Class Of Epidemic Models Research Articles

Optimal control analysis of COVID-19 vaccine epidemic model: a case study.

The purpose of this research is to explore the complex dynamics and impact of vaccination in controlling COVID-19 outbreak. We formulate the classical epidemic compartmental model by introducing vaccination class. Initially, the proposed mathematical model is analyzed qualitatively. The basic reproductive number is computed and its numerical value is estimated using actual reported data of COVID-19 for Pakistan. The sensitivity analysis is performed to analyze the contribution of model embedded parameters in transmission of the disease. Further, we compute the equilibrium points and discussed its local and global stability. In order to investigate the influence of model key parameters on the transmission and controlling of the disease, we perform numerical simulations describing the impact of various scenarios of vaccine efficacy rate and other controlling measures. Further, on the basis of sensitivity analysis, the proposed model is restructured to obtained optimal control model by introducing time-dependent control variables u_1(t) for isolation, u_2(t) for vaccine efficacy and u_3(t) for treatment enhancement. Using optimal control theory and Pontryagin’s maximum principle, the model is optimized and important optimality conditions are derived. In order to explore the impact of various control measures on the disease dynamics, we considered three different scenarios, i.e., single and couple and threefold controlling interventions. Finally, the graphical interpretation of each case is depicted and discussed in detail. The simulation results revealed that although single and couple scenarios can be implemented for the disease minimization but, the effective case to curtail the disease incidence is the threefold scenario which implements all controlling measures at the same time.

Social stress drives the multi-wave dynamics of COVID-19 outbreaks

The dynamics of epidemics depend on how people's behavior changes during an outbreak. At the beginning of the epidemic, people do not know about the virus, then, after the outbreak of epidemics and alarm, they begin to comply with the restrictions and the spreading of epidemics may decline. Over time, some people get tired/frustrated by the restrictions and stop following them (exhaustion), especially if the number of new cases drops down. After resting for a while, they can follow the restrictions again. But during this pause the second wave can come and become even stronger then the first one. Studies based on SIR models do not predict the observed quick exit from the first wave of epidemics. Social dynamics should be considered. The appearance of the second wave also depends on social factors. Many generalizations of the SIR model have been developed that take into account the weakening of immunity over time, the evolution of the virus, vaccination and other medical and biological details. However, these more sophisticated models do not explain the apparent differences in outbreak profiles between countries with different intrinsic socio-cultural features. In our work, a system of models of the COVID-19 pandemic is proposed, combining the dynamics of social stress with classical epidemic models. Social stress is described by the tools of sociophysics. The combination of a dynamic SIR-type model with the classical triad of stages of the general adaptation syndrome, alarm-resistance-exhaustion, makes it possible to describe with high accuracy the available statistical data for 13 countries. The sets of kinetic constants corresponding to optimal fit of model to data were found. These constants characterize the ability of society to mobilize efforts against epidemics and maintain this concentration over time and can further help in the development of management strategies specific to a particular society.

On the optimal control of SIR model with Erlang-distributed infectious period: isolation strategies.

Mathematical models are formal and simplified representations of the knowledge related to a phenomenon. In classical epidemic models, a major simplification consists in assuming that the infectious period is exponentially distributed, then implying that the chance of recovery is independent on the time since infection. Here, we first attempt to investigate the consequences of relaxing this assumption on the performances of time-variant disease control strategies by using optimal control theory. In the framework of a basic susceptible–infected–removed (SIR) model, an Erlang distribution of the infectious period is considered and optimal isolation strategies are searched for. The objective functional to be minimized takes into account the cost of the isolation efforts per time unit and the sanitary costs due to the incidence of the epidemic outbreak. Applying the Pontryagin’s minimum principle, we prove that the optimal control problem admits only bang–bang solutions with at most two switches. In particular, the optimal strategy could be postponing the starting intervention time with respect to the beginning of the outbreak. Finally, by means of numerical simulations, we show how the shape of the optimal solutions is affected by the different distributions of the infectious period, by the relative weight of the two cost components, and by the initial conditions.

Dynamics and simulations of a second order stochastically perturbed SEIQV epidemic model with saturated incidence rate

A second order stochastically perturbed SEIQV epidemic model is studied in this paper. Firstly, we derive sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the model by establishing a suitable stochastic Lyapunov function. Secondly, we obtain adequate conditions for completing eradication and wiping out of the infectious disease from the basic reproduction number of corresponding deterministic model. Thirdly, distinguished from the previous literatures, the equilibrium stability is investigated by combining Hasminskii theory of stability with Lyapunov function. The new method can also be successfully used for some classical epidemic models. Finally, our analytical results are illustrated by computer simulations, including three examples based on disease originated from reality.

