A Well-Posed Fractional Order Cholera Model with Saturated Incidence Rate.

A fractional-order cholera model in the Caputo sense is constructed. The model is an extension of the Susceptible-Infected-Recovered (SIR) epidemic model. The transmission dynamics of the disease are studied by incorporating the saturated incidence rate into the model. This is particularly important since assuming that the increase in incidence for a large number of infected individualsis equivalent to a small number of infected individualsdoes not make much sense. The positivity, boundedness, existence, and uniqueness of the solution of the model are also studied. Equilibrium solutions are computed, and their stability analyses are shown to depend on a threshold quantity, the basic reproduction ratio (R0). It is clearly shown that if R0<1, the disease-free equilibrium is locally asymptotically stable, whereas if R0>1, the endemic equilibrium exists and is locally asymptotically stable. Numerical simulations are carried out to support the analytic results and to show the significance of the fractional order from the biological point of view. Furthermore, the significance of awareness is studied in the numerical section.

Evaluating the impact of double dose vaccination on SARS-CoV-2 spread through optimal control analysis.

This paper presents a new nonlinear epidemic model for the spread of SARS-CoV-2 that incorporates the effect of double dose vaccination. The model is analyzed using qualitative, stability, and sensitivity analysis techniques to investigate the impact of vaccination on the spread of the virus. We derive the basic reproduction number and perform stability analysis of the disease-free and endemic equilibrium points. The model is also subjected to sensitivity analysis to identify the most influential model parameters affecting the disease dynamics. The values of the parameters are estimated with the help of the least square curve fitting tools. Finally, the model is simulated numerically to assess the effectiveness of various control strategies, including vaccination and quarantine, in reducing the spread of the virus. Optimal control techniques are employed to determine the optimal allocation of resources for implementing control measures. Our results suggest that increasing the vaccination coverage, adherence to quarantine measures, and resource allocation are effective strategies for controlling the epidemic. The study provides valuable insights into the dynamics of the pandemic and offers guidance for policymakers in formulating effective control measures.

Role of Vaccines in Controlling the Spread of COVID-19: A Fractional-Order Model.

In this paper, we present a fractional-order mathematical model in the Caputo sense to investigate the significance of vaccines in controlling COVID-19. The Banach contraction mapping principle is used to prove the existence and uniqueness of the solution. Based on the magnitude of the basic reproduction number, we show that the model consists of two equilibrium solutions that are stable. The disease-free and endemic equilibrium points are locally stably when R0<1 and R0>1 respectively. We perform numerical simulations, with the significance of the vaccine clearly shown. The changes that occur due to the variation of the fractional order α are also shown. The model has been validated by fitting it to four months of real COVID-19 infection data in Thailand. Predictions for a longer period are provided by the model, which provides a good fit for the data.

Computational modeling of fractional COVID-19 model by Haar wavelet collocation Methods with real data.

This study explores the use of numerical simulations to model the spread of the Omicron variant of the SARS-CoV-2 virus using fractional-order COVID-19 models and Haar wavelet collocation methods. The fractional order COVID-19 model considers various factors that affect the virus's transmission, and the Haar wavelet collocation method offers a precise and efficient solution to the fractional derivatives used in the model. The simulation results yield crucial insights into the Omicron variant's spread, providing valuable information to public health policies and strategies designed to mitigate its impact. This study marks a significant advancement in comprehending the COVID-19 pandemic's dynamics and the emergence of its variants. The COVID-19 epidemic model is reworked utilizing fractional derivatives in the Caputo sense, and the model's existence and uniqueness are established by considering fixed point theory results. Sensitivity analysis is conducted on the model to identify the parameter with the highest sensitivity. For numerical treatment and simulations, we apply the Haar wavelet collocation method. Parameter estimation for the recorded COVID-19 cases in India from 13 July 2021 to 25 August 2021 has been presented.

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.

Modeling the dynamics of COVID-19 with real data from Thailand.

