Global stability analysis of the role of multi-therapies and non-pharmaceutical treatment protocols for COVID-19 pandemic

Bassey, Bassey Echeng; Atsu, J U

doi:10.1016/j.chaos.2020.110574

Cited by 10 publications

(17 citation statements)

References 23 publications

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“…This observation was in tandem with the average R 0 of 3.28 reported in another study from China [34] , which was obtained later when the population might have acquired some level of immune resistance. Control measures and non-pharmaceutical interventions (such as the rational use of face masks, rigorous public awareness, contact tracing, immediate isolation and prompt treatment 35 , 36 , 37 , 38 ) likely promoted a significant increase in risk perception of the virus and behaviour change [39] , but not sufficient to significantly reduce the community transmission of SARS-CoV-2. It is also worth noting that R 0 estimates can be affected by several factors such as; genetic, behavioural, environmental, etc.…”

Section: Discussionmentioning

confidence: 99%

Investigating the transmission dynamics of SARS-CoV-2 in Nigeria: A SEIR modelling approach

et al. 2022

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This study was designed to investigate the transmission dynamics of the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) to inform policy advisory vital for managing the spread of the virus in Nigeria. We applied the Susceptible-Exposed-Infectious-Recovered (SEIR)-type predictive model to discern the transmission dynamics of SARS-CoV-2 at different stages of the pandemic; incidence, during and after the lockdown from 27th March 2020 to 22nd September 2020 in Nigeria. Our model was calibrated with the COVID-19 data (obtained from the Nigeria Centre for Disease Control) using the “lsqcurvefit” package in MATLAB to fit the “cumulative active cases” and “cumulative death” data. We adopted the Latin hypercube sampling with a partial rank correlation coefficient index to determine the measure of uncertainty in our parameter estimation at a 99% confidence interval (CI). At the incidence of SARS-CoV-2 in Nigeria, the basic reproduction number ( R 0 ) was 6.860; 99%CI [6.003, 7.882]. R 0 decreased by half (3.566; 99%CI [3.503, 3.613]) during the lockdown, and R 0 was 1.238; 99%CI [1.215, 1.262] after easing the lockdown. If all parameters are maintained (as in after easing the lockdown), our model forecasted a gradual and perpetual surge through the next 12 months or more. In the light of our results and available data, evidence of human-to-human transmission at higher rates is still very likely. A timely, proactive, and well-articulated effort should help mitigate the transmission of SARS-CoV-2 in Nigeria.

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Section: Discussionmentioning

confidence: 99%

Investigating the transmission dynamics of SARS-CoV-2 in Nigeria: A SEIR modelling approach

et al. 2022

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“…Moreso, treatment inconsistency occasioned by avoidable truncation, which could lead to colossal drug abuse has not been given the desired attention. For instance, (Bassey and Atsu, 2021), recently formulated a 6-Dimensional deterministic model that accounted for the global stability analysis of the aforementioned novel treatment dynamics but was devoid of the optimal control strategy. That is by extension, the application of optimal control techniques has not been explored to investigate the role of ART abuse in the treatment dynamics of HIV/AIDS infection.…”

Section: Problem Statement and Model Derivationmentioning

confidence: 99%

“…Moreso, in that study, it was recommended that any approach that could maximize healthy CD4 + T-cells was highly encouraged. Therefore, in our quest for maximization of some designated predominant state-space, the present study extending the model by Bassey and Atsu (2021) and incorporating optimality conditions, seeks to explore optimal control techniques for the investigation of the role of ART abuse in the HIV/AIDS treatment dynamics. In that study, designated methodological treatment functions include condom use and antiretroviral therapy, which was administered on a set of 6-Dimensional deterministic compartmental HIV/AIDS dynamic model partitioned into Susceptible population S(t), HIV positive (infective) individuals who are unaware of their HIV status I1(t) aware infective population not ready to receive ART treatment I2(t), HIV positive (infective) individuals receiving ART T(t), HIV positive population who are under ART but truncate the use of ART and then later resume the application of the ART (abuse of ART) TA(t) and full-blown AIDS population A(t).…”

Section: Problem Statement and Model Derivationmentioning

confidence: 99%

Optimal Control Techniques for the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics

