Analysis of the stochastic model for predicting the novel coronavirus disease

Modelling and analysis of fractional-order vaccination model for control of COVID-19 outbreak using real data

In this paper, we construct the SV1V2EIR model to reveal the impact of two-dose vaccination on COVID-19 by using Caputo fractional derivative. The feasibility region of the proposed model and equilibrium points is derived. The basic reproduction number of the model is derived by using the next-generation matrix method. The local and global stability analysis is performed for both the disease-free and endemic equilibrium states. The present model is validated using real data reported for COVID-19 cumulative cases for the Republic of India from 1 January 2022 to 30 April 2022. Next, we conduct the sensitivity analysis to examine the effects of model parameters that affect the basic reproduction number. The Laplace Adomian decomposition method (LADM) is implemented to obtain an approximate solution. Finally, the graphical results are presented to examine the impact of the first dose of vaccine, the second dose of vaccine, disease transmission rate, and Caputo fractional derivatives to support our theoretical results.

Optimal control and cost-effectiveness analysis for a COVID-19 model with individual protection awareness

This paper is focused on the design of optimal control strategies for COVID-19 and the model containing susceptible individuals with awareness of protection and susceptible individuals without awareness of protection is established. The goal of this paper is to minimize the number of infected people and susceptible individuals without protection awareness, and to increase the willingness of susceptible individuals to take protection measures. We conduct a qualitative analysis of this mathematical model. Based on the sensitivity analysis, the optimal control method is proposed, namely personal protective measures, vaccination and awareness raising programs. It is found that combining the three methods can minimize the number of infected people. Moreover, the introduction of awareness raising program in society will greatly reduce the existence of susceptible individuals without protection awareness. To evaluate the most cost-effective strategy we performed a cost-effectiveness analysis using the ICER method.

Fractional optimal control of compartmental SIR model of COVID-19: Showing the impact of effective vaccination

In this work a compartmental SIR model has been proposed for describing the dynamics of COVID-19 with Caputo's fractional derivative(FD). SIR compartmental model has been used here with fractional differential equations(FDEs). The mathematical model of the pandemic consists of three compartments namely susceptible, infected and recovered individuals. The dynamics of the pandemic COVID-19 with FDEs for showing the effect of memory as most of the cell biological systems can be described accurately by FDEs Time dependent control(Effective vaccination) has been applied model to formulated fractional optimal control problem(FOCP) to reduce the viral load. Pontryagin's Maximum Principle(PMP) has been used to formulate FOCP. An effective vaccination is very helpful for controlling the pandemic, which is observed through the numerical simulation via Grunwald-Letnikov(G-L) approximation. All numerical simulation work has been carried in MATLAB platform.

A Simulation Study on Spread of Disease and Control Measures in Closed Population Using ABM

An infectious disease can cause a detrimental effect on national security. A group such as the military called a “closed population”, which is a subset of the general population but has many distinct characteristics, must survive even in the event of a pandemic. Hence, it requires its own distinct solution during a pandemic. In this study, we investigate a simulation analysis for implementing an agent-based model that reflects the characteristics of agents and the environment in a closed population and finds effective control measures for making the closed population functional in the course of disease spreading.

On the accuracy of ARIMA based prediction of COVID-19 spread

COVID-19 was declared a global pandemic by the World Health Organization in March 2020, and has infected more than 4 million people worldwide with over 300,000 deaths by early May 2020. Many researchers around the world incorporated various prediction techniques such as Susceptible-Infected-Recovered model, Susceptible-Exposed-Infected-Recovered model, and Auto Regressive Integrated Moving Average model (ARIMA) to forecast the spread of this pandemic. The ARIMA technique was not heavily used in forecasting COVID-19 by researchers due to the claim that it is not suitable for use in complex and dynamic contexts. The aim of this study is to test how accurate the ARIMA best-fit model predictions were with the actual values reported after the entire time of the prediction had elapsed. We investigate and validate the accuracy of an ARIMA model over a relatively long period of time using Kuwait as a case study. We started by optimizing the parameters of our model to find a best-fit through examining auto-correlation function and partial auto correlation function charts, as well as different accuracy measures. We then used the best-fit model to forecast confirmed and recovered cases of COVID-19 throughout the different phases of Kuwait's gradual preventive plan. The results show that despite the dynamic nature of the disease and constant revisions made by the Kuwaiti government, the actual values for most of the time period observed were well within bounds of our selected ARIMA model prediction at 95% confidence interval. Pearson's correlation coefficient for the forecast points with the actual recorded data was found to be 0.996. This indicates that the two sets are highly correlated. The accuracy of the prediction provided by our ARIMA model is both appropriate and satisfactory.

An SEIR model with infected immigrants and recovered emigrants

We present a deterministic SEIR model of the said form. The population in point can be considered as consisting of a local population together with a migrant subpopulation. The migrants come into the local population for a short stay. In particular, the model allows for a constant inflow of individuals into different classes and constant outflow of individuals from the R-class. The system of ordinary differential equations has positive solutions and the infected classes remain above specified threshold levels. The equilibrium points are shown to be asymptotically stable. The utility of the model is demonstrated by way of an application to measles.

