Pulse Vaccination Research Articles

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.

Epidemic dynamics of complex networks under pulse treatment and vaccination

The dynamics of a new Susceptible-Vaccinated-Infected-Recovered (SVIR) epidemic model in complex networks under constant and pulse control are investigated. Firstly, the epidemic model in complex networks under constant control is proposed. Utilizing the basic reproduction number, the sufficient conditions for stabilizing the epidemic under constant control are established. Since constant control is not conducive to resource conservation, it has been replaced by pulse control in epidemic model. The paper demonstrates the global attractiveness of the disease-free periodic solution of the model under pulse treatment and pulse vaccination. In addition, a sufficient condition is put forward to make sure that the system persists under pulse control, indicating periodic outbreaks of the epidemic. Furthermore, the epidemic is uniformly persistent when the pulse period is greater than the pulse period threshold or the vaccination rate is less than the vaccination threshold. Finally, several numerical simulations prove the feasibility of the theoretical results. By comparing the pulse period with a critical value, the strategy that most contributes to controlling the epidemic propagation is chosen from constant control and pulse control to achieve maximum utilization of resources. Moreover, it shows that decreasing the fraction of pulse treatment and pulse vaccination or prolonging the pulse period is beneficial to epidemic propagation. The topology of complex networks has a non-negligible influence on the epidemic propagation under pulse control, which is demonstrated both theoretically and numerically.

Dynamical behaviors of a network-based SIR epidemic model with saturated incidence and pulse vaccination

Pulse vaccination is an effective strategy to restrain the spread of infectious diseases. This paper proposes a network-based SIR epidemic model incorporating a saturated force of infection and vertical transmission along with pulse vaccination strategy and continuous treatment plan. Dynamical behaviors of the model are analyzed in virtue of the theory for impulsive differential equations. We give the boundedness of solutions and derive the expression of basic reproduction number R0. By the Floquet theorem and comparison principle, we show that the disease-free periodic solution is globally asymptotically stable when R0<1. Moreover, a sufficient condition for the uniform permanence of the system is also obtained. Finally, numerical analyses are given to substantiate the theoretical results and a case for Rubella is studied.

Periodic vaccination for post-pandemic management: Insights from and planning beyond COVID-19

Waning immunity to the SARS-CoV-2 virus and the inevitability of viral mutations necessitate a large-scale periodic revaccination program. Rapid mass vaccination may quickly suppress an epidemic, but it may have an unintended downstream effect of creating a surge in population susceptibility later when vaccinated people lose their immunity all at the same time. To test this hypothesis, we conducted a simulation study comparing pulse vaccination, the repeated administration of “booster” vaccines in large pulses occurring at fixed intervals, and constant vaccination, the continuous administration of booster vaccines at a slower, constant pace. We showed that constant vaccination can maintain population susceptibility and therefore incident deaths at a constant, manageable level; while pulse vaccination can induce large recurrent epidemics. The advantage of constant vaccination is only realized, however, in a post-pandemic scenario when a high level of population immunity has already been attained through a combination of vaccination and natural infection. At the beginning of a novel pandemic, aggressive vaccination is recommended to prioritize immediate protection over long-term protection. In a counterfactual analysis, we showed that prematurely switching to constant vaccination would have significantly increased the disease burden during the Delta variant wave in August 2021.

Stability Analysis of SIRS Model considering Pulse Vaccination and Elimination Disturbance

It is well known that many natural phenomena and human activities do exhibit impulsive effects in the fields of epidemiology. At the same time, compared with a single control strategy, it is obvious that the multiple control strategies are more beneficial to restrain the spread of infectious diseases. In this paper, we consider pulse vaccination and pulse elimination strategies at the same time and establish an SIRS epidemic model with standard incidence. Firstly, according to the stroboscopic mapping method of the discrete dynamical system, the disease-free T periodic solution of the model under the condition of pulse vaccination and pulse elimination is obtained. Secondly, the basic reproductive number R0 is defined, and the local asymptotic stability of the disease-free T periodic solution is proved by Floquet theory for R0&lt;1. Finally, based on the impulsive differential inequality theory, the global asymptotic stability of the disease-free T periodic solution is given for R0&lt;1, and the disease dies out eventually. The results show that in order to stop the disease epidemic, it is necessary to choose the appropriate vaccination rate and elimination rate and the appropriate impulsive period.