In recent years, COVID-19 has evolved into many variants, posing new challenges for disease control and prevention. The Omicron variant, in particular, has been found to be highly contagious. In this study, we constructed and analyzed a mathematical model of COVID-19 transmission that incorporates vaccination and three different compartments of the infected population: asymptomatic [Formula: see text], symptomatic [Formula: see text], and Omicron [Formula: see text]. The model is formulated in the Caputo sense, which allows for fractional derivatives that capture the memory effects of the disease dynamics. We proved the existence and uniqueness of the solution of the model, obtained the effective reproduction number, showed that the model exhibits both endemic and disease-free equilibrium points, and showed that backward bifurcation can occur. Furthermore, we documented the effects of asymptomatic infected individuals on the disease transmission. We validated the model using real data from Thailand and found that vaccination alone is insufficient to completely eradicate the disease. We also found that Thailand must monitor asymptomatic individuals through stringent testing to halt and subsequently eradicate the disease. Our study provides novel insights into the behavior and impact of the Omicron variant and suggests possible strategies to mitigate its spread.

Imputation of missing daily rainfall data; A comparison between artificial intelligence and statistical techniques.

Handling missing values is a critical component of the data processing in hydrological modeling. The key objective of this research is to assess statistical techniques (STs) and artificial intelligence-based techniques (AITs) for imputing missing daily rainfall values and recommend a methodology applicable to the mountainous terrain of northern Thailand. In this study, 30 years of daily rainfall data was collected from 20 rainfall stations in northern Thailand and randomly 25-35 % of data was deleted from four target stations based on Spearman correlation coefficient between the target and neighboring stations. Imputation models were developed on training and testing datasets and statistically evaluated by mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R2), and correlation coefficient (r). This study used STs, including arithmetic averaging (AA), multiple linear regression (MLR), normal-ratio (NR), nonlinear iterative partial least squares (NIPALS) algorithm, and linear interpolation was used.•STs results were compared with AITs, including long-short-term-memory recurrent neural network (LSTM-RNN), M5 model tree (M5-MT), multilayer perceptron neural networks (MLPNN), support vector regression with polynomial and radial basis function SVR-poly and SVR-RBF.•The findings revealed that MLR imputation model achieved an average MAE of 0.98, RMSE of 4.52, and R2 was about 79.6 % at all target stations. On the other hand, for the M5-MT model, the average MAE was 0.91, RMSE was about 4.52, and R2 was around 79.8 % compared to other STs and AITs. M5-MT was most prominent among AITs. Notably, the MLR technique stood out as a recommended approach due to its ability to deliver good estimation results while offering a transparent mechanism and not necessitating prior knowledge for model creation.

Fractional dynamics and stability analysis of COVID-19 pandemic model under the harmonic mean type incidence rate.

In this research, COVID-19 model is formulated by incorporating harmonic mean type incidence rate which is more realistic in average speed. Basic reproduction number, equilibrium points, and stability of the proposed model is established under certain conditions. Runge-Kutta fourth order approximation is used to solve the deterministic model. The model is then fractionalized by using Caputo-Fabrizio derivative and the existence and uniqueness of the solution are proved by using Banach and Leray-Schauder alternative type theorems. For the fractional numerical simulations, we use the Adam-Moulton scheme. Sensitivity analysis of the proposed deterministic model is studied to identify those parameters which are highly influential on basic reproduction number.

COVID-19 Model with High- and Low-Risk Susceptible Population Incorporating the Effect of Vaccines.

It is a known fact that there are a particular set of people who are at higher risk of getting COVID-19 infection. Typically, these high-risk individuals are recommended to take more preventive measures. The use of non-pharmaceutical interventions (NPIs) and the vaccine are playing a major role in the dynamics of the transmission of COVID-19. We propose a COVID-19 model with high-risk and low-risk susceptible individuals and their respective intervention strategies. We find two equilibrium solutions and we investigate the basic reproduction number. We also carry out the stability analysis of the equilibria. Further, this model is extended by considering the vaccination of some non-vaccinated individuals in the high-risk population. Sensitivity analyses and numerical simulations are carried out. From the results, we are able to obtain disease-free and endemic equilibrium solutions by solving the system of equations in the model and show their global stabilities using the Lyapunov function technique. The results obtained from the sensitivity analysis shows that reducing the hospitals' imperfect efficacy can have a positive impact on the control of COVID-19. Finally, simulations of the extended model demonstrate that vaccination could adequately control or eliminate COVID-19.