A two-phase dynamic contagion model for COVID-19

In this paper, we propose a continuous-time stochastic intensity model, namely, two-phase dynamic contagion process (2P-DCP), for modelling the epidemic contagion of COVID-19 and investigating the lockdown effect based on the dynamic contagion model introduced by Dassios and Zhao [24]. It allows randomness to the infectivity of individuals rather than a constant reproduction number as assumed by standard models. Key epidemiological quantities, such as the distribution of final epidemic size and expected epidemic duration, are derived and estimated based on real data for various regions and countries. The associated time lag of the effect of intervention in each country or region is estimated. Our results are consistent with the incubation time of COVID-19 found by recent medical study. We demonstrate that our model could potentially be a valuable tool in the modeling of COVID-19. More importantly, the proposed model of 2P-DCP could also be used as an important tool in epidemiological modelling as this type of contagion models with very simple structures is adequate to describe the evolution of regional epidemic and worldwide pandemic.

Stability analysis of a fractional-order cancer model with chaotic dynamics

In this paper, we develop a three-dimensional fractional-order cancer model. The proposed model involves the interaction among tumor cells, healthy tissue cells and activated effector cells. The detailed analysis of the equilibrium points is studied. Also, the existence and uniqueness of the solution are investigated. The fractional derivative is considered in the Caputo sense. Numerical simulations are performed to illustrate the effectiveness of the obtained theoretical results. The outcome of the study reveals that the order of the fractional derivative has a significant effect on the dynamic process. Further, the calculated Lyapunov exponents give the existence of chaotic behavior of the proposed model. Also, it is observed from the obtained results that decrease in fractional-order [Formula: see text] increases the chaotic behavior of the model.

Extinction and persistence of a stochastic SIRV epidemic model with nonlinear incidence rate

In this paper, a stochastic SIRV epidemic model with general nonlinear incidence and vaccination is investigated. The value of our study lies in two aspects. Mathematically, with the help of Lyapunov function method and stochastic analysis theory, we obtain a stochastic threshold of the model that completely determines the extinction and persistence of the epidemic. Epidemiologically, we find that random fluctuations can suppress disease outbreak, which can provide us some useful control strategies to regulate disease dynamics. In other words, neglecting random perturbations overestimates the ability of the disease to spread. The numerical simulations are given to illustrate the main theoretical results.

Analysis of Atangana-Baleanu fractional-order SEAIR epidemic model with optimal control

We consider a SEAIR epidemic model with Atangana-Baleanu fractional-order derivative. We approximate the solution of the model using the numerical scheme developed by Toufic and Atangana. The numerical simulation corresponding to several fractional orders shows that, as the fractional order reduces from 1, the spread of the endemic grows slower. Optimal control analysis and simulation show that the control strategy designed is operative in reducing the number of cases in different compartments. Moreover, simulating the optimal profile revealed that reducing the fractional-order from 1 leads to the need for quick starting of the application of the designed control strategy at the maximum possible level and maintaining it for the majority of the period of the pandemic.

Modeling and stability analysis of the spread of novel coronavirus disease COVID-19

Towards the end of 2019, the world witnessed the outbreak of Severe Acute Respiratory Syndrome Coronavirus-2 (COVID-19), a new strain of coronavirus that was unidentified in humans previously. In this paper, a new fractional-order Susceptible–Exposed–Infected–Hospitalized–Recovered (SEIHR) model is formulated for COVID-19, where the population is infected due to human transmission. The fractional-order discrete version of the model is obtained by the process of discretization and the basic reproductive number is calculated with the next-generation matrix approach. All equilibrium points related to the disease transmission model are then computed. Further, sufficient conditions to investigate all possible equilibria of the model are established in terms of the basic reproduction number (local stability) and are supported with time series, phase portraits and bifurcation diagrams. Finally, numerical simulations are provided to demonstrate the theoretical findings.

Modeling Ivory Coast COVID-19 cases: Identification of a high-performance model for utilization

This study modelled the reported daily cumulative confirmed, discharged and death Coronavirus disease 2019 (COVID-19) cases using six econometric models in simple, quadratic, cubic and quartic forms and an autoregressive integrated moving average (ARIMA) model. The models were compared employing R-squared and Root Mean Square Error (RMSE). The best model was used to forecast confirmed, discharged and death COVID-19 cases for October 2020 to February 2021. The predicted number of confirmed and death COVID-19 cases are alarming. Good planning and innovative approaches are required to prevent the forecasted alarming infection and death in Ivory Coast. The applications of findings of this study will ensure that the COVID-19 does not crush the Ivory Coast's health, economic, social and political systems.

Optimal control and sensitivity analysis for transmission dynamics of Coronavirus

Analysis of mathematical models designed for COVID-19 results in several important outputs that may help stakeholders to answer disease control policy questions. A mathematical model for COVID-19 is developed and equilibrium points are shown to be locally and globally stable. Sensitivity analysis of the basic reproductive number (R₀) showed that the rate of transmission from asymptomatically infected cases to susceptible cases is the most sensitive parameter. Numerical simulation indicated that a 10% reduction of R₀ by reducing the most sensitive parameter results in a 24% reduction of the size of exposed cases. Optimal control analysis revealed that the optimal practice of combining all three (public health education, personal protective measure, and treating COVID-19 patients) intervention strategies or combination of any two of them leads to the required mitigation of transmission of the pandemic.