Dynamics and Optimal Control of Ebola Transmission

Delving a stochastic SEQAIJR COVID-19 model with hexa delayed and copious control strategies

The actual ideal of the literature is to probe the effect of external undulation on prevalence of COVID-19. Owing to some environmental influences, we enhanced our model to the stochastic perturbations. In this article, we scrutinize a stochastic epidemic COVID-19 model with seven states of epidemiological classification. Incipiently, a sophisticated biological system with the effect of time lags put forward copious strategies. At the outset, aim of this work is to explore the existence and uniqueness of global positive solution. Moment exponential stability are upheld. By fabricating a suitable lyapunov function, the sufficient conditions for the persistence of the disease and the existence of an ergodic stationary distribution are established. To regulate the widespread of COVID-19 infection, the main intent is to curb the disease with the succor of three control measures. Finally, the theoretical results bring into being alive in the form of graphical visualization. By nurturing the comparison study, the parameters of the model system come up with real data of most afflicted countries that layout premier consequences.

Long-term effect of SARS-CoV-2 variant : Challenging issues and controlling strategies

In this study, a latest version of COVID-19 pandemic is hand overed. A Stochastic post COVID-19 delayed model is developed to explore the spread of COVID-19 as well as omicron variant with the correlation of heart attack. This article provides an eradication of the COVID-19 and omicron variant as well as the population who have heart attack after post COVID-19 of these epidemic diseases. Then the existence and uniqueness of global positive solution are studied. Ensuing, In this article, we classify COVID-19 virus and omicron variant which go to extinction and become persistent in mean. By using Lyapunov function, the existence of ergodic stationary distribution are established. Later from the persistent disease as well as extinction, heart disease are ready to develop in the human body. By Eventually, an optimal control strategies are introduced in the form of stochastic post COVID-19 delayed model to control two different types of virus. Finally, the numerical simulation are presented to determine the behavior of dynamical system by utilizing the real data of United Kingdom.

Modelling the impact of some control strategies on the transmission dynamics of Ebola virus in human-bat population: An optimal control analysis

Qualitative research and comprehensive public awareness to nip the transmission of Ebola virus in the bud before it becomes a global threat is fast becoming imperative especially now that the Gambia Ebola virus is mutated. It is therefore necessary to consider and investigate a vector-host transmission model for possible control strategy of this deadly disease. Hence, in this study, we presented a novel and feasible human-bat (host-vector) S h E h I h R h i s R h n i - S b E b I b model which foretells the spread and severity of the Ebola virus from bats to humans to investigate the combined effects of three control strategies viz: (1) allowing specialized and designated agencies to bury deceased from Ebola infection without relatives touching or curdling the remains as usually practiced in most part of Africa as last respect for their departed love ones ( k 1 ), (2) systematic and deliberate depopulation of bats in the metropolis (through persecution with pesticide exposure, pre capturing, chemical timber treatment for roosts destruction) to discourage hunting them for food by virtue of their proximity ( k 2 ) and (3) immediate treatment of infected individuals in isolation ( k 3 ). We established, among others, the endemic equilibrium, disease-free equilibrium, global and local stability, non-negativity, and boundedness of the model to prove the epidemiological feasibility of the model. The reality of the presence of optimal control remarkably influences the dynamics of transmission of the virus and simulated results also confirm the great effect of the combination of the control strategies k 1 , k 2 and k 3 in flattening the curve of Ebola transmission (fig 1 - fig 8). Health workers and policy makers are better informed with fundamental precautions that could help eradicate Ebola from the populace.

Analysis of a Fractional-Order COVID-19 Epidemic Model with Lockdown

The outbreak of the coronavirus disease (COVID-19) has caused a lot of disruptions around the world. In an attempt to control the spread of the disease among the population, several measures such as lockdown, and mask mandates, amongst others, were implemented by many governments in their countries. To understand the effectiveness of these measures in controlling the disease, several mathematical models have been proposed in the literature. In this paper, we study a mathematical model of the coronavirus disease with lockdown by employing the Caputo fractional-order derivative. We establish the existence and uniqueness of the solution to the model. We also study the local and global stability of the disease-free equilibrium and endemic equilibrium solutions. By using the residual power series method, we obtain a fractional power series approximation of the analytic solution. Finally, to show the accuracy of the theoretical results, we provide some numerical and graphical results.