Modelling the spread of covid-19 in the capital of Brazil using numerical solution and cellular automata

The novel coronavirus disease 2019 (COVID-19) still challenges researchers due to its spread and deaths. Hence, the classical epidemic SIR and SEIRD models inspired by the epidemic's outbreak are widely used to predict the evolution of the disease. In addition to classical approaches, describing complex phenomena through Cellular Automata (CA) is a highly effective way to understand the iterations on a populated system. The present research analyzed the usage of CA to generate an epidemic-computational model from a micro perspective based on parameters obtained through a statistical fit from a macro perspective. After validating SIR and SEIRD models with the government official data for Brasilia, Brazil, the authors applied the obtained parameters to the Cellular Automata model. The CA model simulated the spread of the virus from infected to uninfected people in a restrained environment (i.e., a supermarket) under several varied conditions applying an approach never adopted before. The manner of applying CA in this research proved to represent an essential tool in predicting the spread of the coronavirus in confined spaces with random movements of people. The CA numerical open-source presented has the purpose of clarifying how the spread occurs not only as a mathematical curve but in an organic way. The numerical simulations from the CA model allowed the authors to conclude that markets and stores are relevant places where might be infections. Thus, every local store and the market owner should reason about the aspects that could avoid the spread of the disease, coming up with efficient solutions. Each environment has specific features that only those who know them are the ones capable of managing.

Mathematical modeling and analysis of the novel Coronavirus using Atangana–Baleanu derivative

The novel Coronavirus infection disease is becoming more complex for the humans society by giving death and infected cases throughout the world. Due to this infection, many countries of the world suffers from great economic loss. The researchers around the world are very active to make a plan and policy for its early eradication. The government officials have taken full action for the eradication of this virus using different possible control strategies. It is the first priority of the researchers to develop safe vaccine against this deadly disease to minimize the infection. Different approaches have been made in this regards for its elimination. In this study, we formulate a mathematical epidemic model to analyze the dynamical behavior and transmission patterns of this new pandemic. We consider the environmental viral concentration in the model to better study the disease incidence in a community. Initially, the model is constructed with the derivative of integer-order. The classical epidemic model is then reconstructed with the fractional order operator in the form of Atangana–Baleanu derivative with the nonsingular and nonlocal kernel in order to analyze the dynamics of Coronavirus infection in a better way. A well-known estimation approach is used to estimate model parameters from the COVID-19 cases reported in Saudi Arabia from March 1 till August 20, 2020. After the procedure of parameters estimation, we explore some basic mathematical analysis of the fractional model. The stability results are provided for the disease free case using fractional stability concepts. Further, the uniqueness and existence results will be shown using the Picard–Lendelof approach. Moreover, an efficient numerical scheme has been proposed to obtain the solution of the model numerically. Finally, using the real fitted parameters, we depict many simulation results in order to demonstrate the importance of various model parameters and the memory index on disease dynamics and possible eradication.

Optimal existence of fractional order computer virus epidemic model and numerical simulations

Aim of this article is to analyze the fractional order computer epidemic model. To this end, a classical computer epidemic model is extended to the fractional order model by using the Atangana–Baleanu fractional differential operator in Caputo sense. The regularity condition for the solution to the considered system is described. Existence of the solution in the Banach space is investigated and some benchmark results are presented. Steady states of the system is described and stability of the model at these states is also studied, with the help of Jacobian matrix method. Some results for the local stability at disease free equilibrium point and endemic equilibrium point are presented. The basic reproduction number is mentioned and its role on stability analysis is also highlighted. The numerical design is formulated by applying the Atangana–Baleanu integral operator. The graphical solutions are also presented by computer simulations at both the equilibrium points.

The mathematics of multiple lockdowns

While vaccination is the optimal response to an epidemic, recent events have obliged us to explore new strategies for containing worldwide epidemics, like lockdown strategies, where the contacts among the population are strongly reduced in order to slow down the propagation of the infection. By analyzing a classical epidemic model, we explore the impact of lockdown strategies on the evolution of an epidemic. We show that repeated lockdowns have a beneficial effect, reducing the final size of the infection, and that they represent a possible support strategy to vaccination policies.

