A stochastic SICA epidemic model for HIV transmission

Djordjević, Jasmina; Silva, Cristiana J.; Torres, Delfim F. M.

doi:10.1016/j.aml.2018.05.005

Cited by 100 publications

(58 citation statements)

References 10 publications

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“…Therefore, it follows from (7), (8), (9) and (10) that dV2 dt ≤ 0. Furthermore, the largest compact invariant set in (S, I, C, A) | dV2 dt = 0 is just the singleton E * .…”

Section: Proofmentioning

confidence: 98%

“…The part of HIV infected individuals without AIDS symptoms move to the chronic stage (HIV-infected individuals under ART treatment with a low viral load) [32]. In this class, when they respect carefully the ART treatment and do not have a risky behaviour for HIV transmission, individuals have the same life expectancy as uninfected ones and the risk of HIV transmission is greatly reduced [8,32,33]. If the infected individuals do not take ART treatment, then they can transmit the infection and the symptoms will start to appear.…”

Section: Introductionmentioning

confidence: 99%

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A Minimal HIV-AIDS Infection Model with General Incidence Rate and Application to Morocco Data

Lotfi

Mahrouf

Maziane

et al. 2019

Stat., optim. inf. comput.

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We study the global dynamics of a SICA infection model with general incidence rate. The proposed model is calibrated with cumulative cases of infection by HIV-AIDS in Morocco from 1986 to 2015. We first prove that our model is biologically and mathematically well-posed. Stability analysis of different steady states is performed and threshold parameters are identified where the model exhibits clearance of infection or maintenance of a chronic infection. Furthermore, we examine the robustness of the model to some parameter values by examining the sensitivity of the basic reproduction number. Finally, using numerical simulations with real data from Morocco, we show that the model predicts well such reality.

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“…Therefore, it follows from (7), (8), (9) and (10) that dV2 dt ≤ 0. Furthermore, the largest compact invariant set in (S, I, C, A) | dV2 dt = 0 is just the singleton E * .…”

Section: Proofmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

A Minimal HIV-AIDS Infection Model with General Incidence Rate and Application to Morocco Data

Lotfi

Mahrouf

Maziane

et al. 2019

Stat., optim. inf. comput.

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show abstract

“…which is consistent with the continuous results. In Figure 3a, we show the solution in the discrete-time case T = Z determined by (10); in Figure 3b, we plot the solution to (8) for the partial continuous, partial discrete time scale T = [0, 12] ∪ {13, . .…”

Section: Dynamic Sir Modelmentioning

confidence: 99%

“…To model the spreading of diseases between different states, a spatial variable was added, which led to a partial differential system, see [5,6]. Already in 1975, Bailey discussed in [1] the relevance of stochastic terms in the mathematical model of epidemics, which is still an attractive way of modeling the uncertainty of the transmission and vaccines, see [7][8][9][10]. Although these modifications exist, so far there has been no success in generalizing the epidemic models to a general time scale to allow modeling a noncontinuous disease dynamics.…”

Section: Introductionmentioning

confidence: 99%

Exact solution to a dynamic SIR model

Böhner

Streipert

Torres

2019

Nonlinear Analysis: Hybrid Systems

Self Cite

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We investigate an epidemic model based on Bailey's continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and present an alternative solution method to Gleissner's approach. If the coefficients are constant, both solution methods yield the same result. After a brief introduction to time scales, we formulate the SIR (susceptible-infected-removed) model in the general time domain and derive its solution. In the discrete case, this provides the solution to a new discrete epidemic system, which exhibits the same behavior as the continuous model. The last part is dedicated to the analysis of the limiting behavior of susceptible, infected, and removed, which contains biological relevance. MSC 2010: 92D25; 34N05.

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“…Refs. [9][10][11][12][13][14][15][16][17][18]). But as far as we know, the studies on the dynamics of the stochastic SIRD model of Ebola seem to be rare.…”

Section: Introductionmentioning

confidence: 99%

Stationary distribution of a stochastic SIRD epidemic model of Ebola with double saturated incidence rates and vaccination

Wang

Jia

2019

Adv Differ Equ

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In this paper, a stochastic SIRD model of Ebola with double saturated incidence rates and vaccination is considered. Firstly, the existence and uniqueness of a global positive solution are obtained. Secondly, by constructing suitable Lyapunov functions and using Khasminskii's theory, we show that the stochastic model has a unique stationary distribution. Moreover, the extinction of the disease is also analyzed. Finally, numerical simulations are carried out to portray the analytical results. MSC: Primary 37H10; 60H10; secondary 92C60; 92D30

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A stochastic SICA epidemic model for HIV transmission

Cited by 100 publications

References 10 publications

A Minimal HIV-AIDS Infection Model with General Incidence Rate and Application to Morocco Data

A Minimal HIV-AIDS Infection Model with General Incidence Rate and Application to Morocco Data

Exact solution to a dynamic SIR model

Stationary distribution of a stochastic SIRD epidemic model of Ebola with double saturated incidence rates and vaccination

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