Assessment of airborne transmission from coughing processes with thermal plume adjacent to body and radiators on effectiveness of social distancing

The new coronavirus disease COVID-19 has caused a worldwide pandemic to be declared in a very short period of time. The complexity of the infection lies in asymptomatic carriers that can inadvertently transmit the virus through airborne droplets. This kind of viral disease can infect the human body with tiny particles that carry various bacteria that are generated by the respiratory system of infected patients. In this study, numerical results are proposed that demonstrate the effect of human body temperature and temperature from radiators in a room on the spread of the smallest droplets and particles in an enclosed space. The numerical model proposed in this work takes into account the sedimentation of particles and droplets under the action of gravitational sedimentation and transport in a closed room during the processes of breathing, sneezing or coughing. Various cases were considered, taking into account normal human breathing, coughing or sneezing, as well as three different values of the rate of emission of particles from the human mouth. The heat plume, which affects the concentration of particles in the breathing zone, spreads the particle up to a distance of 4.29 m in the direction of the air flow. It can also be seen from the results obtained that the presence of radiators strongly affects the propagation of particles of various sizes in a closed room. From the obtained results, it should be noted that in order to recommend the optimal social distance, it is necessary to take into account many factors, especially momentum, gravity, human body temperature, as well as the process of natural convection, which greatly affect the propagation of particles in a closed room. The conclusions drawn from the results of this work show that, given the environmental conditions, the social distance of 2 m may not be enough.

Modeling and analysis on the transmission of covid-19 Pandemic in Ethiopia

The newest infection is a novel coronavirus named COVID-19, that initially appeared in December 2019, in Wuhan, China, and is still challenging to control. The main focus of this paper is to investigate a novel fractional-order mathematical model that explains the behavior of COVID-19 in Ethiopia. Within the proposed model, the entire population is divided into nine groups, each with its own set of parameters and initial values. A nonlinear system of fractional differential equations for the model is represented using Caputo fractional derivative. Legendre spectral collocation method is used to convert this system into an algebraic system of equations. An inexact Newton iterative method is used to solve the model system. The effective reproduction number (R0) is computed by the next-generation matrix approach. Positivity and boundedness, as well as the existence and uniqueness of solution, are all investigated. Both endemic and disease-free equilibrium points, as well as their stability, are carefully studied. We calculated the parameters and starting conditions (ICs) provided for our model using data from the Ethiopian Public Health Institute (EPHI) and the Ethiopian Ministry of Health from 22 June 2020 to 28 February 2021. The model parameters are determined using least squares curve fitting and MATLAB R2020a is used to run numerical results. The basic reproduction number is R0=1.4575. For this value, disease free equilibrium point is asymptotically unstable and endemic equilibrium point is asymptotically stable, both locally and globally.

Fractional-order backstepping strategy for fractional-order model of COVID-19 outbreak

The coronavirus disease (COVID-19) pandemic has impacted many nations around the world. Recently, new variant of this virus has been identified that have a much higher rate of transmission. Although vaccine production and distribution are currently underway, non-pharmacological interventions are still being implemented as an important and fundamental strategy to control the spread of the virus in countries around the world. To realize and forecast the transmission dynamics of this disease, mathematical models can be very effective. Various mathematical modeling methods have been proposed to investigate the transmission patterns of this new infection. In this paper, we utilized the fractional-order dynamics of COVID-19. The goal is to control the prevalence of the disease using non-pharmacological interventions. In this paper, a novel fractional-order backstepping sliding mode control (FOBSMC) is proposed for non-pharmacological decisions. Recently, new variant of this virus have been identified that have a much higher rate of transmission, so finally the effectiveness of the proposed controller in the presence of new variant of COVID-19 is investigated.

