Impulsive Vaccination Research Articles

The impulsive vaccination in an SVIS diffusive model

This paper examines a reaction-diffusion problem with impulses, which presents a susceptible-vaccinated-infected-susceptible (SVIS) epidemic model with impulsive vaccination. First, the existence and uniqueness of the global solution and the disease-free periodic solution have been established. Second, by considering the principal eigenvalue, the asymptotic behavior of the disease-free periodic solution and the sufficient condition for the persistence of diseases are given, in addition, the mono-tonicity of the principal eigenvalue is investigated. Third, the periodic state of the endemic disease has been explored when vaccination is not completely effective. Finally, the numerical simulations presented reveal the impacts of the infection rate and impulses, and demonstrate that effective vaccination is a reliable way to control the spread of diseases.

Pulse vaccination in a SIR model: Global dynamics, bifurcations and seasonality

We analyze a periodically-forced dynamical system inspired by the SIR model with impulsive vaccination. We fully characterize its dynamics according to the proportion p of vaccinated individuals and the time T between doses. If the basic reproduction number is less than 1 (i.eRp<1), then we obtain precise conditions for the existence and global stability of a disease-free T-periodic solution. Otherwise, if Rp>1, then a globally stable T-periodic solution emerges with positive coordinates.We draw a bifurcation diagram (T,p) and we describe the associated bifurcations. We also find analytically and numerically chaotic dynamics by adding seasonality to the disease transmission rate. In a realistic context, low vaccination coverage and intense seasonality may result in unpredictable dynamics. Previous experiments have suggested chaos in periodically-forced biological impulsive models, but no analytic proof has been given.

On the Properties of a Newly Susceptible, Non-Seriously Infected, Hospitalized, and Recovered Subpopulation Epidemic Model

The COVID-19 outbreak has brought to the forefront the importance of predicting and controlling an epidemic outbreak with policies such as vaccination or reducing social contacts. This paper studies an SIHR epidemic model characterized by susceptible (S), non-seriously infected (I), hospitalized (H), and recovered (R) subpopulations, and dynamic vaccination; vaccination itself and H are fed back, and its dynamics are also determined by a free-design time-dependent function and parameters. From a theoretical analysis, the well-posedness of the model is demonstrated; positivity and the disease-free (Pdf) and endemic (Pee) equilibrium points are analyzed. The controlled reproduction number (Rc) is proved to be a threshold for the local asymptotic stability of Pdf and the existence Pee; when Rc&lt;1 (Rc&gt;1), then Pdf is (not) locally asymptotically stable and Pee does not (does) exist. Simulations have been carried out with data concerning COVID-19 where the importance of keeping Rc&lt;1 to prevent the disease spreading and future deaths is highlighted. We design the control input, since it can be easily adapted to match the user specification, to obtain impulsive and regular vaccination and fulfill the condition Rc&lt;1.

A mathematical model for predicting and controlling COVID-19 transmission with impulsive vaccination

&lt;abstract&gt;&lt;p&gt;This study examines an epidemiological model known as the susceptible-exposed-infected-hospitalized-recovered (SEIHR) model, with and without impulsive vaccination strategies. First, the model was analyzed without impulsive vaccination in the presence of a reinfection effect. Subsequently, it was studied as part of a periodic impulsive vaccination strategy targeting the susceptible population. These vaccination impulses were administered in very brief intervals at specific time instants, with a fixed time gap between each impulse. The two approaches can be modified to respond to different amounts of susceptibility, with control efforts intensifying as susceptibility levels rise. The model's analysis includes crucial aspects such as the non-negativity of solutions, the existence of steady states, and the stability corresponding to the basic reproduction number. We demonstrate that when vaccination measures are taken into account, the basic reproduction number remains as less than one. Therefore, the disease-free equilibrium in the case of vaccination could still be asymptotically stable at the higher disease transmission rate, as compared to the case of no vaccination in which the disease-free equilibrium may no longer be asymptotically stable. Furthermore, we show that when the disease-free equilibrium is stable, the endemic equilibrium cannot be attained, and that when the reproduction number rises above unity, the disease-free equilibrium becomes unstable while the endemic equilibrium becomes stable. We have also derived conditions for the global stability of both equilibriums. To support our theoretical results, we have constructed a time series of numerical simulations and compared them with real-world data from the ongoing SARS-CoV-2 (COVID-19) pandemic.&lt;/p&gt;&lt;/abstract&gt;

Stability Analysis of a Delayed Rumor Propagation Model with Nonlinear Incidence Incorporating Impulsive Vaccination.