Bassey¹,

Henry²

2022

Journal of Mathematics and Statistics

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From the studies of HIV/AIDS transmission and treatment dynamics using mathematical modeling, literature reviews have shown that attention had not been given to the behavioral attitude of screen-aware infectives not ready to receive treatment, HIV-aware infectives that initiated treatment but truncated only to resume treatment later (therapy abuse) and those on consistent treatment protocols. Moreso, following the non-outright eradication of the deadly HI-virus, recommendations have been geared towards exploring optimal control theory for the maximization of healthy uninfected CD4 + T-cells. Therefore, this present investigation seeks and formulated an optimal control 6-Dimensional deterministic mathematical dynamic model, which accounted for the Role of Antiretroviral Therapy (ART) abuse in the treatment dynamics of the HIV/AIDS epidemic. The materials and methods for this model are constituted by a set of 6-Dimensional varying subpopulations interacting with concentrated HI-viral load. Interactions are investigated using bilinear control functions (condom use and ART) with empirically generated data. The model assumed a deterministic approach and was formulated using the fundamental theory of differential equations. Theoretical optimal predictions explored classical numerical methods with optimal control techniques (Pontryagin's maximum principle in conjunction with Hessian matrix) as a basis. Numerical simulations were conducted using in-built Runge-Kutta of the order of precision 4 in a Mathcad surface. Following the derived model for both offoptimal control and onset-optimal control functions and model optimal control pair as well as model optimality system, results of simulations indicated that at off-optimal control function, near zero population extinction was observed. From the application of optimal control functions under optimal control techniques, there exists tremendous rejuvenation of susceptible populations vindicated by a reduction in the rate of ART abuse under a minimal proportion of bilinear control functions. The study concluded that adopting optimal control techniques for the investigation of the role of ART abuse in HIV/AIDS treatment yield highly significant recovery of healthy CD4 + T-Cells at minimal systemic cost when compared with off-optimal control outcome. Therefore, the study not only affirmed the vital concept of optimal control strategy but also, instituted the viability of the model. Thus, this model can be extensively used in Bio-system and applied mathematics.

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“…Moreover, the establishment of appropriate COVID-19 mathematical models will help us to understand the interplay between different pandemic factors [30]. Kamara et al [17] considered a COVID-19 mathematical model with the infectivity of exposed individuals, and analyzed the global stability of disease-free and endemic equilibria, also see Bassey and Atsu [4]. Zamir et al [41] pointed out that exposed individuals, symptomatic infected individuals, asymptomatic infected individuals and stuffs contaminated with COVID-19 would infect susceptible individuals.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of COVID-19 models with asymptomatic infections and quarantine measures

Guo

Yang

et al. 2022

Preprint

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Considering the propagation characteristics of COVID-19 in different regions, the dynamics analysis and numerical demonstration of long-term and short-term models of COVID-19 are carried out, respectively. The long-term model is devoted to investigate the global stability of COVID-19 model with asymptomatic infections and quarantine measures. By using the limit system of the model and Lyapunov function method, it is shown that the COVID-19-free equilibrium V 0 is globally asymptotically stable if the control reproduction number Rc < 1 and globally attractive if Rc = 1, which means that COVID-19 will die out; the COVID-19 equilibrium V∗ is globally asymptotically stable if Rc > 1, which means that COVID-19 will be persistent. In particular, to obtain the local stability of V∗ , we use proof by contradiction and the properties of complex modulus with some novel details, and we prove the weak persistence of the system to obtain the global attractivity of V∗ . Moreover, the final size of the corresponding short-term model is calculated and the stability of its multiple equilibria is analyzed. Numerical simulations of COVID-19 cases show that quarantine measures and asymptomatic infections have a non-negligible impact on the transmission of COVID-19 2020 MSC: 34D23, 37N25, 92D30

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Global stability analysis of the role of multi-therapies and non-pharmaceutical treatment protocols for COVID-19 pandemic

Cited by 10 publications

References 23 publications

Investigating the transmission dynamics of SARS-CoV-2 in Nigeria: A SEIR modelling approach

Investigating the transmission dynamics of SARS-CoV-2 in Nigeria: A SEIR modelling approach

Optimal Control Techniques for the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics

Dynamics of COVID-19 models with asymptomatic infections and quarantine measures

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