Mathematical analysis of a model of Ebola disease with control measures

The re-emergence of the Ebola virus disease has pushed researchers to investigate more on this highly deadly disease in order to better understand and control the outbreak and recurrence of epidemics. It is in this perspective that we formulate a realistic mathematical model for the dynamic transmission of Ebola virus disease, incorporating relevant control measures and factors such as ban on eating bush-meat, social distancing, observance of hygiene rules and containment, waning of the vaccine-induced, imperfect contact tracing and vaccine efficacy, quarantine, hospitalization and screening to fight against the spread of the disease. First, by considering the constant control parameters case, we thoroughly compute the control reproduction number [Formula: see text] from which the dynamics of the model is analyzed. The existence and stability of steady states are established under appropriate assumptions on [Formula: see text]. Also, the effect of all the control measures is investigated and the global sensitivity analysis of the control reproduction number is performed in order to determine the impact of parameters and their relative importance to disease transmission and prevalence. Second, in the time-dependent control parameters case, an optimal control problem is formulated to design optimal control strategies for eradicating the disease transmission. Using Pontryagin’s Maximum Principle, we derive necessary conditions for optimal control of the disease. The cost-effectiveness analysis of all combinations of the control measures is made by calculating the infection averted ratio and the incremental cost-effectiveness ratio. This reveals that combining the four restrictive measures conveyed through educational campaigns, screening, safe burial and the care of patients in health centers for better isolation is the most cost-effective among the strategies considered. Numerical simulations are performed to illustrate the theoretical results obtained.

FRACTIONAL ORDER MODEL FOR THE CORONAVIRUS (COVID-19) IN WUHAN, CHINA

In this paper, the mathematical modeling of five different classes for coronavirus disease-19 (COVID-19) is considered using the fractional arbitrary order derivative in Atangana–Baleanu sense. We use nonlinear analysis for the existence theory of the solution for the suggested model. Additionally, the modified Adam–Bashforth method is used for the numerical approximation of the assumed model. Finally, we simulate the results for 100 days with the help of data from the literature to display the excellency of the suggested model.

A Reliable Solution of Nonlinear Time Dependent Fractional Model of Ebola Virus Disease with Arbitrary Order Derivative in Liouville-Caputo Sense

In this article, the analysis of an arbitrary order Ebola virus disease model is conducted to find out its reliable solution. The fractional derivative is taken in Liouville-Caputo sense. The solution of this nonlinear model is achieved using fractional variational iteration scheme. The convergence analysis of the obtained solution is also presented which confirms that it is positive, bounded and convergent. The outcomes are discussed with figures explaining variation of susceptible, infected, recovered population and number of disease induced deaths with time. The negligible error in successive iterations of various population shows the competency of the presented scheme. The results endorse that FVIM is extremely effective, powerful and easy in usage.

Stability Analysis and Existence of Solutions for a Modified SIRD Model of COVID-19 with Fractional Derivatives

This paper discusses and provides some analytical studies for a modified fractional-order SIRD mathematical model of the COVID-19 epidemic in the sense of the Caputo–Katugampola fractional derivative that allows treating of the biological models of infectious diseases and unifies the Hadamard and Caputo fractional derivatives into a single form. By considering the vaccine parameter of the suspected population, we compute and derive several stability results based on some symmetrical parameters that satisfy some conditions that prevent the pandemic. The paper also investigates the problem of the existence and uniqueness of solutions for the modified SIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.

Caputo SIR model for COVID-19 under optimized fractional order

Everyone is talking about coronavirus from the last couple of months due to its exponential spread throughout the globe. Lives have become paralyzed, and as many as 180 countries have been so far affected with 928,287 (14 September 2020) deaths within a couple of months. Ironically, 29,185,779 are still active cases. Having seen such a drastic situation, a relatively simple epidemiological SIR model with Caputo derivative is suggested unlike more sophisticated models being proposed nowadays in the current literature. The major aim of the present research study is to look for possibilities and extents to which the SIR model fits the real data for the cases chosen from 1 April to 15 March 2020, Pakistan. To further analyze qualitative behavior of the Caputo SIR model, uniqueness conditions under the Banach contraction principle are discussed and stability analysis with basic reproduction number is investigated using Ulam-Hyers and its generalized version. The best parameters have been obtained via the nonlinear least-squares curve fitting technique. The infectious compartment of the Caputo SIR model fits the real data better than the classical version of the SIR model (Brauer et al. in Mathematical Models in Epidemiology 2019). Average absolute relative error under the Caputo operator is about 48% smaller than the one obtained in the classical case ( ν = 1 ). Time series and 3D contour plots offer social distancing to be the most effective measure to control the epidemic.

