Epidemic Disease Model Research Articles

Compartmental Nonlinear Epidemic Disease Model with Mixed Behavior

Compartmental Nonlinear Epidemic Disease Model with Mixed Behavior

Dynamics of an [formula omitted] epidemic model with stochastic optimal control and awareness programs

An unaware susceptible-aware susceptible-vaccinated-infected-recovered (SuSaV IR) epidemic disease model has been developed and extensively examined to better understand the intricate dynamics of the disease transmission with saturated recovery function. A non-linear, monotonically increasing awareness function has been incorporated and its application is contingent upon the number of infected individuals. The spreading threshold R0 and its sensitivity indices are computed to determine both the prevalence and the potential decline of the spread of disease. Contour plots have been generated to explain how alterations in key parameters affect the evolution of infected individuals. In deterministic model, the condition R0<1 ensures the global stability of a disease-free state while R0>1 indicates the presence of a globally stable prevailing state. A numerical approach has been employed to pinpoint the stability switches for R0 which indicates transcritical bifurcation. Subsequently, a corresponding stochastic model is developed to investigate the impact of random external factors represented as white noise. In addition, the global existence and uniqueness of solutions, and the asymptotic behavior of solutions in the vicinity of steady-states are exhibited in the stochastic model. In the stochastic model, the extinction threshold Res is consistently below R0 due to noise intensity, leading to quicker disease extinction. In order to elucidate the influence of parameters and noise intensities on persistence threshold Rps and extinction threshold Res, a comprehensive sensitivity analysis and the variation of each noise intensity have been performed. This study shows that treatment can be used as an effective tool for controlling the spread of disease by lowering R0 and Rps. It has been empirically observed that high environmental fluctuations can serve as a suppressive factor for disease spread in stochastic model with R0,Rps>1 and the higher noise intensities lead to a faster disappearance of the disease. It is noticed that randomness in susceptible and infected individuals can exert a more significant influence on disease mitigation. The spread of infection exhibits a noteworthy dependence on environmental fluctuations. Additionally, to combat and mitigate the spread of disease, we have executed stochastic optimal control measures. Consequently, the control strategy has emerged as a potent tools for effectively managing the propagation of disease.

Mathematical Modeling of the Transmission Dynamics of Covid-19 with Quarantine and Hospitality Treatment

Abstract: This study presents a COVID-19 epidemic disease model that has been tailored to fit the specific circumstances of world. The Nigerian population has been partitioned into seven subpopulations in this model system. These subpopulations include the Susceptible class, Exposed class, Symptomatic Infected class, Asymptomatically Infected class, Quarantined individuals, Hospitalised individuals, and Recovered individuals. The model was augmented with control measures parameters, specifically those related to hospitalisation and quarantine. The disease-free equilibrium and endemic equilibrium points were derived. The determination of the basic reproduction number was achieved through the utilisation of the novel generation matrix. Additionally, an analysis of the local and global stability was conducted, revealing that the system is both locally and globally asymptotically stable at the aforementioned point of R0&lt;1 for the DFE. We did numerical simulations using (Maple 17) software. The results showed the importance of the control measures and social distancing through graph.

Analytic study of pine wilt disease model with Caputo–Fabrizio fractional derivative

In this paper, we construct an analytical study of the epidemic pine wilt disease model in a Caputo–Fabrizio type fractional order; the basic properties of the fractional differential equation and the model are presented; we give the basic properties of the model. Applying the homotopy analysis transform method to obtain numerical solutions to the model, the numerical result represented in graphs is presented.

On new computations of the fractional epidemic childhood disease model pertaining to the generalized fractional derivative with nonsingular kernel

&lt;abstract&gt;&lt;p&gt;The present research investigates the Susceptible-Infected-Recovered (SIR) epidemic model of childhood diseases and its complications with the Atangana-Baleanu fractional derivative operator in the Caputo sense (ABC). With the aid of the Elzaki Adomian decomposition method (EADM), the approximate solutions of the aforesaid model are discussed by exerting the Adomian decomposition method. By employing the fixed point postulates and the Picard–Lindelöf approach, the stability, existence, and uniqueness consequences of the model are demonstrated. Furthermore, we illustrate the essential hypothesis for disease control in order to find the role of unaware infectives in the spread of childhood diseases. Besides that, simulation results and graphical illustrations are presented for various fractional-orders. A comparison analysis is shown with the previous findings. It is hoped that ABC fractional derivative and the projected algorithm will provide new venues in futuristic studies to manipulate and analyze several epidemiological models.&lt;/p&gt;&lt;/abstract&gt;

