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Journal ArticleDOI

COVID-19 Deterministic and Stochastic Modelling with Optimized Daily Vaccinations in Saudi Arabia.

TL;DR: In this article, the authors investigated the stochastic nature of the COVID-19 temporal dynamics by generating a fractional-order dynamic model for the Saudi Arabia second virus wave, which is assumed to start on 1st March 2021.
Abstract: In this paper, we investigate the stochastic nature of the COVID-19 temporal dynamics by generating a fractional-order dynamic model and a fractional-order-stochastic model. Initially, we considered the first and second vaccination doses as multiple vaccinations were initiated worldwide. The concerned models are then tested for the Saudi Arabia second virus wave, which is assumed to start on 1st March 2021. Four daily vaccination scenarios for the first and second dose are assumed for 100 days from the wave beginning. One of these scenarios is based on function optimization using the invasive weed optimization algorithm (IWO). After that, we numerically solve the established models using the fractional Euler method and the Euler-Murayama method. Finally, the obtained virus dynamics using the assumed scenarios and the real one started by the government are compared. The optimized scenario using the IWO effectively minimizes the predicted cumulative wave infections with a 4.4 % lower number of used vaccination doses.
Citations
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Journal ArticleDOI
01 May 2022-Vaccine
TL;DR: In this article , the authors proposed a probabilistic model to quantify the cost-benefit of mass vaccination scenarios against COVID-19 pandemic in Brazil, where three primary vaccine brands in Brazil (CoronaVac, AstraZeneca and Pfizer) were compared.

4 citations

Journal ArticleDOI
11 Jan 2023-Energies
TL;DR: In this paper , a PID-based model reference fractional adaptive controller is proposed, with detailed mathematical modeling, and compared to the other controllers in the survey, the proposed controller proved its superiority over other controllers through its fast response and low rising and settling times.
Abstract: Voltage regulation is a crucial task for electrical grids in the presence of high penetration levels of renewable energies. The regulation of generator excitation improves the stability of the power system. An essential tool for controlling the excitation of generators is the automatic voltage regulator (AVR). It is advised to use a controller to increase the reliability of an AVR. A survey about different types of controllers is proposed in this paper. Then, a novel optimized PID-Based model reference fractional adaptive controller is proposed, with detailed mathematical modeling. The novel controller was compared to the controllers in the survey. The novel proposed controller proved its superiority over the other controllers through its fast response and low rising and settling times. Moreover, the proposed controller smoothly and instantaneously tracked dynamic reference changes.

2 citations

Journal ArticleDOI
TL;DR: In this paper , an epidemic model to understand COVID-19 transmission vaccination and therapy considerations was constructed and the model's equilibria were examined, and the reproduction parameter was calculated via a next-generation matrix method, symbolized by $ \mathcal{R}_0 $.
Abstract: In this research work, we construct an epidemic model to understand COVID-19 transmission vaccination and therapy considerations. The model's equilibria were examined, and the reproduction parameter was calculated via a next-generation matrix method, symbolized by $ \mathcal{R}_0 $. We have shown that the infection-free steady state of our system is locally asymptotically stable for $ \mathcal{R}_0 < 1 $. Also, the local asymptotic stability of the endemic steady state has been established for $ \mathcal{R}_0 > 1 $. We have used a partial rank correlation coefficient method for sensitivity analysis of the threshold parameter $ \mathcal{R}_0 $. The contribution of vaccination to the threshold parameter is explored through graphical results. In addition to this, the uniqueness and existence of the solution to the postulated model of COVID-19 infection is shown. We ran various simulations of the proposed COVID-19 dynamics with varied input parameters to scrutinize the complex dynamics of COVID-19 infection. We illustrated the variation in the dynamical behavior of the system with different values of the input parameters. The key factors of the system are visualized for the public health officials for the control of the infection.

