probabilistic description Abstract. In this paper a complete probabilistic description for the solution of random homogeneous linear second-order differential equations via the computation of its two first probability density functions is given. As a consequence, all unidimensional and two-dimensional statistical moments can be straightforwardly determined, in particular, mean, variance and covariance functions, as well as the first-order conditional law. With the aim of providing more generality, in a first step, all involved input parameters are assumed to be statistically dependent random variables having an arbitrary joint probability density function. Secondly, the particular case that just initial conditions are random variables is also analysed. Both problems have common and distinctive feature which are highlighted in our analysis. The study is based on Random Variable Transformation method. As a consequence of our study, the well-known deterministic results are nicely generalized. Several illustrative examples are included.Mathematics Subject Classification (2010). 60H35, 60H10, 37H10. Keywords. Random Variable Transformation method, first and second probability density functions, random homogeneous linear second-order differential equations. MotivationThe quantification of uncertainty in dynamic models is currently playing an important role in many applied areas. Classical deterministic differential equations, which have demonstrated to be powerful tools for analysing problems that appear in areas such as Physics, Engineering, Chemistry, Epidemiology, etc., need to consider randomness in their formulation in order to account for measurement errors and inherent complexity of problems underThis work was completed with the support of our T E X-pert. [4][5][6]. However, it is important to point out that in the random context besides computing the solution stochastic process (s.p.), say Z(t), it is also of great interest the determination of its main statistical properties. Most of the contributions focus on the computation of the mean, µ Z (t) = E[Z(t)], and the variance, σ 2 Z (t) = V[Z(t)], functions of the solution s.p. However, a more convenient goal is the determination of its first probability density function (1-p.d.f.), f 1 (z, t), since from it one can easily compute not just these two first statistical moments,but also the one-dimensional statistical moment of any orderThe 1-p.d.f. characterizes, from a probabilistic point of view, the solution s.p. Z(t) at every time instant t. In general, more challenging is the determination of the rest of the so-called fidis (finite dimensional distributions), i.e., the n-dimensional p.d.f.'s of the solution s.p. for n ≥ 2, because it usually involves complex developments...

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“…In other words, the combined effects of government intervention and hospitalization condition are considered to prevent an outbreak. However, it is more natural to consider perturbations of contagion coefficients through the Wiener process or treat them directly as random variables since the transmission coefficients are usually unknown in practice (see, for example, [17,18] and references therein). Here, we focus on the deterministic epidemic model and leave the consideration of randomness in epidemiological model as our future work.…”

Section: Introductionmentioning

confidence: 99%

Complex Dynamics of an SIR Epidemic Model with Nonlinear Saturate Incidence and Recovery Rate

Cui

Qiu

Liu

et al. 2017

Entropy

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Susceptible-infectious-removed (SIR) epidemic models are proposed to consider the impact of available resources of the public health care system in terms of the number of hospital beds. Both the incidence rate and the recovery rate are considered as nonlinear functions of the number of infectious individuals, and the recovery rate incorporates the influence of the number of hospital beds. It is shown that backward bifurcation and saddle-node bifurcation may occur when the number of hospital beds is insufficient. In such cases, it is critical to prepare an appropriate amount of hospital beds because only reducing the basic reproduction number less than unity is not enough to eradicate the disease. When the basic reproduction number is larger than unity, the model may undergo forward bifurcation and Hopf bifurcation. The increasing hospital beds can decrease the infectious individuals. However, it is useless to eliminate the disease. Therefore, maintaining enough hospital beds is important for the prevention and control of the infectious disease. Numerical simulations are presented to illustrate and complement the theoretical analysis.

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A comprehensive probabilistic solution of random SIS-type epidemiological models using the random variable transformation technique

Cited by 50 publications

References 23 publications

On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density

On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density

Solving Random Homogeneous Linear Second-Order Differential Equations: A Full Probabilistic Description

Complex Dynamics of an SIR Epidemic Model with Nonlinear Saturate Incidence and Recovery Rate

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