The presence of information asymmetry can hinder the public's ability to make well-informed decisions, resulting in unwarranted suspicion and the widespread dissemination of rumors. Therefore, it is crucial to provide individuals with consistent and dependable scientific education. Regular popular science education is considered a periodic impulsive intervention to mitigate the impact of information asymmetry and promote a more informed and discerning public. Drawing on these findings, this paper proposes a susceptible-hesitant-infected-refuting-recovered (SHIDR) rumor-spreading model to explain the spread of rumors. The model incorporates elements such as time delay, nonlinear incidence, and refuting individuals. Firstly, by applying the comparison theorem of an impulsive differential equation, we calculate two thresholds for rumor propagation. Additionally, we analyze the conditions of global attractiveness of the rumor-free periodic solution. Furthermore, we consider the condition for the rumor's permanence. Finally, numerical simulations are conducted to validate the accuracy of our findings. The results suggest that increasing the proportion of impulsive vaccination, reducing the impulsive period, or prolonging the delay time can effectively suppress rumors.

Dynamic behaviors and non-instantaneous impulsive vaccination of an SAIQR model on complex networks

We establish an SAIQR epidemic network model, in which asymptomatic infected people (A) are as contagious as infected people (I). The basic reproductive number R0 is calculated, and the globally asymptotically stable of the disease-free equilibrium, the globally attractive and globally asymptotically stable of the endemic equilibrium are obtained. For the control of epidemic transmission, we take into account the non-instantaneous impulsive vaccination in the model, calculate the basic reproduction number R0⁎ of the model, and demonstrate that the disease-free T-periodic solution is globally attractive and the model is permanent. Finally, we choose scale-free network to simulate numerically and validate the results of this paper.

Stochastic stability and impulsive vaccination of multicompartment nonlinear epidemic model with incidence rate

In this work, we consider a multicompartment nonlinear epidemic model with temporary immunity and a saturated incidence rate. N(t) at time t, this population is divide into seven sub-classes. N(t) = S(t) + E(t) + I(t) + I1(t) + I2(t) + I3(t) + Q(t). where S(t),E(t); I(t); I(t); I1(t),I2(t); I3(t) and Q(t) denote the sizes of the population susceptible to disease, exposed, infectious members and quarantine members with the possibility of infection through temporary immunity, respectively.The stability of a disease-free status equilibrium and the existence of endemic equilibrium determined by the ratio called the basic reproductive number. The multicompartment non linear epidemic model with saturated rate has been studied the stochastic stability of the free disease equilibrium under certain conditions, and obtain the conditions of global attractivity of the infection.

Stability analysis of a nonlocal SIHRDP epidemic model with memory effects.

The prediction and control of COVID-19 is critical for ending this pandemic. In this paper, a nonlocal SIHRDP (S-susceptible class, I-infective class (infected but not hospitalized), H-hospitalized class, R-recovered class, D-death class and P-isolated class) epidemic model with long memory is proposed to describe the multi-wave peaks for the spread of COVID-19. Based on the basic reproduction number R_0, which is completely controlled by fractional order, the stability of the proposed system is studied. Furthermore, the numerical simulation is conducted to gauge the performance of the proposed model. The results on Hunan, China, reveal that R_0<1 suggests that the disease-free equilibrium point is globally asymptotically stable. Likewise, the situation of the multi-peak case in China is presented, and it is clear that the nonlocal epidemic system has a superior fitting effect than the classical model. Finally an adaptive impulsive vaccination is introduced based on the proposed system. Then employing the real data of France, India, the USA and Argentina, parameters identification and short-term forecasts are carried out to verify the effectiveness of the proposed model in describing the case of multiple peaks. Moreover, the implementation of vaccine control is expected once the hospitalized population exceeds 20% of the total population. Numerical results of France, Indian, the USA and Argentina shed light on the varied effect of vaccine control in different countries. According to the vaccine control imposed on France, no obvious effect is observed even consider reducing human contact. As for India, although there will be a temporary increase in hospitalized admissions after execution of vaccination control, COVID-19 will eventually disappear. Results on the USA have seen most significant effect of vaccine control, the number of hospitalized individuals drops off and the disease is eventually eradicated. In contrast to the USA, vaccine control in Argentina has also been very effective, but COVID-19 cannot be completely eradicated.