Wildlife vaccination strategies for eliminating bovine tuberculosis in white-tailed deer populations.

Many pathogens of humans and livestock also infect wildlife that can act as a reservoir and challenge disease control or elimination. Efficient and effective prioritization of research and management actions requires an understanding of the potential for new tools to improve elimination probability with feasible deployment strategies that can be implemented at scale. Wildlife vaccination is gaining interest as a tool for managing several wildlife diseases. To evaluate the effect of vaccinating white-tailed deer (Odocoileus virginianus), in combination with harvest, in reducing and eliminating bovine tuberculosis from deer populations in Michigan, we developed a mechanistic age-structured disease transmission model for bovine tuberculosis with integrated disease management. We evaluated the impact of pulse vaccination across a range of vaccine properties. Pulse vaccination was effective for reducing disease prevalence rapidly with even low (30%) to moderate (60%) vaccine coverage of the susceptible and exposed deer population and was further improved when combined with increased harvest. The impact of increased harvest depended on the relative strength of transmission modes, i.e., direct vs indirect transmission. Vaccine coverage and efficacy were the most important vaccine properties for reducing and eliminating disease from the local population. By fitting the model to the core endemic area of bovine tuberculosis in Michigan, USA, we identified feasible integrated management strategies involving vaccination and increased harvest that reduced disease prevalence in free-ranging deer. Few scenarios led to disease elimination due to the chronic nature of bovine tuberculosis. A long-term commitment to regular vaccination campaigns, and further research on increasing vaccines efficacy and uptake rate in free-ranging deer are important for disease management.

Mathematical modeling of infectious diseases and the impact of vaccination strategies.

Mathematical modeling plays a crucial role in understanding and combating infectious diseases, offering predictive insights into disease spread and the impact of vaccination strategies. This paper explored the significance of mathematical modeling in epidemic control efforts, focusing on the interplay between vaccination strategies, disease transmission rates, and population immunity. To facilitate meaningful comparisons of vaccination strategies, we maintained a consistent framework by fixing the vaccination capacity to vary from 10 to 100% of the total population. As an example, at a 50% vaccination capacity, the pulse strategy averted approximately 45.61% of deaths, while continuous and hybrid strategies averted around 45.18 and 45.69%, respectively. Sensitivity analysis further indicated that continuous vaccination has a more direct impact on reducing the basic reproduction number $ R_0 $ compared to pulse vaccination. By analyzing key parameters such as $ R_0 $, pulse vaccination coefficients, and continuous vaccination parameters, the study underscores the value of mathematical modeling in shaping public health policies and guiding decision-making during disease outbreaks.

Novel corona virus disease dynamical models with pulse vaccination

Due to the widespread and serious prevalence of the 2019 novel corona virus disease (COVID-19), COVID-19, has seriously affected people’s lives and the economic development. To study the transmission dynamics of COVID-19 and find effective measures to control, prevent and ultimately eliminate COVID-19 are one of the main problems now. In this paper, we build a pulse mathematical model of COVID-19 with vaccination. Using the principle of stroboscopic mapping and the basic reproduction number R0, we show that if R0<1, the disease-free periodic solution is globally asymptotically stable; If R0>1, the model is persistent and there exists a positive periodic solution; Using the bifurcation theory, there is a supercritical bifurcation for the model if R0=1. Finally, the numerical simulation and sensitivity analysis shows that reducing the novel corona virus infection rate and increasing the cure rate are more effective than increasing the vaccination rate. In order to comprehensively and quickly control the spread of the epidemic, excepting for vaccination, some other measures need to be implemented, such as reducing the population exposure rate and using specific drugs, which provides useful suggestions for the governments to prevent, control and ultimately eliminate COVID-19.