1 citations

Journal ArticleDOI
14 Dec 2022-Symmetry
TL;DR: In this paper , a piecewise derivative framework with singular and non-singular kernels is proposed to investigate the evolution of rotavirus with regard to the effect of vaccination and the existence of a solution of the piecewise Rotavirus model is investigated via fixed-point results.
Abstract: Many diseases are caused by viruses of different symmetrical shapes. Rotavirus particles are approximately 75 nm in diameter. They have icosahedral symmetry and particles that possess two concentric protein shells, or capsids. In this research, using a piecewise derivative framework with singular and non-singular kernels, we investigate the evolution of rotavirus with regard to the effect of vaccination. For the considered model, the existence of a solution of the piecewise rotavirus model is investigated via fixed-point results. The Adam–Bashforth numerical method along with the Newton polynomial is implemented to deduce the numerical solution of the considered model. Various versions of the stability of the solution of the piecewise rotavirus model are presented using the Ulam–Hyres concept and nonlinear analysis. We use MATLAB to perform the numerical simulation for a few fractional orders to study the crossover dynamics and evolution and effect of vaccination on rotavirus disease. To check the validity of the proposed approach, we compared our simulated results with real data from various countries.

1 citations

Journal ArticleDOI
TL;DR: In this paper , a stochastic SIQR epidemic model with non-monotone incidence is investigated, where the disease-free equilibrium of the deterministic model is globally asymptotically stable by using the Lyapunov method.
Abstract: In this paper, a stochastic SIQR epidemic model with non-monotone incidence is investigated. First of all, we consider the disease-free equilibrium of the deterministic model is globally asymptotically stable by using the Lyapunov method. Secondly, the existence and uniqueness of positive solution to the stochastic model is obtained. Then, the sufficient condition for extinction of the stochastic model is established. Furthermore, a unique stationary distribution to stochastic model will exist by constructing proper Lyapunov function. Finally, numerical examples are carried out to illustrate the theoretical results, with the help of numerical simulations, we can see that the higher intensities of the white noise or the bigger of the quarantine rate can accelerate the extinction of the disease. This theoretically explains the significance of quarantine strength (or isolation measures) when an epidemic erupts.
References
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Book
01 Jun 1992
TL;DR: In this article, a time-discrete approximation of deterministic Differential Equations is proposed for the stochastic calculus, based on Strong Taylor Expansions and Strong Taylor Approximations.
Abstract: 1 Probability and Statistics- 2 Probability and Stochastic Processes- 3 Ito Stochastic Calculus- 4 Stochastic Differential Equations- 5 Stochastic Taylor Expansions- 6 Modelling with Stochastic Differential Equations- 7 Applications of Stochastic Differential Equations- 8 Time Discrete Approximation of Deterministic Differential Equations- 9 Introduction to Stochastic Time Discrete Approximation- 10 Strong Taylor Approximations- 11 Explicit Strong Approximations- 12 Implicit Strong Approximations- 13 Selected Applications of Strong Approximations- 14 Weak Taylor Approximations- 15 Explicit and Implicit Weak Approximations- 16 Variance Reduction Methods- 17 Selected Applications of Weak Approximations- Solutions of Exercises- Bibliographical Notes

6,284 citations

Journal ArticleDOI
TL;DR: A novel numerical stochastic optimization algorithm inspired from colonizing weeds to mimic robustness, adaptation and randomness of Colonizing weeds in a simple but effective optimizing algorithm designated as Invasive Weed Optimization (IWO).

1,183 citations

Journal ArticleDOI
21 Jan 2021-Science
TL;DR: This article used a mathematical model to compare five age-stratified prioritization strategies for the SARS-CoV-2 vaccine and found that individual-level serological tests to redirect doses to seronegative individuals improved the marginal impact of each dose while potentially reducing existing inequities in COVID-19 impact.
Abstract: Limited initial supply of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccine raises the question of how to prioritize available doses. We used a mathematical model to compare five age-stratified prioritization strategies. A highly effective transmission-blocking vaccine prioritized to adults ages 20 to 49 years minimized cumulative incidence, but mortality and years of life lost were minimized in most scenarios when the vaccine was prioritized to adults greater than 60 years old. Use of individual-level serological tests to redirect doses to seronegative individuals improved the marginal impact of each dose while potentially reducing existing inequities in COVID-19 impact. Although maximum impact prioritization strategies were broadly consistent across countries, transmission rates, vaccination rollout speeds, and estimates of naturally acquired immunity, this framework can be used to compare impacts of prioritization strategies across contexts.