Joint impacts of media, vaccination and treatment on an epidemic Filippov model with application to COVID-19

A non-smooth SIR Filippov system is proposed to investigate the impacts of three control strategies (media coverage, vaccination and treatment) on the spread of an infectious disease. We synthetically consider both the number of infected population and its changing rate as the switching condition to implement the curing measures. By using the properties of the Lambert W function, we convert the proposed switching condition to a threshold value related to the susceptible population. The classical epidemic model involving media coverage, linear functions describing injecting vaccine and treatment strategies is examined when the susceptible population exceeds the threshold value. In addition, we consider another SIR model accompanied with the vaccination and treatment strategies represented by saturation functions when the susceptible population is smaller than the threshold value. The dynamics of these two subsystems and the sliding domain are discussed in detail. Four types of local sliding bifurcation are investigated, including boundary focus, boundary node, boundary saddle and boundary saddle-node bifurcations. In the meantime, the global bifurcation involving the appearance of limit cycles is examined, including touching bifurcation, homoclinic bifurcation to the pseudo-saddle and crossing bifurcation. Furthermore, the influence of some key parameters related to the three treatment strategies is explored. We also validate our model by the epidemic data sets of A/H1N1 and COVID-19, which can be employed to reveal the effects of media report and existing strategy related to the control of emerging infectious diseases on the variations of confirmed cases.

High-Order Mean-Field Approximations for Adaptive Susceptible-Infected-Susceptible Model in Finite-Size Networks

Exact solutions of epidemic models are critical for identifying the severity and mitigation possibility for epidemics. However, solving complex models can be difficult when interfering conditions from the real-world are incorporated into the models. In this paper, we focus on the generally unsolvable adaptive susceptible-infected-susceptible (ASIS) epidemic model, a typical example of a class of epidemic models that characterize the complex interplays between the virus spread and network structural evolution. We propose two methods based on mean-field approximation, i.e., the first-order mean-field approximation (FOMFA) and higher-order mean-field approximation (HOMFA), to derive the exact solutions to ASIS models. Both methods demonstrate the capability of accurately approximating the metastable-state statistics of the model, such as the infection fraction and network density, with low computational cost. These methods are potentially powerful tools in understanding, mitigating, and controlling disease outbreaks and infodemics.

New Fuzzy Fractional Epidemic Model Involving Death Population

In this research, we propose a new change in classical epidemic models by including the change in the rate of death in the overall population. The existing models like Susceptible-Infected-Recovered (SIR) and Susceptible-Infe... | Find, read and cite all the research you need on Tech Science Press

Simulation of deterministic compartmental models for infectious diseases dynamics

Infectious diseases are caused by pathogenic microorganisms and can spread through different ways. Mathematical models and computational simulation have been used extensively to investigate the transmission and spread of infectious diseases. In other words, mathematical model simulation can be used to analyse the dynamics of infectious diseases, aiming to understand the effects and how to control the spread. In general, these models are based on compartments, where each compartment contains individuals with the same characteristics, such as susceptible, exposed, infected, and recovered. In this paper, we cast further light on some classical epidemic models, reporting possible outcomes from numerical simulation. Furthermore, we provide routines in a repository for simulations.

On the Carrying and Evolution Matrices in Epidemic Models

This study presents a technical characterization of classical epidemic models of compartments by decomposing the state into an infectious sub-state (or infective compartment) and a non-infective sub-state (or non-infective compartment). Then, the linearized infective part of the model is discussed through a positivity/stability viewpoint from linear algebraic tools. Some relevant properties of the transition and transmission matrices are described in a general context. The main advantage of the given formalism is that the linearized behavior about the equilibrium steady-state is general in the sense that it is independent of the particular epidemic model due to the compartmental structure performed analysis. The performed study is made in the absence and in the presence of delayed dynamics.

Emergence of nonlinear crossover under epidemic dynamics in heterogeneous networks.

