On a new conceptual mathematical model dealing the current novel coronavirus-19 infectious disease

Fractional order SEIQRD epidemic model of Covid-19: A case study of Italy

The fractional order SEIQRD compartmental model of COVID-19 is explored in this manuscript with six different categories in the Caputo approach. A few findings for the new model's existence and uniqueness criterion, as well as non-negativity and boundedness of the solution, have been established. When RCovid19<1 at infection-free equilibrium, we prove that the system is locally asymptotically stable. We also observed that RCovid 19<1, the system is globally asymptotically stable in the absence of disease. The main objective of this study is to investigate the COVID-19 transmission dynamics in Italy, in which the first case of Coronavirus infection 2019 (COVID-19) was identified on January 31st in 2020. We used the fractional order SEIQRD compartmental model in a fractional order framework to account for the uncertainty caused by the lack of information regarding the Coronavirus (COVID-19). The Routh-Hurwitz consistency criteria and La-Salle invariant principle are used to analyze the dynamics of the equilibrium. In addition, the fractional-order Taylor's approach is utilized to approximate the solution to the proposed model. The model's validity is demonstrated by comparing real-world data with simulation outcomes. This study considered the consequences of wearing face masks, and it was discovered that consistent use of face masks can help reduce the propagation of the COVID-19 disease.

Extinction and persistence of a stochastic delayed Covid-19 epidemic model

We formulated a Coronavirus (COVID-19) delay epidemic model with random perturbations, consisting of three different classes, namely the susceptible population, the infectious population, and the quarantine population. We studied the proposed problem to derive at least one unique solution in the positive feasweible region of the non-local solution. Sufficient conditions for the extinction and persistence of the proposed model are established. Our results show that the influence of Brownian motion and noise on the transmission of the epidemic is very large. We use the first-order stochastic Milstein scheme, taking into account the required delay of infected individuals.

Modelling and forecasting new cases of Covid-19 in Nigeria: Comparison of regression, ARIMA and machine learning models

Covid-19 remains a global pandemic threatening hundreds of countries in the world. The impact of Covid-19 has been felt in almost every aspect of life and it has introduced globally, a new normal of livelihood. This global pandemic has triggered unparalleled global health and economic crisis. Therefore, modelling and forecasting the dynamics of this pandemic is very crucial as it will help in decision making and strategic planning. Nigeria as the most populous country in Africa and most populous black nation in the world has been adversely affected by Covid-19 pandemic. This study models and compares forecasting performance of regression, ARIMA and Machine Learning models in predicting new cases of Covid-19 in Nigeria. The study obtained data on daily new cases of Covid-19 in Nigeria between 27th February, 2020 and 30th November, 2021. Graphical analysis showed that Nigeria had witnessed three waves of Covid-19 with the first wave between 27th February, 2020 and 23rd October, 2020, the second wave between 24th October, 2020 and 20th June, 2021 and the third wave between 21st June, 2021 and 30th November, 2021.The second wave recorded the highest spikes in new cases compared to the first wave and third wave. Result reveals that in terms of forecasting performance, inverse regression model outperformed other regression models considered as it shows lowest RMSE of 0.4130 compared with other regression models. Also, the ARIMA (4, 1, 4) outperformed other ARIMA models as it reveals the highest R² of 0.856 (85.6%), least RMSE (0.6364), AIC (-8.6024) and BIC (-8.5299). Result reveals that Fine tree which is one of the Machine Learning models is more reliable in forecasting new cases of Covid-19 in Nigeria compared to other models as Fine tree gave the highest R² of 0.90 (90.0%) and least RMSE of 0.22165. Result of 15 days forecasting indicates that Covid-19 pandemic is not over yet in Nigeria as new cases of Covid-19 is projected to increase on 15/12/2021 with predicted new cases of 988 compared with that of 14/12/2021, where only 729 new cases was predicted. This therefore emphasizes the need to strengthen and maintain the existing Covid-19 preventive measures in Nigeria.