536 citations

Journal ArticleDOI
TL;DR: An SEIR model is implemented to compute the infected population and the number of casualties of an epidemic disease caused by a new coronavirus in Northern Italy with a strong contagion rate and shows how isolation measures, social distancing, and knowledge of the diffusion conditions help to understand the dynamics of the epidemic.
Abstract: An epidemic disease caused by a new coronavirus has spread in Northern Italy with a strong contagion rate. We implement an SEIR model to compute the infected population and the number of casualties of this epidemic. The example may ideally regard the situation in the Italian Region of Lombardy, where the epidemic started on February 24, but by no means attempts to perform a rigorous case study in view of the lack of suitable data and the uncertainty of the different parameters, namely, the variation of the degree of home isolation and social distancing as a function of time, the initial number of exposed individuals and infected people, the incubation and infectious periods, and the fatality rate. First, we perform an analysis of the results of the model by varying the parameters and initial conditions (in order for the epidemic to start, there should be at least one exposed or one infectious human). Then, we consider the Lombardy case and calibrate the model with the number of dead individuals to date (May 5, 2020) and constrain the parameters on the basis of values reported in the literature. The peak occurs at day 37 (March 31) approximately, with a reproduction ratio R 0 of 3 initially, 1.36 at day 22, and 0.8 after day 35, indicating different degrees of lockdown. The predicted death toll is approximately 15,600 casualties, with 2.7 million infected individuals at the end of the epidemic. The incubation period providing a better fit to the dead individuals is 4.25 days, and the infectious period is 4 days, with a fatality rate of 0.00144/day [values based on the reported (official) number of casualties]. The infection fatality rate (IFR) is 0.57%, and it is 2.37% if twice the reported number of casualties is assumed. However, these rates depend on the initial number of exposed individuals. If approximately nine times more individuals are exposed, there are three times more infected people at the end of the epidemic and IFR = 0.47%. If we relax these constraints and use a wider range of lower and upper bounds for the incubation and infectious periods, we observe that a higher incubation period (13 vs. 4.25 days) gives the same IFR (0.6 vs. 0.57%), but nine times more exposed individuals in the first case. Other choices of the set of parameters also provide a good fit to the data, but some of the results may not be realistic. Therefore, an accurate determination of the fatality rate and characteristics of the epidemic is subject to knowledge of the precise bounds of the parameters. Besides the specific example, the analysis proposed in this work shows how isolation measures, social distancing, and knowledge of the diffusion conditions help us to understand the dynamics of the epidemic. Hence, it is important to quantify the process to verify the effectiveness of the lockdown.

208 citations

ReportDOI
TL;DR: Testing at a higher rate in conjunction with targeted quarantine policies can (i) dampen the economic impact of the coronavirus and (ii) reduce peak symptomatic infections—relevant for hospital capacity constraints.
Abstract: We extend the baseline Susceptible-Exposed-Infectious-Recovered (SEIR) infectious disease epidemiology model to understand the role of testing and case-dependent quarantine. Our model nests the SEIR model. During a period of asymptomatic infection, testing can reveal infection that otherwise would only be revealed later when symptoms develop. Along with those displaying symptoms, such individuals are deemed known positive cases. Quarantine policy is case-dependent in that it can depend on whether a case is unknown, known positive, known negative, or recovered. Testing therefore makes possible the identification and quarantine of infected individuals and release of non-infected individuals. We fix a quarantine technology-a parameter determining the differential rate of transmission in quarantine-and compare simple testing and quarantine policies. We start with a baseline quarantine-only policy that replicates the rate at which individuals are entering quarantine in the US in March, 2020. We show that the total deaths that occur under this policy can occur under looser quarantine measures and a substantial increase in random testing of asymptomatic individuals. Testing at a higher rate in conjunction with targeted quarantine policies can (i) dampen the economic impact of the coronavirus and (ii) reduce peak symptomatic infections-relevant for hospital capacity constraints. Our model can be plugged into richer quantitative extensions of the SEIR model of the kind currently being used to forecast the effects of public health and economic policies.

186 citations