Dynamic behaviors of a modified SIR model with nonlinear incidence and recovery rates

Stochastic intelligent computing solvers for the SIR dynamical prototype epidemic model using the impacts of the hospital bed

The present investigations are related to design a stochastic intelligent solver using the infrastructure of artificial neural networks (ANNs) and scaled conjugate gradient (SCG), i.e. ANNs-SCG for the numerical simulations of SIR dynamical prototype system based impacts of hospital bed. The SIR dynamical model is defined into three classes, susceptible patients in the hospital, infected population and recovered people. The proposed results are obtained through the sample statics of verification, testing and training of the dataset. The selection of the statics for training, testing and validation is chosen as 80%, 8% and 12%. A dataset is proposed based on the Adams scheme for the comparison of dynamical SIR prototype using the impacts of hospital bed. The numerical solutions are presented through the ANNs-SCG in order to reduce the values of the mean square error. To achieve the reliability, capability, accuracy, and competence of ANNs-SCG, the mathematical solutions are presented in the form of error histograms (EHs), regression, state transitions (STs) and correlation.

Stochastic forecasting of variable small data as a basis for analyzing an early stage of a cyber epidemic

Security Information and Event Management (SIEM) technologies play an important role in the architecture of modern cyber protection tools. One of the main scenarios for the use of SIEM is the detection of attacks on protected information infrastructure. Consorting that ISO 27001, NIST SP 800-61, and NIST SP 800-83 standards objectively do not keep up with the evolution of cyber threats, research aimed at forecasting the development of cyber epidemics is relevant. The article proposes a stochastic concept of describing variable small data on the Shannon entropy basis. The core of the concept is the description of small data by linear differential equations with stochastic characteristic parameters. The practical value of the proposed concept is embodied in the method of forecasting the development of a cyber epidemic at an early stage (in conditions of a lack of empirical information). In the context of the research object, the stochastic characteristic parameters of the model are the generation rate, the death rate, and the independent coefficient of variability of the measurement of the initial parameter of the research object. Analytical expressions for estimating the probability distribution densities of these characteristic parameters are proposed. It is assumed that these stochastic parameters of the model are imposed on the intervals, which allows for manipulation of the nature and type of the corresponding functions of the probability distribution densities. The task of finding optimal functions of the probability distribution densities of the characteristic parameters of the model with maximum entropy is formulated. The proposed method allows for generating sets of trajectories of values of characteristic parameters with optimal functions of the probability distribution densities. The example demonstrates both the flexibility and reliability of the proposed concept and method in comparison with the concepts of forecasting numerical series implemented in the base of Matlab functions.

A non-linear mathematical model for analysing the impact of COVID-19 disease on higher education in developing countries

This study proposes a non-linear mathematical model for analysing the effect of COVID-19 dynamics on the student population in higher education institutions. The theory of positivity and boundedness of solution is used to investigate the well-posedness of the model. The disease-free equilibrium solution is examined analytically. The next-generation operator method calculates the basic reproduction number ( R 0 ) . Sensitivity analyses are carried out to determine the relative importance of the model parameters in spreading COVID-19. In light of the sensitivity analysis results, the model is further extended to an optimal control problem by introducing four time-dependent control variables: personal protective measures, quarantine (or self-isolation), treatment, and management measures to mitigate the community spread of COVID-19 in the population. Simulations evaluate the effects of different combinations of the control variables in minimizing COVID-19 infection. Moreover, a cost-effectiveness analysis is conducted to ascertain the most effective and least expensive strategy for preventing and controlling the spread of COVID-19 with limited resources in the student population.

Relating quanta conservation and compartmental epidemiological models of airborne disease outbreaks in buildings

We investigate the underlying assumptions and limits of applicability of several documented models for outbreaks of airborne disease inside buildings by showing how they may each be regarded as special cases of a system of equations which combines quanta conservation and compartmental epidemiological modelling. We investigate the behaviour of this system analytically, gaining insight to its behaviour at large time. We then investigate the characteristic timescales of an indoor outbreak, showing how the dilution rate of the space, and the quanta generation rate, incubation rate and removal rate associated with the illness may be used to predict the evolution of an outbreak over time, and may also be used to predict the relative performances of other indoor airborne outbreak models. The model is compared to a more commonly used model, in which it is assumed the environmental concentration of infectious aerosols adheres to a quasi-steady-state, so that the the dimensionless quanta concentration is equal to the the infectious fraction. The model presented here is shown to approach this limit exponentially to within an interval defined by the incubation and removal rates. This may be used to predict the maximum extent to which a case will deviate from the quasi steady state condition.