Using simulation modelling and systems science to help contain COVID-19: A systematic review

This study systematically reviews applications of three simulation approaches, that is, system dynamics model (SDM), agent-based model (ABM) and discrete event simulation (DES), and their hybrids in COVID-19 research and identifies theoretical and application innovations in public health. Among the 372 eligible papers, 72 focused on COVID-19 transmission dynamics, 204 evaluated both pharmaceutical and non-pharmaceutical interventions, 29 focused on the prediction of the pandemic and 67 investigated the impacts of COVID-19. ABM was used in 275 papers, followed by 54 SDM papers, 32 DES papers and 11 hybrid model papers. Evaluation and design of intervention scenarios are the most widely addressed area accounting for 55% of the four main categories, that is, the transmission of COVID-19, prediction of the pandemic, evaluation and design of intervention scenarios and societal impact assessment. The complexities in impact evaluation and intervention design demand hybrid simulation models that can simultaneously capture micro and macro aspects of the socio-economic systems involved.

Mathematical Analysis of COVID-19 Transmission Dynamics Model in Ghana with Double-Dose Vaccination and Quarantine

The discovery of vaccines for COVID-19 has been helpful in the fight against the spread of the disease. Even with these vaccines, the virus continues to spread in many countries, with some vaccinated persons even reported to have been infected, calling for administration of booster vaccines. The need for continued use of nonpharmaceutical interventions to complement the administration of vaccines cannot therefore be overemphasized. This study presents a novel mathematical model to study the impact of quarantine and double-dose vaccination on the spread of the disease. The local stability analysis of the COVID-19-free and endemic equilibria is examined using the Lyapunov second technique. The equilibria are found to be locally asymptotically stable if ℛ 0 < 1 and ℛ 0 > 1, respectively. Besides other analytical results, numerical simulations are performed to illustrate the analytical results established in the paper.

Modeling of COVID-19 spread with self-isolation at home and hospitalized classes

This work examines the impacts of self-isolation and hospitalization on the population dynamics of the Corona-Virus Disease. We developed a new nonlinear deterministic model eight classes compartment, with self-isolation and hospitalized being the most effective tools. There are (Susceptible S C ( t ) , Exposed E ( t ) , Asymptomatic infected I A ( t ) , Symptomatic infected A S ( t ) , Self-isolation T M ( t ) , Hospitalized T H ( t ) , Healed H ( t ) , and Susceptible individuals previously infected H C ( t ) ). The expression of basic reproduction number R 0 comes from the next-generation matrix method. With suitably constructed Lyapunov functions, the global asymptotic stability of the non-endemic equilibria Σ 0 for R 0 < 1 and that of endemic equilibria Σ ∗ for R 0 > 1 are established. The computed value of R 0 = 3 . 120277403 proves the endemic level of the epidemic. The outbreak will lessen if a policy is enforced like self-isolation and hospitalization. This is related to those policies that can reduce the number of direct contacts between infected and susceptible individuals or waning immunity individuals. Various simulations are presented to appreciate self-isolation at home and hospitalized strategies if applied sensibly. By performing a global sensitivity analysis, we can obtain parameter values that affect the model through a combination of Latin Hypercube Sampling and Partial Rating Correlation Coefficients methods to determine the parameters that affect the number of reproductions and the increase in the number of COVID cases. The results obtained show that the rate of self-isolation at home and the rate of hospitalism have a negative relationship. On the other hand, infections will decrease when the two parameters increase. From the sensitivity of the results, we formulate a control model using optimal control theory by considering two control variables. The result shows that the control strategies minimize the spread of the COVID infection in the population.

A new versatile modification of the Rayleigh distribution for modeling COVID-19 mortality rates

The aim of this paper is to specify a new flexible statistical model to analyze COVID-19 mortality rates in Italy and Canada. A new versatile lifetime distribution with four parameters is proposed by using the exponentiated generalized class of distributions and the gull alpha power Rayleigh distribution to form the exponentiated generalized gull alpha power Rayleigh (EGGAPR) distribution. This new distribution is characterized by a tractable cumulative distribution function. To estimate the unknown parameters of the proposed distribution the maximum likelihood estimation method is used. In evaluating the effectiveness of the MLE method graphical displays of the Monte Carlo simulation are presented. The EGGAPR distribution is compared to its sub-models which include the exponentiated gull alpha Rayleigh distribution, the gull alpha Rayleigh distribution, exponentiated generalized Rayleigh distribution, exponentiated Rayleigh distribution and the Rayleigh distribution. Different measures of goodness-of-fit are used to investigate whether the EGGAPR distribution is more flexible and fit than its sub-models in modeling COVID-19 mortality rates.

