Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay

Arenas, Abraham J.; González-Parra, Gilberto; Naranjo, Jhon J.; Cogollo, Myladis R.; Espriella, N. De La

doi:10.3390/math9030257

Cited by 12 publications

(8 citation statements)

References 114 publications

(186 reference statements)

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“…Mathematical models that consider time delays have been proposed and studied previously [27][28][29][30]. These models are useful to gain insight on epidemics and a variety of viruses [31][32][33][34][35][36]. In this paper, we extend the mathematical model presented in [37].…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of Toxoplasmosis Considering a Time Delay in the Infectivity of Oocysts

2022

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In this paper, we study the effect of the introduction of a time delay on the dynamics of toxoplasmosis. This time delay is the elapsed time from when oocysts become present in the environment and when they become infectious. We construct a mathematical model that includes cats and oocysts in the environment. We include the effect of oocysts, since they are crucial for the dynamics of toxoplasmosis. The likelihood of the acquisition of Toxoplasma gondii infection depends on the environmental load of the parasite. Furthermore, the model considers the possibility of vaccination of the feline host. In the mathematical model, we consider directly the infection of cats through the oocysts shed by other cats. We prove that the basic reproduction number R0 is a secondary parameter that determines the global dynamics of toxoplasmosis in cat populations. We study the effect of the time delay on the stability of the steady states. We find that the time delay cannot change the stability of the endemic state, which is an important result from the biological point of view. Numerical simulations are performed to support the theoretical results and obtain further insight into understanding toxoplasmosis dynamics in cat populations.

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Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of Toxoplasmosis Considering a Time Delay in the Infectivity of Oocysts

2022

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“…e individual infected with Human immunodeficiency virus (HIV) has a weak immune system [1][2][3][4][5]. HIV is the virus that invades targeted human T-cells directly [6,7].…”

Section: Introductionmentioning

confidence: 99%

A New Generalized Fractional-Order Derivative and Bifurcation Analysis of Cholera and Human Immunodeficiency Co-Infection Dynamic Transmission

Cheneke

Koya

Edessa

2022

International Journal of Mathematics and Mathematical Sciences

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In this study, the co-infection of HIV and cholera model has been developed and analyzed. The new fractional-order derivative is applied and the behavior of the solution is interpreted. The order of new generalized fractional-order derivative implication is presented. A new method is incorporated to determine the forward bifurcation at a threshold R 0 = 1 . The developed method is used to determine the stability of steady-state points. The full model and the submodels’ disease-free equilibrium are locally asymptotically stable if the corresponding reproduction number is less than one and unstable if the production number is greater than one. The only HIV model exhibits forward bifurcation at the threshold point, R 0 = 1 . The numerical simulations solutions obtained using a new generalized fractional-order derivative shows that the total human population size approaches the disease-free equilibrium if the order of the fractional derivative is higher. Also, the simulated results show that the memory effects toward the invading disease are less whenever the order of the fractional derivative is near 0 but higher whenever the order of the fractional derivative is near 1. Furthermore, V. cholerae concentration in the environment increases whenever the intrinsic growth rate increases. The numerical solutions are carried out using MATLAB software.

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“…In recent years, there has been an increase in the number of studies on HIV/AIDS transmission [12][13][14][15][16][17][18][19][20][21][22]. For example, Moya and Marrero [12] presented a stochastic model using Markov chains to study the transmission of HIV/AIDS and control chain elements proposed control strategies.…”

Section: Introductionmentioning

confidence: 99%

“…Sultanoglu et al [20] proposed a mathematical model to assess the dynamics of HIV infection in Cyprus. Arenas et al [21] proposed a mathematical model to describe intracellular infection accounting for the time delay between HIV entry and the production of new virus using differential delay equations. Li et al [22] formulated a mathematical model to evaluate the impact of PrEP, biomedical interventions, and their combinations and studied it over 20 years.…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Model for HIV/AIDS Under Pre-Exposure and Post-Exposure Prophylaxis

Moya

Rodrigues

Pietrus

et al. 2022

BIOMATH

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HIV/AIDS has a strong impact on society, the economy, and health. Early diagnosis of cases, adherence to treatment, and prevention are important factors in controlling the epidemic in the population. In this paper, we present a new mathematical model for the study of HIV/AIDS transmission. Our model is stratified in men and women, to account for the main forms of sexual transmission homosexual and heterosexual relationships, and infectiousness in the HIV and AIDS stages. In addition, in the construction of the model, we take into account the influence of Pre-Exposure Prophylaxis (PrEP) and Post-Exposure Prophylaxis (PEP) to study the impact of these implementations, diagnosis, and effectiveness of treatment based on viral load undetectability. We study the basic reproduction number by subpopulation (men and women) and general. Working by subpopulations allows us to study men who have sex with men who have a strong impact on virus transmission. Also, we study the infection-free equilibrium points due to their relationship with the basic reproduction number and demonstrate the global stability by subpopulation and general. To explore our model, we performed computational simulations on a scenario designed with data from the literature and assumed, studying the influence of the parameters associated with the use of PrEP, PEP, and undetectability on the basic reproduction number by varying them individually and jointly. We concluded that in women the basic reproduction number is always lower than unity and that in men the parameter associated with the undetectability of the viral load in HIV men has a strong influence on the dynamics. We also address the impact of PrEP, PEP, and undetectability in HIV and AIDS on the compartments, considering different scenarios varying the parameters jointly and independently and by sex which show difficulty in reducing women with AIDS. The scenario that showed the best results in the reduction of the number of HIV and AIDS cases was when the parameters associated with undetectability in HIV and AIDS men and women take the 90-90-90 that is proposed in the World Health Organization (WHO) strategy.

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Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay

Cited by 12 publications

References 114 publications

Mathematical Modeling of Toxoplasmosis Considering a Time Delay in the Infectivity of Oocysts

Mathematical Modeling of Toxoplasmosis Considering a Time Delay in the Infectivity of Oocysts

A New Generalized Fractional-Order Derivative and Bifurcation Analysis of Cholera and Human Immunodeficiency Co-Infection Dynamic Transmission

A Mathematical Model for HIV/AIDS Under Pre-Exposure and Post-Exposure Prophylaxis

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