Pre-exposure prophylaxis HIV/AIDS mathematical model with non classical isolation

Djomegni, P.M. Tchepmo; Tekle, Andualem; Dawed, Mohammed Yiha

doi:10.1007/s13160-020-00422-2

Cited by 8 publications

(6 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Biologically, this parameter R 0 is stated as: "the average number of secondary infections generated by a typical single JE infected individual in the entirely susceptible individuals in which a few people have been immunized", [31].…”

Section: Steady-states and Basic Reproductive Numbermentioning

confidence: 99%

The impact of time delay in the transmission of Japanese encephalitis without vaccination

Baniya

Keval

2021

Proyecciones (Antofagasta)

View full text Add to dashboard Cite

In the manuscript, the influence of time delay on the transmission of Japanese encephalitis model without vaccination model has been studied. The time delay is because of the existence of an incubation period during which the JE virus reproduces enough in the mosquitoes with the goal that it tends to be transmitted by the mosquitoes to people. The motivation behind this manuscript is to assess the influence of the time delay it takes to infect susceptible human populations after interacting with infected mosquitoes. The steady-states and the threshold value R0 of the delay model were resolved. This value assists with setting up the circumstance that ensure the asymptotic stability of relating equilibrium points. Utilizing the delay as a bifurcation parameter, we built up the circumstance for the presence of a ”Hopf bifurcation”. Moreover, we infer an express equation to decide the stability and direction of ”Hopf bifurcation” at endemic equilibrium by using center manifold theory and normal structure strategy. It has been seen that delay plays a vital role in stability exchanging. In addition, larger values of virus transmission rate from an infected mosquito to susceptible individuals and the natural mortality of humans of a model affect the existence of ”Hopf bifurcation”. Finally, to understand some analytical outcomes, the delay framework is simulated numerically.

show abstract

Section: Steady-states and Basic Reproductive Numbermentioning

confidence: 99%

The impact of time delay in the transmission of Japanese encephalitis without vaccination

Baniya

Keval

2021

Proyecciones (Antofagasta)

View full text Add to dashboard Cite

show abstract

“…Therefore, the model is epidemically well-posed and meaningful since all the state variables are non-negative for all (Djomegni et al. 2020 ; Rabiu et al. 2020 , 2020 ; Rabiu and Akinyemi 2016 ) .…”

Section: Analysis Of the Modelmentioning

confidence: 99%

“…variables are non-negative for all t ≥ 0 (Djomegni et al 2020;Rabiu and Akinyemi 2016) . Hence, Σ is a feasible region and it is sufficient to study the model in Σ .…”

Section: Basic Properties Of the Modelmentioning

confidence: 99%

Optimal Control Strategies and Sensitivity Analysis of an HIV/AIDS-Resistant Model with Behavior Change

2021

View full text Add to dashboard Cite

Despite several research on HIV/AIDS, it is still incumbent to investigate more effective control measures to mitigate its infection level. Therefore, we introduce an HIV/AIDS-resistant model with behavior change and study its basic properties. In order to determine the most sensitive parameters that are responsible for disease transmission with respect to the basic reproduction number and those responsible for disease prevalence with respect to the endemic equilibrium, the sensitivity analysis was established and it was confirmed that the influx rate of people into the infected population and total abstinence from all risk practices and endemic areas are some of the most sensitive parameters for disease spread and disease eradication, respectively. Furthermore, by considering controls denoting the government’s intervention in promoting and encouraging behavior change, representing intake of balanced nutritional supplementation, and connoting antiretroviral therapy (ART), an optimal control problem was developed and analyzed. Before the establishment of the necessary conditions of the optimal control using Pontryagin’s Maximum Principle, we proved the existence of the optimal control triplet where is the control set at time t ,) which has been neglected by many researchers in recent years. Using the Runge–Kutta scheme, the optimal control problem was solved to understand the best combination of control strategies. Using the demographic and epidemiological data for South Africa on HIV/AIDS, a numerical simulation was carried out and results are presented on 3D surface plots. The obtained results suggested that the combination of all the considered control measures is the best method to ensure disease eradication.

show abstract

“…In recent years, mathematical modelling is becoming key techniques in the area of infectious disease propagation and control [13][14][15][16][17][18]. The studies on the mathematical analysis of human diseases and epidemic models have been conducted, which combine numerical studies with dynamic system methodologies such as stability analysis, LaSalles invariance principle, Routh-Hurwitz criterion and Lyapunov function [19].…”

Section: Introductionmentioning

confidence: 99%

Mathematical model and stability analysis on the transmission dynamics of skin sores

et al. 2022

View full text Add to dashboard Cite

In this study, a nonlinear deterministic model for the transmission dynamics of skin sores (impetigo) disease is developed and analyzed by the help of stability of differential equations. Some basic properties of the model including existence and positivity as well as boundedness of the solutions of the model are investigated. The disease-free and endemic equilibrium were investigated, as well as the basic reproduction number, R0, also calculated using the next-generation matrix approach. When R0 < 1, the model's stability analysis reveals that the system is asymptotically stable at disease-free critical point globally as well as locally. If R0 > 1, the system is asymptotically stable at disease-endemic equilibrium both locally and globally. The long-term behavior of the skin sores model's steady state solution in a population is investigated using numerical simulations of the model.

show abstract

Pre-exposure prophylaxis HIV/AIDS mathematical model with non classical isolation

Cited by 8 publications

References 8 publications

The impact of time delay in the transmission of Japanese encephalitis without vaccination

The impact of time delay in the transmission of Japanese encephalitis without vaccination

Optimal Control Strategies and Sensitivity Analysis of an HIV/AIDS-Resistant Model with Behavior Change

Mathematical model and stability analysis on the transmission dynamics of skin sores

Contact Info

Product

Resources

About