Numerical simulation of the novel coronavirus spreading

The COVID-19 virus outbreak has affected most of the world in 2020. This paper deals with artificial intelligence (AI) methods that can address the problem of predicting scale, dynamics and sensitivity of the outbreak to preventive actions undertaken with a view to combatting the epidemic. In our study, we developed a cellular automata (CA) model for simulating the COVID-19 disease spreading. The enhanced infectious disease dynamics  S E I R (Susceptible, Exposed, Infectious, and Recovered) model was applied to estimate the epidemic trends in Poland, France, and Spain. We introduced new parameters into the simulation framework which reflect the statistically confirmed dependencies such as age-dependent death probability, a different definition of the contact rate and enhanced parameters reflecting population mobility. To estimate key epidemiological measures and to predict possible dynamics of the disease, we juxtaposed crucial CA framework parameters to the reported COVID-19 values, e.g. length of infection, mortality rates and the reproduction number. Moreover, we used real population density and age structures of the studied epidemic populations. The model presented allows for the examination of the effectiveness of preventive actions and their impact on the spreading rate and the duration of the disease. It also shows the influence of structure and behavior of the populations studied on key epidemic parameters, such as mortality and infection rates. Although our results are critically dependent on the assumptions underpinning our model and there is considerable uncertainty associated with the outbreaks at such an early epidemic stage, the obtained simulation results seem to be in general agreement with the observed behavior of the real COVID-19 disease, and our numerical framework can be effectively used to analyze the dynamics and efficacy of epidemic containment methods.

A fractional order epidemic model for the simulation of outbreaks of Ebola

The Ebola outbreak in 2014 caused many infections and deaths. Some literature works have proposed some models to study Ebola virus, such as SIR, SIS, SEIR, etc. It is proved that the fractional order model can describe epidemic dynamics better than the integer order model. In this paper, we propose a fractional order Ebola system and analyze the nonnegative solution, the basic reproduction number R 0 , and the stabilities of equilibrium points for the system firstly. In many studies, the numerical solutions of some models cannot fit very well with the real data. Thus, to show the dynamics of the Ebola epidemic, the Gorenflo-Mainardi-Moretti-Paradisi scheme (GMMP) is taken to get the numerical solution of the SEIR fractional order Ebola system and the modified grid approximation method (MGAM) is used to acquire the parameters of the SEIR fractional order Ebola system. We consider that the GMMP method may lead to absurd numerical solutions, so its stability and convergence are given. Then, the new fractional orders, parameters, and the root-mean-square relative error g ( U ∗ ) = 0.4146 are obtained. With the new fractional orders and parameters, the numerical solution of the SEIR fractional order Ebola system is closer to the real data than those models in other literature works. Meanwhile, we find that most of the fractional order Ebola systems have the same order. Hence, the fractional order Ebola system with different orders using the Caputo derivatives is also studied. We also adopt the MGAM algorithm to obtain the new orders, parameters, and the root-mean-square relative error which is g ( U ∗ ) = 0.2744 . With the new parameters and orders, the fractional order Ebola systems with different orders fit very well with the real data.

An optimal control model of the spread of the COVID-19 pandemic in Iraq: Deterministic and chance-constrained model

Many studies have attempted to understand the true nature of COVID-19 and the factors influencing the spread of the virus. This paper investigates the possible effect the COVID-19 pandemic spreading in Iraq considering certain factors, that include isolation and weather. A mathematical model of cases representing inpatients, recovery, and mortality was used in formulating the control variable in this study to describe the spread of COVID-19 through changing weather conditions between 17th March and 15th May, 2020. Two models having deterministic and an uncertain number of daily cases were used in which the solution for the model using the Pontryagin maximum principle (PMP) was derived. Additionally, an optimal control model for isolation and each factor of the weather factors was also achieved. The results simulated the reality of such an event in that the cases increased by 118%, with an increase in the number of people staying outside of their house by 25%. Further, the wind speed and temperature had an inverse effect on the spread of COVID-19 by 1.28% and 0.23%, respectively. The possible effect of the weather factors with the uncertain number of cases was higher than the deterministic number of cases. Accordingly, the model developed in this study could be applied in other countries using the same factors or by introducing other factors.