On the Supervision of a Saturated SIR Epidemic Model with Four Joint Control Actions for a Drastic Reduction in the Infection and the Susceptibility through Time.

This paper presents and studies a new epidemic SIR (Susceptible–Infectious–Recovered) model with susceptible recruitment and eventual joint vaccination efforts for both newborn and susceptible individuals. Furthermore, saturation effects in the infection incidence terms are eventually assumed for both the infectious and the susceptible subpopulations. The vaccination action on newborn individuals is assumed to be applied to a fraction of them while that on the susceptible general population is of linear feedback type reinforced with impulsive vaccination actions (in practice, very strong and massive vaccination controls) at certain time points, based on information on the current levels of the susceptible subpopulation. Apart from the above vaccination controls, it is also assumed that the average of contagion contacts can be controlled via intervention measures, such as confinements or isolation measures, social distance rules, use of masks, mobility constraints, etc. The main objectives of the paper are the achievement of a strictly decreasing infection for all time periods and that of the susceptible individuals over the initial period if they exceed the disease-free equilibrium value. The monitoring mechanism is the combined activation of intervention measures to reduce the contagion contacts together with the impulsive vaccination to reduce susceptibility. The susceptibility and recovery levels of the disease-free equilibrium point are suitably prefixed by the design of the regular feedback vaccination on the susceptible subpopulation.

Computational modeling of human papillomavirus with impulsive vaccination.

In this study, a new SIVS epidemic model for human papillomavirus (HPV) is proposed. The global dynamics of the proposed model are analyzed under pulse vaccination for the susceptible unvaccinated females and males. The threshold value for the disease-free periodic solution is obtained using the comparison theory for ordinary differential equations. It is demonstrated that the disease-free periodic solution is globally stable if the reproduction number is less than unity under some defined parameters. Moreover, we found the critical value of the pulse vaccination for susceptible females needed to control the HPV. The uniform persistence of the disease for some parameter values is also analyzed. The numerical simulations conducted agreed with the theoretical findings. It is found out using numerical simulation that the pulse vaccination has a good impact on reducing the disease.

On an SEIR Epidemic Model with Vaccination of Newborns and Periodic Impulsive Vaccination with Eventual On-Line Adapted Vaccination Strategies to the Varying Levels of the Susceptible Subpopulation

This paper investigates a susceptible-exposed-infectious-recovered (SEIR) epidemic model with demography under two vaccination effort strategies. Firstly, the model is investigated under vaccination of newborns, which is fact in a direct action on the recruitment level of the model. Secondly, it is investigated under a periodic impulsive vaccination on the susceptible in the sense that the vaccination impulses are concentrated in practice in very short time intervals around a set of impulsive time instants subject to constant inter-vaccination periods. Both strategies can be adapted, if desired, to the time-varying levels of susceptible in the sense that the control efforts be increased as those susceptible levels increase. The model is discussed in terms of suitable properties like the positivity of the solutions, the existence and allocation of equilibrium points, and stability concerns related to the values of the basic reproduction number. It is proven that the basic reproduction number lies below unity, so that the disease-free equilibrium point is asymptotically stable for larger values of the disease transmission rates under vaccination controls compared to the case of absence of vaccination. It is also proven that the endemic equilibrium point is not reachable if the disease-free one is stable and that the disease-free equilibrium point is unstable if the reproduction number exceeds unity while the endemic equilibrium point is stable. Several numerical results are investigated for both vaccination rules with the option of adapting through ime the corresponding efforts to the levels of susceptibility. Such simulation examples are performed under parameterizations related to the current SARS-COVID 19 pandemic.