Potential diffusion processes of real-world systems are relevant to the underlying network structure and dynamical mechanisms. The vast majority of the existing work on spreading dynamics, in response to a large-scale network, is built on the condition of the infinite initial state, i.e., the extremely small seed size. The impact of an increasing seed size on the persistent diffusion has been less investigated. Based on classical epidemic models, this paper offers a framework for studying such impact through observing a crossover phenomenon in a two-diffusion-process dynamical system. The two diffusion processes are triggered by nodes with a high and low centrality, respectively. Specifically, given a finite initial state in networks with scale-free degree distributions, we demonstrate analytically and numerically that the diffusion process triggered by low centrality nodes pervades faster than that triggered by high centrality nodes from a certain point. The presence of the crossover phenomenon reveals that the dynamical process under the finite initial state is far more than the vertical scaling of the spreading curve under an infinite initial state. Further discussion emphasizes the persistent infection of individuals in epidemic dynamics as the essential reason rooted in the crossover, while the finite initial state is the catalyst directly leading to the emergence of this phenomenon. Our results provide valuable implications for studying the diversity of hidden dynamics on heterogeneous networks.

Agent-based approach to modeling the process of viral marketing

The space of social networks and the Internet challenge classic marketing tools and offers new, modern, effective technologies that improve consumer value. The high rate of technology change poses the problem of effective marketing. In the context of digitalization, new technologies are rapidly forming new market platforms and ways to satisfy their requirements. In this regard, marketers are forced to constantly upgrade their tools and approaches. One effective approach to improving consumer demand is viral marketing. In a highly competitive environment, many more companies are resorting to the viral marketing apparatus. Viral marketing can be based on sound marketing principles, but at the same time become a dangerous tool. Classical epidemic spread models do not take into account the features of modern viral marketing technologies and social networks. The article discusses the concept of viral marketing as a modern tool to increase the consumer value of goods and services. The advantages and disadvantages of this advertising tool are revealed. The main stages of building a viral campaign are described. The conditions under which viral marketing is developing successfully are identified. An agent-graph model of the spread of viral information based on the epidemiological approach that takes into account the basic principles of interaction in a social network is built.

Analysis of The Dynamics of The Classical Epidemic Model with Beta Distributed Random Components

In this study, the classical epidemic model of Kermack and McKendrick is analyzed with beta distributed random components. A random analysis is done for the deterministic epidemic model by transforming the parameters and initial values of the system to random variables with beta distribution. The approximations for the expectations of the model variables are compared with the deterministic results to comment on the randomness of the cases with random parameters and random initial values. Results for some numerical characteristics of these two cases are also given to investigate the accuracy of the approximations for the expected values.

Epidemic evolution models to the test of Covid-19

We illustrate a suitable adaptation and modification of classical epidemic evolution models that proves helpful in the study of Covid-19 spread in Italy.

The effect of a generalized nonlinear incidence rate on the stochastic SIS epidemic model

In this paper, we aim to analyze the classical SIS epidemic model with a generalized force of infection (including nonmonotonic cases), where the transmission rate is perturbed by white noise. Using Feller's test for explosions, we prove that the disease dies out with probability one without any restriction on the model parameters.

Differential Security Game in Heterogeneous Device-to-Device Offloading Network Under Epidemic Risks

Cooperative computation among peer mobile devices via device-to-device (D2D) links, a.k.a. D2D offloading, is a promising technology to enhance mobile computing performance and reduce core wireless network traffic. However, D2D offloading also creates new security risks as malware can relatively easily compromise mobile devices participating in D2D offloading and propagate across the entire network. In this article, we build an epidemic model to understand the malware propagation process in the D2D offloading-enabled mobile network where devices have heterogeneous computation demand and new devices can enter the system over time. This model also allows mobile devices to intentionally enter a “non-cooperative” state as a preventive defense strategy to thwart malware propagation. We prove a thresholding result of the malware propagation similar to that in classic epidemic models under given static defender (i.e. the network operator) and attacker strategies. We further model the strategic interaction between the defender and the attacker as a zero-sum differential game. The existence of a saddle-point equilibrium is proved, and the optimal dynamic defense and attack strategies are derived based on the Pontryagin's maximum principle, which are proven to be a bang-bang control strategy. Simulation results validate the proposed model and show that the dynamic optimal strategies significantly improve the system utility compared with baseline strategies.

Modeling quarantine during epidemics and mass-testing using drones.

We extend the classical SIR epidemic spread model by introducing the "quarantined" compartment. We solve (numerically) the differential equations that govern the extended model and quantify how quarantining "flattens the curve" for the proportion of infected population over time. Furthermore, we explore the potential of using drones to deliver tests, enabling mass-testing for the infection; we give a method to estimate the drone fleet needed to deliver the tests in a metropolitan area. Application of our models to COVID-19 spread in Sweden shows how the proposed methods could substantially decrease the peak number of infected people, almost without increasing the duration of the epidemic.