An epidemiological model for analysing pandemic trends of novel coronavirus transmission with optimal control.

Symptomatic and asymptomatic individuals play a significant role in the transmission dynamics of novel Coronaviruses. By considering the dynamical behaviour of symptomatic and asymptomatic individuals, this study examines the temporal dynamics and optimal control of Coronavirus disease propagation using an epidemiological model. Biologically and mathematically, the well-posed epidemic problem is examined, as well as the threshold quantity with parameter sensitivity. Model parameters are quantified and their relative impact on the disease is evaluated. Additionally, the steady states are investigated to determine the model's stability and bifurcation. Using the dynamics and parameters sensitivity, we then introduce optimal control strategies for the elimination of the disease. Using real disease data, numerical simulations and model validation are performed to support theoretical findings and show the effects of control strategies.

Modelling the dynamics of acute and chronic hepatitis B with optimal control.

This article examines hepatitis B dynamics under distinct infection phases and multiple transmissions. We formulate the epidemic problem based on the characteristics of the disease. It is shown that the epidemiological model is mathematically and biologically meaningful of its well-posedness (positivity, boundedness, and biologically feasible region). The reproductive number is then calculated to find the equilibria and the stability analysis of the epidemic model is performed. A backward bifurcation is also investigated in the proposed epidemic problem. With the help of two control measures (treatment and vaccination), we develop control strategies to minimize the infected population (acute and chronic). To solve the proposed control problem, we utilize Pontryagin's Maximum Principle. Some simulations are conducted to illustrate the investigation of the analytical work and the effect of control analysis.

Dynamics of a Fractional-Order Delayed Model of COVID-19 with Vaccination Efficacy.

In this study, we provide a fractional-order mathematical model that considers the effect of vaccination on COVID-19 spread dynamics. The model accounts for the latent period of intervention strategies by incorporating a time delay τ. A basic reproduction number, R0, is determined for the model, and prerequisites for endemic equilibrium are discussed. The model's endemic equilibrium point also exhibits local asymptotic stability (under certain conditions), and a Hopf bifurcation condition is established. Different scenarios of vaccination efficacy are simulated. As a result of the vaccination efforts, the number of deaths and those affected have decreased. COVID-19 may not be effectively controlled by vaccination alone. To control infections, several non-pharmacological interventions are necessary. Based on numerical simulations and fitting to real observations, the theoretical results are proven to be effective.

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.

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.

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.

Analysis and control of Aedes Aegypti mosquitoes using sterile-insect techniques with Wolbachia.

Combining Sterile and Incompatible Insect techniques can significantly reduce mosquito populations and prevent the transmission of diseases between insects and humans. This paper describes impulsive differential equations for the control of a mosquito with Wolbachia. Several interesting conditions are created when sterile male mosquitoes are released impulsively, ensuring both open- and closed-loop control. To determine the wild mosquito population size in real-time, we propose an open-loop control system, which uses impulsive and constant releases of sterile male mosquitoes. A closed-loop control scheme is also being investigated, which specifies the release of sterile mosquitoes according to the size of the wild mosquito population. To eliminate or reduce a mosquito population below a certain threshold, the Sterile insect technique involves mass releases of sterile insects. Numerical simulations verify the theoretical results.

A fractional-order model with different strains of COVID-19.

This study examines the dynamics of COVID-19 variants using a Caputo-Fabrizio fractional order model. The reproduction ratio R 0 and equilibrium solutions are determined. The purpose of this article is to use a non-integer order derivative in order to present information about the model solutions, uniqueness, and existence using a fixed point theory. A detailed analysis of the existence and uniqueness of the model solution is conducted using fixed point theory. For the computation of the iterative solution of the model, the fractional Adams-Bashforth method is used. Using the estimated values of the model parameters, numerical results are used to support the significance of the fractional-order derivative. The graphs provide useful information about the complexity of the model, and provide reliable information about the model for any case, integer or non-integer. Also, we demonstrate that any variant with the largest basic reproduction ratio will automatically outperform the other variant.

Fractional-order discontinuous systems with indefinite LKFs: An application to fractional-order neural networks with time delays.

In this article, we discuss bipartite fixed-time synchronization for fractional-order signed neural networks with discontinuous activation patterns. The Filippov multi-map is used to convert the fixed-time stability of the fractional-order general solution into the zero solution of the fractional-order differential inclusions. On the Caputo fractional-order derivative, Lyapunov-Krasovskii functional is proved to possess the indefinite fractional derivatives for fixed-time stability of fragmentary discontinuous systems. Furthermore, the fixed-time stability of the fractional-order discontinuous system is achieved as well as an estimate of the new settling time.. The discontinuous controller is designed for the delayed fractional-order discontinuous signed neural networks with antagonistic interactions and new conditions for permanent fixed-time synchronization of these networks with antagonistic interactions are also provided, as well as the settling time for permanent fixed-time synchronization. Two numerical simulation results are presented to demonstrate the effectiveness of the main results.

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.

Analysis of a stochastic HBV infection model with delayed immune response.

Considering the environmental factors and uncertainties, we propose, in this paper, a higher-order stochastically perturbed delay differential model for the dynamics of hepatitis B virus (HBV) infection with immune system. Existence and uniqueness of an ergodic stationary distribution of positive solution to the system are investigated, where the solution fluctuates around the endemic equilibrium of the deterministic model and leads to the stochastic persistence of the disease. Under some conditions, infection-free can be obtained in which the disease dies out exponentially with probability one. Some numerical simulations, by using Milstein's scheme, are carried out to show the effectiveness of the obtained results. The intensity of white noise plays an important role in the treatment of infectious diseases.

Mathematical model of COVID-19 with comorbidity and controlling using non-pharmaceutical interventions and vaccination.

Pandemic is an unprecedented public health situation, especially for human beings with comorbidity. Vaccination and non-pharmaceutical interventions only remain extensive measures carrying a significant socioeconomic impact to defeating pandemic. Here, we formulate a mathematical model with comorbidity to study the transmission dynamics as well as an optimal control-based framework to diminish COVID-19. This encompasses modeling the dynamics of invaded population, parameter estimation of the model, study of qualitative dynamics, and optimal control problem for non-pharmaceutical interventions (NPIs) and vaccination events such that the cost of the combined measure is minimized. The investigation reveals that disease persists with the increase in exposed individuals having comorbidity in society. The extensive computational efforts show that mean fluctuations in the force of infection increase with corresponding entropy. This is a piece of evidence that the outbreak has reached a significant portion of the population. However, optimal control strategies with combined measures provide an assurance of effectively protecting our population from COVID-19 by minimizing social and economic costs.