Estimations and Control of Julia Sets of the SIS Model Perturbed by Noise

The estimations and control of Julia sets of the SIS(susceptible-infectious-susceptible) model under noise perturbation are studied. At first, a discrete SIS model is introduced, and the effects of additive and multiplicative noises on the fractal characteristics of the SIS model are discussed. Then, estimations of the Julia sets of the SIS model under additive and multiplicative noise perturbations are given, respectively. At last, the feedback control method is used to set appropriate controllers to realize control of the Julia set, and the influence of noise on the Julia set of the SIS model is reduced. The reason why this method is effective is also explained.

Predictive approach of COVID-19 propagation via multiple-terms sigmoidal transition model

The COVID-19 pandemic with its new variants has severely affected the whole world socially and economically. This study presents a novel data analysis approach to predict the spread of COVID-19. SIR and logistic models are commonly used to determine the duration at the end of the pandemic. Results show that these well-known models may provide unrealistic predictions for countries that have pandemics spread with multiple peaks and waves. A new prediction approach based on the sigmoidal transition (ST) model provided better estimates than the traditional models. In this study, a multiple-term sigmoidal transition (MTST) model was developed and validated for several countries with multiple peaks and waves. This approach proved to fit the actual data better and allowed the spread of the pandemic to be accurately tracked. The UK, Italy, Saudi Arabia, and Tunisia, which experienced several peaks of COVID-19, were used as case studies. The MTST model was validated for these countries for the data of more than 500 days. The results show that the correlating model provided good fits with regression coefficients (R2) > 0.999. The estimated model parameters were obtained with narrow 95% confidence interval bounds. It has been found that the optimum number of terms to be used in the MTST model corresponds to the highest R2, the least RMSE, and the narrowest 95% confidence interval having positive bounds.

Dynamical Analysis of a Modified Epidemic Model with Saturated Incidence Rate and Incomplete Treatment

This paper addresses a modified epidemic model with saturated incidence and incomplete treatment. The existence of all equilibrium points is analyzed. A reproduction number R0 is determined. Next, it is found that the non-endemic point P0 is stable in case R0<1, but unstable in case R0>1. The special conditions to analyze the local and global stability of the non-endemic and endemic points are investigated. Globally, the sensitivity analysis of the system is studied by combining the Latin Hypercube Sampling and Partial Rating Correlation Coefficients methods. By using the Pontryagins maximum principle, the optimal control problem is studied. Various numerical results are given to support our analysis.

Numerical analysis of a bi-modal covid-19 SITR model

This study presents a structure preserving nonstandard finite difference scheme to analyze a susceptible-infected-treatment-recovered (SITR) dynamical model of coronavirus 2019 (covid-19) with bimodal virus transmission in susceptible population. The underlying model incorporates the possible treatment measures as the emerging scenario of covid-19 vaccines. Keeping in view the fact that the real time data for covid-19 is updated at discrete time steps, we propose a new structure preserving numerical scheme for the proposed model. The proposed numerical scheme produces realistic solutions of the complex bi-modal SITR nonlinear model, converges unconditionally to steady states and reflects dynamical consistency with continuous sense of the model. The analysis of the model reveals that the model remains stable at the steady state points. The basic reproduction number Rcovid falls less than 1 when treatment rate is increased and disease will die out. On the other hand, it predicts that human population may face devastating effects of pandemic if the treatment measures are not strictly implemented.

Dynamical analysis of novel COVID-19 epidemic model with non-monotonic incidence function

In this study, we developed and analyzed a mathematical model for explaining the transmission dynamics of COVID-19 in India. The proposed SI u I k R model is a modified version of the existing SIR model. Our model divides the infected class I of SIR model into two classes: I u (unknown infected class) and I k (known infected class). In addition, we consider R a recovered and reserved class, where susceptible people can hide them due to fear of the COVID-19 infection. Furthermore, a non-monotonic incidence function is deemed to incorporate the psychological effect of the novel coronavirus diseases on India's community. The epidemiological threshold parameter, namely the basic reproduction number, has been formulated and presented graphically. With this threshold parameter, the local and global stability analysis of the disease-free equilibrium and the endemic proportion equilibrium based on disease persistence have been analyzed. Lastly, numerical results of long-run prediction using MATLAB show that the fate of this situation is very harmful if people are not following the guidelines issued by the authority.