Stochastic COVID-19 SEIQ epidemic model with time-delay

In this work, we consider an epidemic model for corona-virus (COVID-19) with random perturbations as well as time delay, composed of four different classes of susceptible population, the exposed population, the infectious population and the quarantine population. We investigate the proposed problem for the derivation of at least one and unique solution in the positive feasible region of non-local solution. For one stationary ergodic distribution, the necessary result of existence is developed by applying the Lyapunov function in the sense of delay-stochastic approach and the condition for the extinction of the disease is also established. Our obtained results show that the effect of Brownian motion and noise terms on the transmission of the epidemic is very high. If the noise is large the infection may decrease or vanish. For validation of our obtained scheme, the results for all the classes of the problem have been numerically simulated.

Optimal control for COVID-19 pandemic with quarantine and antiviral therapy

In the absence of a proper cure for the disease, the recent pandemic caused by COVID-19 has been focused on isolation strategies and government measures to control the disease, such as lockdown, media coverage, and improve public hygiene. Mathematical models can help when these intervention mechanisms find some optimal strategies for controlling the spread of such diseases. We propose a set of nonlinear dynamic systems with optimal strategy including practical measures to limit the spread of the virus and to diagnose and isolate infected people while maintaining consciousness for citizens. We have used Pontryagin's maximum principle and solved our system by the finite difference method. In the end, several numerical simulations have been executed to verify the proposed model using Matlab. Also, we pursued the resilience of the parameters of control of the nonlinear dynamic systems, so that we can easily handle the pandemic situation.

A vigorous study of fractional order COVID-19 model via ABC derivatives

The newly arose irresistible sickness known as the Covid illness (COVID-19), is a highly infectious viral disease. This disease caused millions of tainted cases internationally and still represent a disturbing circumstance for the human lives. As of late, numerous mathematical compartmental models have been considered to even more likely comprehend the Covid illness. The greater part of these models depends on integer-order derivatives which cannot catch the fading memory and crossover behavior found in many biological phenomena. Along these lines, the Covid illness in this paper is studied by investigating the elements of COVID-19 contamination utilizing the non-integer Atangana-Baleanu-Caputo derivative. Using the fixed-point approach, the existence and uniqueness of the integral of the fractional model for COVID is further deliberated. Along with Ulam-Hyers stability analysis, for the given model, all basic properties are studied. Furthermore, numerical simulations are performed using Newton polynomial and Adams Bashforth approaches for determining the impact of parameters change on the dynamical behavior of the systems.

Modeling the survival times of the COVID-19 patients with a new statistical model: A case study from China

Over the past few months, the spread of the current COVID-19 epidemic has caused tremendous damage worldwide, and unstable many countries economically. Detailed scientific analysis of this event is currently underway to come. However, it is very important to have the right facts and figures to take all possible actions that are needed to avoid COVID-19. In the practice and application of big data sciences, it is always of interest to provide the best description of the data under consideration. The recent studies have shown the potential of statistical distributions in modeling data in applied sciences, especially in medical science. In this article, we continue to carry this area of research, and introduce a new statistical model called the arcsine modified Weibull distribution. The proposed model is introduced using the modified Weibull distribution with the arcsine-X approach which is based on the trigonometric strategy. The maximum likelihood estimators of the parameters of the new model are obtained and the performance these estimators are assessed by conducting a Monte Carlo simulation study. Finally, the effectiveness and utility of the arcsine modified Weibull distribution are demonstrated by modeling COVID-19 patients data. The data set represents the survival times of fifty-three patients taken from a hospital in China. The practical application shows that the proposed model out-classed the competitive models and can be chosen as a good candidate distribution for modeling COVID-19, and other related data sets.

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.