The analysis of mode-locking topology in an SIR epidemic dynamics model with impulsive vaccination control: Infinite cascade of Stern-Brocot sum trees

Abstract We report the topology of stable periodic solutions of an SIR epidemic dynamics model with impulsive vaccination control, a hybrid discrete/continuous non-smooth system, in the parameter plane spanned by the pulse period T and the quantity of pulse vaccination b. This mode-locking topology is governed by an invariant torus (a pair of frequencies) initiated from Hopf bifurcations rather than the fast-slow time scales, and its periodicity is in perfect agreement with the so-called Stern-Brocot sum tree, a derived tree from “Farey algorithm”. More surprisingly, the mode-locking order is unfolded in a way that never encountered before to emerge organized according to the reciprocal of the Stern-Brocot sum tree. Furthermore, the global organization of mode-locking is not isolated structure but an infinite Stern-Brocot sum tree cascade when tuning the control parameter T. The results obtained contribute a new framework to classify mode-locking oscillations observed in the hybrid system.

Effect of pulse vaccination on dynamics of dengue with periodic transmission functions

Pulse vaccination is a repeated vaccination policy, which plays a tremendous role in the global fight against communicable diseases in terms of saving medical resources and decreasing the economic burden. In this article, we propose a dynamic model of dengue infection with periodic transmission functions and seasonality in vector population. Furthermore, we introduce a pulse vaccination strategy in the susceptible host population to examine how frequency and intensity of implementation of this strategy affect the dynamics of dengue infection. We successfully obtained the threshold dynamics by defining the basic reproduction number R0, which is the spectral radius of the next generation operator and governs whether the disease dies out or not. It has been established that the infection-free periodic solution of the proposed impulsive system is globally asymptotically stable if mbox{R}_{0}<1 and is unstable otherwise. Moreover, we found that the dengue infection is uniformly persistent for the proposed system if mbox{R}_{0}>1. Finally, we execute the system numerically to illustrate the piecewise solutions of the proposed system with impulsive vaccination measure and to investigate the influence of different control parameters on the basic reproduction. The finding indicates that a frequent implementation of the vaccination strategy with great intensity and the use of mosquito nets can essentially lead to a decline of new infections.

Dynamical Behavior and Bifurcation Analysis of the SIR Model with Continuous Treatment and State-Dependent Impulsive Control

In this study, we propose a state-dependent impulsive model describing the susceptible individuals-triggered interventions. We find that the model with susceptible individuals-guided impulsive interventions can exhibit very complex dynamical behaviors with rich biological meanings. We note that this formulated impulsive model has disease-free periodic solution, and we can investigate the threshold dynamics by defining the control reproduction number. We study the existence and stability of the disease-free periodic solution (DFPS) for [Formula: see text]. Our results show that, even if the basic reproduction number [Formula: see text], the DFPS can still be stable when the threshold level of susceptible population [Formula: see text], indicating that with a proper chosen [Formula: see text], the state-dependent impulsive strategy can effectively control the development of the infectious disease and eradicate the disease eventually. By employing the bifurcation theory, we investigate the bifurcation phenomenon near the DFPS with respect to some key parameters, and observe that a positive order-1 periodic solution can bifurcate from the DFPS via a transcritical bifurcation. By utilizing numerical simulation, we further explore the existence and stability of the positive order-[Formula: see text] periodic solutions, and found the feasibility of stable positive order-1, order-2 and order-3 periodic solutions, that imply the existence of chaos. In particular, we find that there can be three positive order-1 periodic solutions simultaneously, in which one is stable and the other two are unstable. Our finding indicates that the comprehensive strategy combining continuous treatment with state-dependent impulsive vaccination and isolation plays a crucial role in controlling the prevalence and further spread of the infectious diseases.

An index to quantify individual social responsibility in the decision to be vaccinated.

In the context of generic infectious disease studies, the aim of this paper is to quantify and represent the individual social responsibility based on whether or not a single individual is vaccinated. Although the objective of this study is merely educational the approach implemented is based on a classical mathematical model named S.I.R. (Susceptible-Infected-Recovered) using an impulsive vaccination strategy. Dates of vaccination and fraction of individuals vaccinated are used as parameters. In addition, numerical simulations are conducted to represent the outcomes regarding the reduction of infected cases through tables and graphs.

