Analysis of a virus-resistant HIV-1 model with behavior change in non-progressors

Rabiu, Musa; Willie, Robert; Parumasur, Nabendra

doi:10.11145/j.biomath.2020.06.143

Cited by 8 publications

(8 citation statements)

References 20 publications

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“…When all interventions are set to zero as appeared in equation 20, the reproduction number becomes 19.6815 (> 1 which is not locally asymptotically stable). All these are in good agreement with the expressions in equation 21and (22).…”

Section: Impacts Of the Control Measures On The Reproduction Numbersupporting

confidence: 88%

“…Hence, it is sufficient to study the COVID-19 model in χ. Thus, we conclude that the model (3)-(12) is epidemiologically welposed and attracting [9,21,22].…”

Section: Invariant Regionmentioning

confidence: 58%

“…social distancing, quarantine, treatment and vaccination) are fully implemented, the threshold parameters can be brought down to less than unity and consequently ensure the eradication of the pandemic. This has been simulated under equations (19)- (22) as mentioned earlier.…”

Section: Impacts Of Social Distancing With Varying Level Of Vaccinatimentioning

confidence: 99%

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Assessment of the Impacts of Pharmaceutical and Non-pharmaceutical Intervention on COVID-19 in South Africa Using Mathematical Model

Rabiu

Ezugwu

Mbah

2020

Preprint

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The novel coronal virus has spread across more than 213 countries within the space of six months causing devastating public health hazard and monumental economic loss. In the absence of clinically approved pharmaceutical intervention, attentions are shifted to non-pharmaceutical controls to mitigate the burden of the novel pandemic. In this regard, a ten mutually exclusive compartmental mathematical model is developed to investigate possible effects of both pharmaceutical and non-pharmaceutical controls incorporating both private and government’s quarantine and treatments. Several reproduction numbers were calculated and used to determine the impact of both control measures as well as projected benefits of social distancing, treatments and vaccination. We investigate and compare the possible impact of social distancing incorporating different levels of vaccination, with vaccination programme incorporating different levels of treatment. Using the officially published South African COVID-19 data, the numerical simulation shows that the community reproduction threshold will be 30 when there is no social distancing but will drastically reduced to 5 (about 83% reduction) when social distancing is enforced. Furthermore, when there is vaccination with perfect efficacy, the community reproduction threshold will be 4 which increases to 12 (about 67% increment) with-out vaccination. We also established that the implementation of both interventions is enough to curtail the spread of COVID-19 pandemic in South Africa which is in confirmation with the recommendation of the world health organization.

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Section: Impacts Of the Control Measures On The Reproduction Numbersupporting

confidence: 88%

“…Hence, it is sufficient to study the COVID-19 model in χ. Thus, we conclude that the model (3)-(12) is epidemiologically welposed and attracting [9,21,22].…”

Section: Invariant Regionmentioning

confidence: 58%

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Assessment of the Impacts of Pharmaceutical and Non-pharmaceutical Intervention on COVID-19 in South Africa Using Mathematical Model

Rabiu

Ezugwu

Mbah

2020

Preprint

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“… 2020 ; Rabiu et al. 2020 , 2020 ; Rabiu and Akinyemi 2016 ) . Hence, is a feasible region and it is sufficient to study the model in .…”

Section: Analysis Of the Modelmentioning

confidence: 98%

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

2021

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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.

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“…The disease-free equilibrium of (2.2)-(2.7) is given by where . We calculate the control reproduction number using the next generation matrix operator [13, 59] on (2.2)-(2.7) as used by [46, 51]. The matrix for the rates of new infections ℱ and that of transfer of infected individuals, 𝒱 at the DFE are given by …”

Section: Model Analysismentioning

confidence: 99%

Assessing the potential impact of immunity waning on the dynamics of COVID-19: an endemic model of COVID-19

Musa

Iyaniwura

2021

Preprint

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We developed an endemic model of COVID-19 to assess the impact of vaccination and immunity waning on the dynamics of the disease. Our model exhibits the phenomenon of back-ward bifurcation and bi-stability, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium. The epidemiological implication of this is that the control reproduction number being less than unity is no longer sufficient to guarantee disease eradication. We showed that this phenomenon could be eliminated by either increasing the vaccine efficacy or by reducing the disease transmission rate (adhering to non-pharmaceutical interventions). Furthermore, we numerically investigated the impacts of vaccination and waning of both vaccine-induced immunity and post-recovery immunity on the disease dynamics. Our simulation results show that the waning of vaccine-induced immunity has more effect on the disease dynamics relative to post-recovery immunity waning, and suggests that more emphasis should be on reducing the waning of vaccine-induced immunity to eradicate COVID-19.

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Analysis of a virus-resistant HIV-1 model with behavior change in non-progressors

Cited by 8 publications

References 20 publications

Assessment of the Impacts of Pharmaceutical and Non-pharmaceutical Intervention on COVID-19 in South Africa Using Mathematical Model

Assessment of the Impacts of Pharmaceutical and Non-pharmaceutical Intervention on COVID-19 in South Africa Using Mathematical Model

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

Assessing the potential impact of immunity waning on the dynamics of COVID-19: an endemic model of COVID-19

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