Maximum entropy approach to reliability analysis based epidemic disease model

This study analyzes the dynamic model of epidemic disease system based on the maximum entropy approach to reliability. The epidemic disease system is assumed to be composed of several classes, namely susceptible class, infective class, resistance class, exposed class and so on. The dynamics of the populations in each class are depicted by a number of differential equations, where the populations transmitting between the classes are the averages of transmitting populations in microscopic stochastic transmission process. In microscopic transmission process, several basic variables are assumed to be random, such as incubation period, hospitalization duration and so on. To infer the probability distributions of these variables is a main task of this study. Inspired by the recent study of reliability, the maximum entropy based approach is applied to determine the parameters in the dynamic model. The basic idea of this study is presented below. In this study, degrade (hazard) function, which is a fundamental quantity in the disciplines of risk and reliability analysis, is associated with death rate, incidence rate and healing rate. Specifically, death rate and healing rate of the infective people are associated with hazard rate and repair rate of the repaired system in reliability theory, respectively; the incidence rate is associated to the hazard rate during incubation period. By means of the maximum entropy principle, the moments of the period from onset to death, the period from onset to recovery and the incubation period are fused to infer the most probable death rate, incidence rate and healing rate. Applying the maximum-entropy based statistical inference, the information of macroscopic transmission process is fused, such as average values, fluctuations and median values. To the best of our knowledge, the traditional fitting approaches to determine parameters usually rely on the information of macroscopic phenomenon. It is different from these fitting approaches that the maximum-entropy based approach applied in this study relies on the information of microscopic process. Thus this approach is adapted to practice scenario where the limitations of information access and number of samples both exist. And the parameter determination is independent on the choice of the macroscopic epidemic disease dynamic model. After applying the maximum entropy principle based inference and the SEIR (susceptible-infective-exposed-removed) model, several discussions associated with coronavirus disease 2019 (COVID-19) are made. With the help of recent information of microscopic transmission process, the parameters in SEIR model are determined directly by the maximum-entropy principle. Then with numerical calculation, dynamics of the populations in infective class, resistance class and exposed class are obtained. Besides, some typical phenomena are revealed by the analytical and numerical results. For example, the calculation shows that the peak of the infectious ratio in transmission process is unique; the infectious ratio of steady state tends to zero when the immunity duration is much larger than the healing period. Additionally, limited immunity duration model is also considered. The relationship between the infectious ratio of steady state and the proportion of immunization duration to healing period is presented.

Global Existence and Blow-up of Solutions to a Coupled Parabolic System

In this paper, we investigate the global existence and blow-up properties of the solutions of highly nonlinear coupled SIR epidemic disease model with cross-diffusion terms and no flux type boundary conditions. Under the suitable assumptions on the nonlinear source functions we prove the global existence and blow-up of the solutions. Further, we prove that the blow-up property of the solutions only depends on the first eigenvalue of -Δ in a bounded domain Ω. Finally, we present the numerical simulations to illustrate the theoretical results.

The impact of media converge on complex networks on disease transmission.

In this paper, we propose an epidemic disease model about the effect of media coverage on complex networks, where the contacts between nodes are treated as a social network. We calculate the basic reproduction number R0 and get that the disease-free equilibrium is locally and globally asymptotically stable if R0< 1, otherwise disease-free equilibrium is unstable and there exists a unique endemic equilibrium, and the disease is permanent. And two immunization strategies are considered: proportional and target immunization. By comparing two immunization strategies, it is found that the target immunization is better than the proportional immunization. Finally, numerical simulations verify our results and some discussions of vaccination strategies are done in the control of infectious dseases.

Identifying Critical Parameters in SIR Model for Spread of Disease

Calculating analytical approximate solutions for non-linear infectious disease models is a difficult task. Such models often require computational tools to analyse analytical approximate methods which appear in some theoretical and practical applications in systems biology. They represent key critical elements and give some approximate solutions for such systems. The SIR epidemic disease model is given as the non-linear system of ODE’s. Then, we use a proper scaling to reduce the number of parameters. We suggest Elzaki transform method to find analytical approximate solutions for the simplified model. The technique plays an important role in calculating the analytical approximate solutions. The local and global dynamics of the model are also studied. An investigation of the behaviour at infinity was conducted via finding the lines and singular points at infinity. Model dynamic results are computed in numerical simulations using Pplane8 and SimBiology Toolbox for Mathlab. Results provide a good step forward for describing the model dynamics. More interestingly, the simplified model could be accurate, robust, and used by biologists for different purposes such as identifying critical model elements.

