Mathematical analysis of HIV/AIDS stochastic dynamic models

Emvudu, Yves; Danhrée, Bongor; Koïna, Rodoumta

doi:10.1016/j.apm.2016.05.007

Cited by 28 publications

(5 citation statements)

References 15 publications

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“…It is presently thought that mathematical models have been crucial instruments in qualitative and quantitatively studying the transmission and management of infectious diseases 3 . Numerous academics used theoretical viewpoints and simulations performed numerically to analyze the transmission of various infectious diseases 4 – 7 .…”

Section: Introductionmentioning

confidence: 99%

Introducing a novel mean-reverting Ornstein–Uhlenbeck process based stochastic epidemic model

Nabati

2024

Sci Rep

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The major objective of this paper is to examine a novel mean-reverting Ornstein–Uhlenbeck process-based stochastic SIRD model for transmission the epidemic disease that is a great crisis in numerous societies. For this purpose, the deterministic model is further converted into the stochastic form by allowing the infection rate satisfies the mean-reverting Ornstein–Uhlenbeck process to account the uncertainties involved in epidemic spread. At first using Lyapunov functions, the solution’s uniqueness and positivity will be demonstrated. Subsequently, the stochastic epidemic threshold $$\Re_{0}^{S}$$ ℜ 0 S that controls the disease’s extinction and persistence in the mean is identified analytically. It has been established that when $$\Re_{0}^{S} < 1$$ ℜ 0 S < 1 the disease will extinguish, whereas if $$\Re_{0}^{S} > 1$$ ℜ 0 S > 1 the disease is persistent. At last, several numerical simulations are presented to demonstrate the findings of the hypothetical investigation results. These simulations served to vividly illustrate and validate the implications derived from the hypothetical analysis.

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Section: Introductionmentioning

confidence: 99%

Introducing a novel mean-reverting Ornstein–Uhlenbeck process based stochastic epidemic model

Nabati

2024

Sci Rep

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“…From the explanation in the previous paragraph, we can see that it is necessary to pay attention to the sub-populations receiving treatment for HIV/AIDS, then the authors examine a model that includes subpopulations both infected with HIV and infected who progress to AIDS and receive treatment. Emvudu, Y., Bongor, D., & Koïna entitle Mathematical analysis of HIV/AIDS stochastic dynamic models examines a Deterministic Model of HIV/AIDS with Treatment in their article [13]. The model in this study then becomes a reference to this study by adding new parameters that represent the displacement from compartment T to compartment H so that the SHAT model is formed.…”

Section: Introductionmentioning

confidence: 99%

Modeling Hiv/Aids Using Shat Model

Chandra,

Permata

2023

BAREKENG: J. Math. & App.

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HIV/AIDS gets on the list of deadly infectious diseases, but there is no right medicine and vaccination for it until now. Indonesia is also inseparable from the spread of HIV/AIDS year by year number of people living with HIV/AIDS in Indonesia continues to grow. The peak of HIV cases over the last twelve years (starting from 2020) in Indonesia was 50,282 cases in 2019, then the peak of AIDS was 12,214 in 2013. The purpose of the study is to model the spread of HIV/AIDS and test it with data on the growth of HIV/AIDS in Indonesia from 2006 to 2018. The steps taken in conducting this research are to determine the equilibrium point, calculate the basic reproduction number, analyze the stability of the equilibrium point, and numeric simulation of the SHAT model with the Maple 18 tool. Numerical simulation produces a value of . Based on calculations using the Routh-Hurwitz table, we can find that the system will be asymptotically stable towards a disease-free equilibrium point, namely . Based on the results obtained, it can conclude that HIV/AIDS will not become an epidemic in Indonesia.

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“…Stochastic models incorporates these factors by taking into account randomness and add some additional degree of realism thereby producing more realistic and useful outputs. Some of the stochastic studies on diseases can be found in [35,53,40,22]. Sufficient conditions for extinction and persistence of a stochastic SIS model is discussed in [54].…”

Section: Introductionmentioning

confidence: 99%

Optimal Drug Regimen and Combined Drug Therapy and Its Efficacy in the Treatment of COVID-19: A Within-Host Modeling Study

Chhetri

Dkk

et al. 2022

Acta Biotheor

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The COVID-19 pandemic has resulted in more than 524 million cases and 6 million deaths worldwide. Various drug interventions targeting multiple stages of COVID-19 pathogenesis can significantly reduce infection-related mortality. The current within-host mathematical modeling study addresses the optimal drug regimen and efficacy of combination therapies in the treatment of COVID-19. The drugs/interventions considered include Arbidol, Remdesivir, Interferon (INF) and Lopinavir/Ritonavir. It is concluded that these drugs, when administered singly or in combination, reduce the number of infected cells and viral load. Four scenarios dealing with the administration of a single drug, two drugs, three drugs and all four are discussed. In all these scenarios, the optimal drug regimen is proposed based on two methods. In the first method, these medical interventions are modeled as control interventions and a corresponding objective function and optimal control problem are formulated. In this framework, the optimal drug regimen is derived. Later, using the comparative effectiveness method, the optimal drug regimen is derived based on the basic reproduction number and viral load. The average number of infected cells and viral load decreased the most when all four drugs were used together. On the other hand, the average number of susceptible cells decreased the most when Arbidol was administered alone. The basic reproduction number and viral load decreased the most when all four interventions were used together, confirming the previously obtained finding of the optimal control problem. The results of this study can help physicians make decisions about the treatment of the life-threatening COVID-19 infection.

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Mathematical analysis of HIV/AIDS stochastic dynamic models

Cited by 28 publications

References 15 publications

Introducing a novel mean-reverting Ornstein–Uhlenbeck process based stochastic epidemic model

Introducing a novel mean-reverting Ornstein–Uhlenbeck process based stochastic epidemic model

Modeling Hiv/Aids Using Shat Model

Optimal Drug Regimen and Combined Drug Therapy and Its Efficacy in the Treatment of COVID-19: A Within-Host Modeling Study

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