A Fractional Order Model Studying the Role of Negative and Positive Attitudes towards Vaccination.

A fractional-order model consisting of a system of four equations in a Caputo-Fabrizio sense is constructed. This paper investigates the role of negative and positive attitudes towards vaccination in relation to infectious disease proliferation. Two equilibrium points, i.e., disease-free and endemic, are computed. Basic reproduction ratio is also deducted. The existence and uniqueness properties of the model are established. Stability analysis of the solutions of the model is carried out. Numerical simulations are carried out and the effects of negative and positive attitudes towards vaccination areclearly shown; the significance of the fractional-order from the biological point of view is also established. The positive effect of increasing awareness, which in turn increases positive attitudes towards vaccination, is also shown numerically.The results show that negative attitudes towards vaccination increase infectious disease proliferation and this can only be limited by mounting awareness campaigns in the population. It is also clear from our findings that the high vaccine hesitancy during the COVID-19 pandemicisan important problem, and further efforts should be madeto support people and give them correct information about vaccines.

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.

Exploring the nanomechanical concepts of development through recent updates in magnetically guided system.

This article outlines an analytical analysis of unsteady mixed bioconvection buoyancy-driven nanofluid thermodynamics and gyrotactic microorganisms motion in the stagnation domain of the impulsively rotating sphere with convective boundary conditions. To make the equations physically realistic, zero mass transfer boundary conditions have been used. The Brownian motion and thermophoresis effects are incorporated in the nanofluid model. Magnetic dipole effect has been implemented. A system of partial differential equations is used to represent thermodynamics and gyrotactic microorganisms motion, which is then transformed into dimensionless ordinary differential equations. The solution methodology is involved by homotopy analysis method. The results obtained are based on the effect of dimensionless parameters on the velocity, temperature, nanoparticles concentration and density of the motile microorganisms profiles. The primary velocity increases as the mixed convection and viscoelastic parameters are increased while it decreases as the buoyancy ratio, ferro-hydrodynamic interaction and rotation parameters are increased. The secondary velocity decreases as viscoelastic parameter increases while it increases as the rotation parameter increases. Temperature is reduced as the Prandtl number and thermophoresis parameter are increased. The nanoparticles concentration is increased as the Brownian motion parameter increases. The motile density of gyrotactic microorganisms increases as the bioconvection Rayleigh number, rotation parameter and thermal Biot number are increased.

Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function.

In this paper, we consider a fractional COVID-19 epidemic model with a convex incidence rate. The Atangana-Baleanu fractional operator in the Caputo sense is taken into account. We establish the equilibrium points, basic reproduction number, and local stability at both the equilibrium points. The existence and uniqueness of the solution are proved by using Banach and Leray-Schauder alternative type theorems. For the fractional numerical simulations, we use the Toufik-Atangana scheme. Optimal control analysis is carried out to minimize the infection and maximize the susceptible people.

Computational optimization for the deposition of bioconvection thin Oldroyd-B nanofluid with entropy generation.

The behavior of an Oldroyd-B nanoliquid film sprayed on a stretching cylinder is investigated. The system also contains gyrotactic microorganisms with heat and mass transfer flow. Similarity transformations are used to make the governing equations non-dimensional ordinary differential equations and subsequently are solved through an efficient and powerful analytic technique namely homotopy analysis method (HAM). The roles of all dimensionless profiles and spray rate have been investigated. Velocity decreases with the magnetic field strength and Oldroyd-B nanofluid parameter. Temperature is increased with increasing the Brownian motion parameter while it is decreased with the increasing values of Prandtl and Reynolds numbers. Nanoparticle's concentration is enhanced with the higher values of Reynolds number and activation energy parameter. Gyrotactic microorganism density increases with bioconvection Rayleigh number while it decreases with Peclet number. The film size naturally increases with the spray rate in a nonlinear way. A close agreement is achieved by comparing the present results with the published results.