An SIQR mode with impulsive vaccination and impulsive elimination

An SIQR mode with impulsive vaccination and impulsive elimination

Dynamics of cholera epidemics with impulsive vaccination and disinfection

Waterborne diseases have a tremendous influence on human life. The contaminated drinking water causes water-borne disease like cholera. Pulse vaccination is an important and effective strategy for the elimination of infectious diseases. A waterborne disease like cholera can also be controlled by using impulse technique. In this paper, we have proposed a delayed SEIRB epidemic model with impulsive vaccination and disinfection. We have studied the pulse vaccination strategy and sanitation to control the cholera disease. The existence and stability of the disease-free and endemic periodic solution are investigated both analytically and numerically. It is shown that there exists an infection-free periodic solution, using the impulsive dynamical system defined by the stroboscopic map. It is observed that the infection-free periodic solution is globally attractive when the impulse period is less than some critical value. From the analysis of the model, we have obtained a sufficient condition for the permanence of the epidemic with pulse vaccination. The main highlight of this paper is to introduce impulse technique along with latent period into the SEIRB epidemic model to investigate the role of pulse vaccination and disinfection on the dynamics of the cholera epidemics.

Modelling the effects of contaminated environments in mainland China on seasonal HFMD infections and the potential benefit of a pulse vaccination strategy

Substantial and increasing outbreaks of EV71-related hand, foot and mouth disease (HFMD) have occurred recently in mainland China with serious consequences for child health. The HFMD pathogens can survive for long periods outside the host in suitable conditions, and hence indirect transmission via free-living pathogens in the environment cannot be ignored. We propose a novel mathematical model of both periodic direct transmission and indirect transmission followed by incorporation of an impulsive vaccination strategy. By applying Floquet theory and the comparison theorem of impulsive differential equations, we obtained a threshold parameter which governs the extinction or the uniform persistence of the disease. The rate, frequency and timing of pulse vaccination were found to affect the basic reproduction number and the number of infected individuals significantly. In particular, frequent vaccination with a high coverage rate leads to declines in the basic reproduction number. Moreover, for a given rate of vaccination or frequency, numerical studies suggested that there was an optimal time (September, just before the start of new school terms) when the basic reproduction number and hence new HFMD infections could be minimised. Frequent high intensity vaccinations at a suitable time (e.g. September) and regular cleaning of the environment are effective measures for controlling HFMD infections.

On the discretization and control of an SEIR epidemic model with a periodic impulsive vaccination

This paper deals with the discretization and control of an SEIR epidemic model. Such a model describes the transmission of an infectious disease among a time-varying host population. The model assumes mortality from causes related to the disease. Our study proposes a discretization method including a free-design parameter to be adjusted for guaranteeing the positivity of the resulting discrete-time model. Such a method provides a discrete-time model close to the continuous-time one without the need for the sampling period to be as small as other commonly used discretization methods require. This fact makes possible the design of impulsive vaccination control strategies with less burden of measurements and related computations if one uses the proposed instead of other discretization methods. The proposed discretization method and the impulsive vaccination strategy designed on the resulting discretized model are the main novelties of the paper. The paper includes (i) the analysis of the positivity of the obtained discrete-time SEIR model, (ii) the study of stability of the disease-free equilibrium point of a normalized version of such a discrete-time model and (iii) the existence and the attractivity of a globally asymptotically stable disease-free periodic solution under a periodic impulsive vaccination. Concretely, the exposed and infectious subpopulations asymptotically converge to zero as time tends to infinity while the normalized subpopulations of susceptible and recovered by immunization individuals oscillate in the context of such a solution. Finally, a numerical example illustrates the theoretic results.

Modelling the use of impulsive vaccination to control Rift Valley Fever virus transmission

In this paper, we propose a vector-bone dynamical model to against the transmission of Rift Valley Fever (RVF) between ruminants and mosquitoes, where impulsive vaccination for susceptible ruminants is introduced. By using the comparison principle, integral and differential inequalities, and some of analytical skills, the threshold values for the stability of the disease-free periodic solution and uniform persistence of disease are obtained. These values characterize the evolution and extinction of the disease. Numerical simulations are carried out to illustrate the main theoretical results and the feasibility of the impulsive vaccination control strategy.