A Mathematical Study of an Epidemic Disease Model Spread by Rumors

Mathematical models are widely used in order to understand the dynamics of the disease. In this study we focus a very important issue regarding the rumors spread about the disease propagation in the community. This study based on the ground realities faces to the individuals of Pakistan about an unauthentic information about the disease vaccination awareness. The present study is composed in the form of a mathematical model. A mathematical approach is used to obtain the necessary results. The proposed model is stable both locally and globally. For the basic reproduction number the disease free equilibrium is stable locally as well as globally. Further, the disease persistence occurs when the basic reproduction number exceeds than unity. The endemic equilibrium is stable locally as well as globally when the basic reproduction number exceeds than unity. The numerical solution of the model is presented in the form of the graphics by choosing such suitable parameters. Copyright © 2016 American Scientific Publishers All rights reserved.

SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects

We first propose a new epidemic disease model governed by system of impulsive delay differential equations. Then, based on theories for impulsive delay differential equations, we skillfully solve the difficulty in analyzing the global dynamical behavior of the model with pulse vaccination and impulsive population input effects at two different periodic moments. We prove the existence and global attractivity of the “infection-free” periodic solution and also the permanence of the model. We then carry out numerical simulations to illustrate our theoretical results, showing us that time delay, pulse vaccination, and pulse population input can exert a significant influence on the dynamics of the system which confirms the availability of pulse vaccination strategy for the practical epidemic prevention. Moreover, it is worth pointing out that we obtained an epidemic control strategy for controlling the number of population input.

Analysis of an epidemic model with awareness programs by media on complex networks

In this paper, we propose an epidemic disease model about the effect of awareness programs on complex networks, where the contacts between nodes are treated as a social network. Two forms on increasing rate of awareness programs, which are a constant and the change with the number of infected individuals, are analyzed. Through dynamical analysis, we obtain the basic reproduction number R0 and prove the stability of disease-free equilibrium and endemic equilibrium. Furthermore, numerical simulations about the model are taken to reach that, on the one hand, the two forms, which are increasing rate of awareness programs, respectively, have advantages and disadvantages on preventing and controlling diseases, and they are complementary; on the other hand, awareness programs have more effects on nodes with smaller degrees.

STUDY OF STOCHASTIC SYSTEMS FOR EPIDEMIC DISEASE MODELS

As we know there are two kind of systems in modeling epidemic disease, deterministic systems and stochastic systems. This two systems relate to deterministic and stochastic epidemic disease models, respectively. Almost we use deterministic model for big population size and stochastic model for small population size. To use stochastic models for epidemic disease models, can obtain good results with less error. Study and solving of full stochastic models has not been yet investigated so more. In this article we use the homotopy analysis method to solve the full stochastic susceptible-infective epidemic disease model in disease-free equilibrium point.

Analysis of SE τ IR ω S epidemic disease models with vertical transmission in complex networks

When the role of network topology is taken into consideration, one of the objectives is to understand the possible implications of topological structure on epidemic models. As most real networks can be viewed as complex networks, we propose a new delayed SEτIRωS epidemic disease model with vertical transmission in complex networks. By using a delayed ODE system, in a small-world (SW) network we prove that, under the condition R0 ≤ 1, the disease-free equilibrium (DFE) is globally stable. When R0 > 1, the endemic equilibrium is unique and the disease is uniformly persistent. We further obtain the condition of local stability of endemic equilibrium for R0 > 1. In a scale-free (SF) network we obtain the condition R1 > 1 under which the system will be of non-zero stationary prevalence.

Global attractivity and permanence of a delayed SVEIR epidemic model with pulse vaccination and saturation incidence

In this study, we formulate and analyze a new SVEIR epidemic disease model with time delay and saturation incidence, and analyze the dynamic behavior of the model under pulse vaccination. Using the discrete dynamical system determined by the stroboscopic map, we obtain an ‘infection-free’ periodic solution, further, show that the ‘infection-free’ periodic solution is globally attractive for some parameters of the model under appropriate conditions. The permanence of the model is investigated analytically. By computer simulation it is concluded that a large vaccination rate or a short pulse of vaccination or a long latent period are each a sufficient condition for the extinction of the disease.