Mathematical analysis of pulse vaccination in controlling the dynamics of measles transmission

Although the incidence of measles has been significantly reduced through vaccination, it remains an important public health problem. In this paper, a measles model with pulse vaccination is formulated to investigate the influential pulse vaccination on the period of time for the extinction of the disease. The threshold value of the formulated model, called the control reproduction number and denoted by R∗, is derived. It is found that the disease-free periodic solution of the model exists and is globally attractivity whenever R∗<1 in the sense that measles is eliminated. If R∗>1, the positive solution of the model exists and is permanent which indicates the disease persists in the community. Theoretical conditions for disease eradication under various constraints are given. The effect of pulse vaccination is explored using data from Thailand. The results obtained can guide policymakers in deciding on the optimal scheduling in order to achieve the strategic plan of measles elimination by vaccination.

An improved ISR-WV rumor propagation model based on multichannels with time delay and pulse vaccination

The rapid development of the Internet has broadened the channels of dissemination of information, it has also led to the rapid and widespread propagation of rumors, which can have a serious negative impact socially. In this paper, an improved ISR-WV rumor propagation model integrating multichannels is proposed by considering the system’s time delay, and the influence of different channels of propagation on the dynamic process is further analyzed. Moreover, the basic reproduction number R 0, rumor-free equilibrium, and rumor-prevailing equilibrium, as well as their stability, are deduced. Then, an optimal control problem with pulse vaccination is designed. Finally, the validity of the model and theoretical results is verified by numerical simulations and a practical application. The results show that the rumor propagation threshold R 0 is more sensitive to the rate of the propagation of the information base channel. The shorter the thinking time τ 1 required for the ignorant to react after obtaining the information, the larger the final scale of propagation. Under this condition, the time delay τ 2 spent by a spreader in producing a video is negatively related to the final scale of the propagation; conversely, a longer τ 1 implies that the person tends to more cognizant, which can suppress the spread of rumors. Under this condition, τ 2 has little effect on the final scale of propagation. In addition, the results also prove that timely implementation of the pulse vaccination control strategy of popular science education can effectively control the propagation of rumors and reduce their negative impact.

Dynamics of a diffusive viral infection model with impulsive CTL immune response

To explore the impacts of pulse vaccination on the dynamical behaviors of virus, the current paper investigates the persistence and global attractivity of a diffusive viral infection model incorporated with impulsive CTL immune response while the stronger logistic growth mechanism. Based on the comparison principle and the proper upper and lower solutions, we first discuss the existence of the infection-free steady state, and define the crucial CTL-activated viral infection reproduction number R 0 . Then, the fundamental extinction and uniform persistence behaviors of virus are distinguished by various cases of the threshold parameter R 0 . Finally, the existence and global attractivity of the positive steady state are still established by employing Brouwer's fixed point theorem and auxiliary functional. Our results indicate that high vaccination rates will stimulate the CTL response more effectively, and thus eventually can force the virus to eradicate.

An SIS epidemic model in a patchy environment with pulse vaccination and quarantine

An SIS epidemic model in an m-patch environment with pulse vaccination and quarantine at two different fixed moments is formulated by impulsive differential equations in this paper. The sufficient conditions for the extinction and persistence of the disease are derived and the threshold value R0 is obtained by using the persistence theory of impulsive systems, the impulsive-type Floquet theory and the perturbation techniques. That is, the infection-free periodic solution is globally asymptotically stable if R0<1, and the impulsive system becomes uniformly persistent if R0>1. When m=2, two special cases are considered to illustrate joint impact of the pulse vaccination and quarantine and population mobility on the disease dynamics. Numerical simulations are given to show the effectiveness of the theoretical results.