Fractional order mathematical modeling of novel corona virus (COVID-19)

In this manuscript, the mathematical model of COVID-19 is considered with eight different classes under the fractional-order derivative in Caputo sense. A couple of results regarding the existence and uniqueness of the solution for the proposed model is presented. Furthermore, the fractional-order Taylor's method is used for the approximation of the solution of the concerned problem. Finally, we simulate the results for 50 days with the help of some available data for fractional differential order to display the excellency of the proposed model.

Mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data

We discuss a fractional-order SIRD mathematical model of the COVID-19 disease in the sense of Caputo in this article. We compute the basic reproduction number through the next-generation matrix. We derive the stability results based on the basic reproduction number. We prove the results of the solution existence and uniqueness via fixed point theory. We utilize the fractional Adams-Bashforth method for obtaining the approximate solution of the proposed model. We illustrate the obtained numerical results in plots to show the COVID-19 transmission dynamics. Further, we compare our results with some reported real data against confirmed infected and death cases per day for the initial 67 days in Wuhan city.

An optimal control model of COVID-19 pandemic: a comparative study of five countries

This paper formulates an optimal control model of COVID-19 pandemic spreading. We discuss the health sector performance of Argentina, Hungary, Egypt, Malaysia, and Iraq. A mathematical model describes an actual case number of COVID-19. We investigate three strategies depend on recovery rate, death rate, and together (optimal). These strategies represent the percent of the health sector development. The explicit solution of the model using the Pontryagin maximum principle is derived. The results showed the ranking of countries based on the new percent of the recovery and death cases. A new percent as a result to the control variable value (health sector development). Also, the development percent of the health sector of each country, was determined. For example, 0.005 led to a significant reduce the death rates in Malaysia. Meanwhile, a half of death rates could reduce by this percent in Egypt.

Mathematical model to assess the imposition of lockdown during COVID-19 pandemic

Nigeria, like most other countries in the world, imposes lockdown as a measure to curtail the spread of COVID-19. But, it is known fact that in some countries the lockdown strategy could bring the desired results while in some the situation could worsen the spread of the virus due to poor management and lack of facilities, palliatives and incentives. To this regard, we feel motivated to develop a new mathematical model that assesses the imposition of the lockdown in Nigeria. The model comprises of a system of five ODE. Mathematical analysis of the model were carried out, where boundedness, computation of equilibria, calculation of the basic reproduction ratio and stability analysis of the equilibria were carried out. We finally study the numerical outcomes of the governing model in respect of the approximate solutions. To this aim, we employed the effective ODE45, Euler, RK-2 and RK-4 schemes and compare the results.

Study of transmission dynamics of COVID-19 mathematical model under ABC fractional order derivative

The current research work is devoted to address some results related to the existence and stability as well as numerical finding of a novel Coronavirus disease (COVID-19) by using a mathematical model. By using fixed point results we establish existence results for the proposed model under Atangana-Baleanu-Caputo (ABC) derivative with fractional order. Further, using the famous numerical technique due to Adams Bashforth, we simulate the concerned results for two famous cities of China known as Wuhan and Huanggang which are interconnected cities. The graphical presentations are given to observe the transmission dynamics from February 1 a=2020 to April 20, 2020 through various fractional order. The concerned dynamics is global in nature due to the various values of fractional order.

Mathematical modeling for the outbreak of the coronavirus (COVID-19) under fractional nonlocal operator

A mathematical model for the spread of the COVID-19 disease based on a fractional Atangana-Baleanu operator is studied. Some fixed point theorems and generalized Gronwall inequality through the AB fractional integral are applied to obtain the existence and stability results. The fractional Adams-Bashforth is used to discuss the corresponding numerical results. A numerical simulation is presented to show the behavior of the approximate solution in terms of graphs of the spread of COVID-19 in the Chinese city of Wuhan. We simulate our table for the data of Wuhan from February 15, 2020 to April 25, 2020 for 70 days. Finally, we present a debate about the followed simulation in characterizing how the transmission dynamics of infection can take place in society.

Fractional order mathematical modeling of COVID-19 transmission

In this article, the mathematical model with different compartments for the transmission dynamics of coronavirus-19 disease (COVID-19) is presented under the fractional-order derivative. Some results regarding the existence of at least one solution through fixed point results are derived. Then for the concerned approximate solution, the modified Euler method for fractional-order differential equations (FODEs) is utilized. Initially, we simulate the results by using some available data for different fractional-order to show the appropriateness of the proposed method. Further, we compare our results with some reported real data against confirmed infected and death cases per day for the initial 67 days in Wuhan city.

Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan

We propose a compartmental mathematical model for the spread of the COVID-19 disease with special focus on the transmissibility of super-spreaders individuals. We compute the basic reproduction number threshold, we study the local stability of the disease free equilibrium in terms of the basic reproduction number, and we investigate the sensitivity of the model with respect to the variation of each one of its parameters. Numerical simulations show the suitability of the proposed COVID-19 model for the outbreak that occurred in Wuhan, China.

Effect of sexual transmission on the West Africa Ebola outbreak in 2014: a mathematical modelling study

The outbreak of the Ebola virus has resulted in significant morbidity and mortality in the affected areas, and Ebola virus RNA has been found in the semen of the survivors after 9 months of symptom onset. However, the role that sexual transmission played in the transmission is not very clear. In this paper, we developed a compartmental model for Ebola virus disease (EVD) dynamics, which includes three different infectious routes: contact with the infectious, contact with dead bodies, and transmission by sexual behaviour with convalescent survivors. We fitted the model to daily cumulative cases from the first reported infected case to October 25, 2014 for the epidemic in Sierra Leone, Liberia and Guinea. The basic reproduction numbers in these countries were estimated as 1.6726 (95%CI:1.5922–1.7573), 1.8162 (95%CI:1.7660–1.8329) and 1.4873 (95%CI:1.4770–1.4990), respectively. We calculated the contribution of sexual transmission to the basic reproduction number R₀ as 0.1155 (6.9%), 0.0236 (2.8%) and 0.0546 (3.7%) in Sierra Leone, Liberia and Guinea, respectively. Sensitivity analysis shows that the transmission rates caused by contacts with alive patients and sexual activities with convalescent patients have stronger impacts on the R₀. These results suggest that isolating the infectious individuals and advising the recovery men to avoid sexual intercourse are efficient ways for the eradication of endemic EVD.

Optimal time-profiles of public health intervention to shape voluntary vaccination for childhood diseases

In order to seek the optimal time-profiles of public health systems (PHS) Intervention to favor vaccine propensity, we apply optimal control (OC) to a SIR model with voluntary vaccination and PHS intervention. We focus on short-term horizons, and on both continuous control strategies resulting from the forward-backward sweep deterministic algorithm, and piecewise-constant strategies (which are closer to the PHS way of working) investigated by the simulated annealing (SA) stochastic algorithm. For childhood diseases, where disease costs are much larger than vaccination costs, the OC solution sets at its maximum for most of the policy horizon, meaning that the PHS cannot further improve perceptions about the net benefit of immunization. Thus, the subsequent dynamics of vaccine uptake stems entirely from the declining perceived risk of infection (due to declining prevalence) which is communicated by direct contacts among parents, and unavoidably yields a future decline in vaccine uptake. We find that for relatively low communication costs, the piecewise control is close to the continuous control. For large communication costs the SA algorithm converges towards a non-monotone OC that can have oscillations.

IoT-based cloud framework to control Ebola virus outbreak

Ebola is a deadly infectious virus that spreads very quickly through human-to-human transmission and sometimes death. The continuous detection and remote monitoring of infected patients are required in order to prevent the spread of Ebola virus disease (EVD). Healthcare services based on Internet of Things (IoT) and cloud computing technologies are emerging as a more effective and proactive solution which provides remote continuous monitoring of patients. A novel architecture based on Radio Frequency Identification Device (RFID), wearable sensor technology, and cloud computing infrastructure is proposed for the detection and monitoring of Ebola infected patients. The aim of this work is to prevent the spreading of the infection at the early stage of the outbreak. The J48 decision tree is used to evaluate the level of infection in a user depending on his symptoms. RFID is used to automatically sense the close proximity interactions (CPIs) between users. Temporal Network Analysis (TNA) is applied to describe and monitor the current state of the outbreak using the CPI data. The performance and accuracy of our proposed model are evaluated on Amazon EC2 cloud using synthetic data of two million users. Our proposed model provided 94 % accuracy for the classification and 92 % of the resource utilization.