Global attractivity and permanence of a SVEIR epidemic model with pulse vaccination and time delay

In this study, we propose a new SVEIR epidemic disease model with time delay, and analyze the dynamic behavior of the model under pulse vaccination. Pulse vaccination is an effective strategy for the elimination of infectious disease. Using the discrete dynamical system determined by the stroboscopic map, we obtain an ‘infection-free’ periodic solution. We also show that the ‘infection-free’ periodic solution is globally attractive when some parameters of the model under appropriate conditions. The permanence of the model is investigated analytically. Our results indicate that a large vaccination rate or a short pulse of vaccination or a long latent period is a sufficient condition for the extinction of the disease.

Impulsive vaccination of SEIR epidemic model with time delay and nonlinear incidence rate

In this paper, an SEIR epidemic disease model with time delay and nonlinear incidence rate is studied, and the dynamical behavior of the model under pulse vaccination is analyzed. Using the discrete dynamical system determined by the stroboscopic map, we show that there exists an infection-free periodic solution. Further, we show that the infection-free periodic solution is globally attractive when the period of impulsive effect is less than some critical value. Using a new modelling method, we obtain a sufficient condition for the permanence of the epidemic model with pulse vaccination. We show that time delay, pulse vaccination can bring different effects on the dynamic behavior of the model by numerical analysis. Our results also show the time delay is “profitless”. The main feature of this paper is to introduce time delay and impulse into the SEIR epidemic model and to give pulse vaccination strategies.

Two profitless delays for an SEIRS epidemic disease model with vertical transmission and pulse vaccination

Since the investigation of impulsive delay differential equations is beginning, the literature on delay epidemic models with pulse vaccination is not extensive. In this paper, we propose a new SEIRS epidemic disease model with two profitless delays and vertical transmission, and analyze the dynamics behaviors of the model under pulse vaccination. Using the discrete dynamical system determined by the stroboscopic map, we obtain a ‘infection-free’ periodic solution, further, show that the ‘infection-free’ periodic solution is globally attractive when some parameters of the model are under appropriate conditions. Using a new modeling method, we obtain sufficient condition for the permanence of the epidemic model with pulse vaccination. We show that time delays, pulse vaccination and vertical transmission can bring different effects on the dynamics behaviors of the model by numerical analysis. Our results also show the delays are “profitless”. In this paper, the main feature is to introduce two discrete time delays, vertical transmission and impulse into SEIRS epidemic model and to give pulse vaccination strategies.

Global dynamics behaviors for new delay SEIR epidemic disease model with vertical transmission and pulse vaccination

A robust SEIR epidemic disease model with a profitless delay and vertical transmission is formulated, and the dynamics behaviors of the model under pulse vaccination are analyzed. By use of the discrete dynamical system determined by the stroboscopic map, an ‘infection-free’ periodic solution is obtained, further, it is shown that the ‘infection-free’ periodic solution is globally attractive when some parameters of the model are under appropriate conditions. Using the theory on delay functional and impulsive differential equation, the sufficient condition with time delay for the permanence of the system is obtained, and it is proved that time delays, pulse vaccination and vertical transmission can bring obvious effects on the dynamics behaviors of the model. The results indicate that the delay is ‘profitless’.

A delayed epidemic model with stage-structure and pulses for pest management strategy

From a biological pest management standpoint, epidemic diseases models have become important tools in control of pest populations. This paper deals with an impulsive delay epidemic disease model with stage-structure and a general form of the incidence rate concerning pest control strategy, in which the pest population is subdivided into three subgroups: pest eggs, susceptible pests, infectious pests that do not attack crops. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact periodic susceptible pest-eradication solution of the system and observe that the susceptible pest-eradication periodic solution is globally attractive, provided that the amount of infective pests released periodically is larger than some critical value. When the amount of infective pests released is less than another critical value, the system is shown to be permanent, which implies that the trivial susceptible pest-eradication solution loses its attractivity. Our results indicate that besides the release amount of infective pests, the incidence rate, time delay and impulsive period can have great effects on the dynamics of our system.