Towards a new combination therapy with vectored immunoprophylaxis for HIV: Modeling “shock and kill” strategy

Latently infected cells are considered as a major barrier to curing Human Immunodeficiency Virus (HIV) infection. Reactivation of latently infected cells followed by killing the actively infected cells may be a potential strategy (“shock and kill”) to purge the latent reservoir. Based on vectored immunoprophylaxis (VIP) experiment that can elicit bNAbs, in this paper a mathematical model is formulated to explore the efficacy of “shock and kill” strategy with VIP. We derive the basic reproduction number R0 of the model and show that R0 completely determines the dynamics of the model: if R0<1, the disease-free equilibrium is globally asymptotically stable; if R0>1, the system is uniformly persistent. Numerical simulations suggest that the “shock and kill” strategy with VIP can effectively control HIV infection while this strategy cannot eradicate the reservoir without VIP although it can alleviate the HIV infection. To model the administration of drugs and vaccine more realistically, pharmacokinetics and pulse vaccination are incorporated into the model of ordinary differential equations. The resultants are described by impulsive differential equations. The thresholds are obtained for the frequency and strength of the vaccination to eliminate the viruses. Furthermore, the most appropriate times are numerically investigated for starting a short-term latency-reversing agents (LRAs) treatment relative to ART considering the toxicity of LRAs. The results show that LRAs treatment at the beginning of ART might be a better option. These results have important implications for the design of HIV cure-related clinical trials.

A plague epidemic disease optimizing approach

In order to solve some optimization problems with multi-local optimal solutions, a plague infectious disease optimization (PIDO) algorithm is proposed by the dynamic model of plague infectious disease with pulse vaccination and time delay. In this algorithm, it is assumed that there are several villagers living in a village, each villager is characterized by some characteristics. The plague virus is prevalent in the village, and the villagers contract the infectious disease through effective contact with sick rats. The plague virus attacks is the few characteristics of the human body. Under the action of the plague virus, the growth status of each villager will be randomly transformed among 4 states of susceptibility, exposure, morbidity and recovery, thus a random search is achieved for the global optimal solution. The physical strength degree of villagers is described by the human health index (HHI). The higher the villager’s HHI index, the stronger the physique and the higher the surviving likelihood. 9 operators (S_S, S_E, E_E, E_I, E_R, I_I, I_R, R_R, R_S) are designed in the PIDO algorithm, and each operator only deals with the 1/1000∼1/100 of the total number of variables each time. The case study results show that PIDO algorithm has the characteristics of fast search speed and global convergence, and it is suitable for solving global optimization problems with higher dimensions.

Stability analysis and optimal control of rumor spreading model under media coverage considering time delay and pulse vaccination

Information asymmetry often interferes with the public's judgment, creates unnecessary suspicion, and leads to the wanton spread of rumors. Therefore, it is necessary to carry out regular science education to improve personal cultural literacy and restrain the spread of rumors. In this paper, regular popular science education is introduced into the rumor spreading model as periodic pulse vaccination. On this basis, an improved rumor spreading model under media coverage is constructed in combination with time delay. Two thresholds are calculated by using the comparison theorem of impulse differential equation. The conditions of global attractively and persistence of rumor spreading are analyzed. Then, the optimal control problem under pulse vaccination is designed to minimize the rumor spreading scale and control cost, then the optimality conditions are obtained by using the Pontryagin's minimum principle. Finally, the theoretical results are verified by numerical simulations. It shown that increasing the proportion of pulse vaccination or shortening the pulse period or prolonging time delay contribute to the restraint of rumors. Increasing the pulse period or decreasing the delay time both aggravate the rumor spreading. Meanwhile, the introduction of the optimal pulse control can shorten the spreading time of rumors and reduce the losses caused by rumors.

Threshold dynamics of an SEAIR epidemic model with application to COVID-19

In this paper, a Susceptible-Exposed-Asymptomatic-Infectious-Recovered (SEAIR) epidemic model with application to COVID-19 is established by capturing the key features of the disease. The global dynamics of the model is analyzed by constructing appropriate Lyapunov functions utilizing the basic reproduction number \(R_0\) as an index. We obtain that when \(R_{0}<1\), the disease-free equilibrium is globally asymptotically stable. While for \(R_{0}>1\), the endemic equilibrium is globally asymptotically stable. Furthermore, we consider the pulse vaccination for the disease and give an impulsive differential equations model. The definition of the basic reproduction number \(R_{0}\) of this system is given by utilizing the next generation operator. By the comparison theorem and persistent theory, we obtain that when \(R_{0}<1\)}, the disease-free periodic solution is globally asymptotically stable. Otherwise, the disease will persist and there will be at least one nontrivial periodic solution. Numerical simulations to verify our conclusions are given at the end of each of these theorems.

