Mathematical analysis of a disease-resistant model with imperfect vaccine, quarantine and treatment

Rabiu, Musa; Willie, Robert; Parumasur, Nabendra

doi:10.1007/s11587-020-00496-7

Cited by 20 publications

(20 citation statements)

References 13 publications

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“…This genetic mutation has been reported to be inborn. There are very few paper on resistant mathematical model, some of them are [25], [13] and [15] but the resistance was modeled on influenza and SARS which is quite different from HIV/AIDS. This still remains a biological research question needed to be answered.…”

Section: Introductionmentioning

confidence: 99%

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

Rabiu

Willie²,

Parumasur³

2020

BIOMATH

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We develop a virus-resistant HIV-1 mathematical model with behavioural change in HIV-1 resistant non-progressors. The model has both disease-free and endemic equilibrium points that are proved to be locally asymptotically stable depending on the value of the associated reproduction numbers. In both models, a non-linear Goh{Volterra Lyapunov function was used to prove that the endemic equilibrium point is globally asymptotically stable for special case while the method of Castillo-Chavez was used to prove the global asymptotic stability of the disease-free equilibrium point. In both the analytic and numerical results, this study shows that in the context of resistance to HIV/AIDS, total abstinence can also play an important role in protection against this notorious infectious disease.

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Section: Introductionmentioning

confidence: 99%

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

Rabiu

Willie²,

Parumasur³

2020

BIOMATH

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“…But unfortunately, from (3), (where all model parameters are assumed positive) which shows that S ( t ) > 0. Consequently, following the same approach, we claim that the solutions S v ( t ), S uv ( t ), E ( t ), G Q ( t ), P Q ( t ), I ( t ), P T ( t ), G T ( t ) and R ( t ) are positive for all time t ≥ 0 [9, 21, 22].…”

Section: Analytic Resultsmentioning

confidence: 91%

“…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: Analytic Resultsmentioning

confidence: 95%

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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“…The available works that examined the effects of resistance are (Jia and Xiao 2018 ; Khanh 2016 ; Rabiu et al. 2020 ), where all of them incorporated it in flu model which is very much different from this study. Uniquely, our model also incorporates time-dependent controls (government’s intervention in promoting and encouraging behavior change, intake of balanced nutritional supplementation and ART) to determine the best combination of strategies capable in dealing with the virus spread.…”

Section: Introductionmentioning

confidence: 83%

“… 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: 96%

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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Mathematical analysis of a disease-resistant model with imperfect vaccine, quarantine and treatment

Cited by 20 publications

References 13 publications

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

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

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

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