Identification of Immunogenic MHC Class II Human HER3 Peptides that Mediate Anti-HER3 CD4+ Th1 Responses and Potential Use as a Cancer Vaccine.

The HER3/ERBB3 receptor is an oncogenic receptor tyrosine kinase that forms heterodimers with EGFR family members and is overexpressed in numerous cancers. HER3 overexpression associates with reduced survival and acquired resistance to targeted therapies, making it a potential therapeutic target in multiple cancer types. Here, we report on immunogenic, promiscuous MHC class II-binding HER3 peptides, which can generate HER3-specific CD4+ Th1 antitumor immune responses. Using an overlapping peptide screening methodology, we identified nine MHC class II-binding HER3 epitopes that elicited specific Th1 immune response in both healthy donors and breast cancer patients. Most of these peptides were not identified by current binding algorithms. Homology assessment of amino acid sequence BLAST showed >90% sequence similarity between human and murine HER3/ERBB3 peptide sequences. HER3 peptide-pulsed dendritic cell vaccination resulted in anti-HER3 CD4+ Th1 responses that prevented tumor development, significantly delayed tumor growth in prevention models, and caused regression in multiple therapeutic models of HER3-expressing murine tumors, including mammary carcinoma and melanoma. Tumors were robustly infiltrated with CD4+ T cells, suggesting their key role in tumor rejection. Our data demonstrate that class II HER3 promiscuous peptides are effective at inducing HER3-specific CD4+ Th1 responses and suggest their applicability in immunotherapies for human HER3-overexpressing tumors.

Correction to: Dynamic behavior of prostate cancer cells under antitumor immunity and pulse vaccination in a random environment

Correction to: Dynamic behavior of prostate cancer cells under antitumor immunity and pulse vaccination in a random environment

Dynamic behavior of prostate cancer cells under antitumor immunity and pulse vaccination in a random environment

Dynamic behavior of prostate cancer cells under antitumor immunity and pulse vaccination in a random environment

The burden of hand, foot, and mouth disease among children under different vaccination scenarios in China: a dynamic modelling study

BackgroundHand, foot, and mouth disease (HFMD) is a common illness in young children. A monovalent vaccine has been developed in China protecting against enterovirus-71, bivalent vaccines preventing HFMD caused by two viruses are under development.ObjectiveTo predict and compare the incidence of HFMD under different vaccination scenarios in China.MethodsWe developed a compartmental model to capture enterovirus transmission and the natural history of HFMD in children aged 0–5, and calibrated to reported cases in the same age-group from 2015 to 2018. We compared the following vaccination scenarios: different combinations of monovalent and bivalent vaccine; a program of constant vaccination to that of pulse vaccination prior to seasonal outbreaks.ResultsWe estimate 1,982,819, 2,258,846, 1,948,522 and 2,398,566 cases from 2015 to 2018. Increased coverage of monovalent vaccine from 0 to 80% is predicted to decrease the cases by 797,262 (49.1%). Use of bivalent vaccine at an 80% coverage level would decrease the cases by 828,560. Use of a 2.0× pulse vaccination for the bivalent vaccine in addition to 80% coverage would reduce cases by over one million. The estimated R0 for HFMD in 2015–2018 was 1.08, 1.10, 1.35 and 1.17.ConclusionsOur results point to the benefit of bivalent vaccine and using a pulse vaccination in specific months over routine vaccination. Other ways to control HFMD include isolation of patients in the early stage of dissemination, more frequent hand-washing and ventilation, and better treatment options for patients.