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In recent years, the suppression of disease population in pest control has gained popularity and remains a pressing issue in agricultural production. Additionally, the mathematical modeling method is often exploited to study the dynamics of different infectious diseases. A new pest control model with multiple delays and impulsive effects is developed and investigated. Firstly, the global attractivity of infection-free periodic solution of the system is proved by applying the theory of impulsive differential equation and comparative theorem. Secondly, the persistence of the infection-free periodic solution of the proposed model is also proved. Finally, the theoretical analysis results are validated by numerical simulations and some suggestions on how to better control the pests are presented.

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, 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.

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 R01, 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.

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. • The impact of population topology about individual heterogeneity on epidemic is studied. • Pulse vaccination and pulse treatment are both considered, which save resources and costs. • Several dynamical behaviors of a new SVIR epidemic model are investigated. • Numerical simulations show pulse control can more effectively control the spread of epidemic. [ABSTRACT FROM AUTHOR]

Seasonal influenza (also known as flu) is responsible for considerable morbidity and mortality across the globe. The three recognized pathogens that cause epidemics during the winter season are influenza A, B and C. The influenza virus is particularly dangerous due to its mutability. Vaccines are an effective tool in preventing seasonal influenza, and their formulas are updated yearly according to the WHO recommendations. However, in order to facilitate decision-making in the planning of the intervention, policymakers need information on the projected costs and quantities related to introducing the influenza vaccine in order to help governments obtain an optimal allocation of the vaccine each year. In this paper, an approach based on a Controlled Elitism Non-Dominated Sorting Genetic Algorithm (CENSGA) model is introduced to optimize the allocation of the influenza vaccination. A bi-objective model is formulated to control the infection volume, and reduce the unit cost of the vaccination campaign. An SIR (Susceptible–Infected–Recovered) model is employed for representing a potential epidemic. The model constraints are based on the epidemiological model, time management and vaccine quantity. A two-phase optimization process is proposed: guardian control followed by contingent controls. The proposed approach is an evolutionary metaheuristic multi-objective optimization algorithm with a local search procedure based on a hash table. Moreover, in order to optimize the scheduling of a set of policies over a predetermined time to form a complete campaign, an extended CENSGA is introduced with a variable-length chromosome (VLC) along with mutation and crossover operations. To validate the applicability of the proposed CENSGA, it is compared with the classical Non-Dominated Sorting Genetic Algorithm (NSGA-II). The results indicate that optimal vaccination campaigns with compromise tradeoffs between the two conflicting objectives can be designed effectively using CENSGA, providing policymakers with a number of alternatives to accommodate the best strategies. The results are analyzed using graphical and statistical comparisons in terms of cardinality, convergence, distribution and spread quality metrics, illustrating that the proposed CENSGA is effective and useful for determining the optimal vaccination allocation campaigns. [ABSTRACT FROM AUTHOR]

Controlling the mosquito population is a big challenge for humans. In this paper, we have studied the effects of impulsive control strategies on the spread of mosquito-borne diseases considering the latent period. Therefore, we proposed and analyzed a mosquito-borne disease model governed by a system of impulsive delay differential equations. The proposed mosquito-borne disease model also accounts for three different impulsive control strategies, namely vaccination, pesticides, and adulticides. Two thresholds R 1 and R 2 established for the global attractivity of the disease-free state and the persistence of the endemic state. The non-trivial disease-free solution of the proposed model is globally asymptotically stable if R 1 and R 2 less than one. It is shown that a unique positive endemic periodic solution exists only when R 1 and R 2 greater than unity, which makes for the persistence of the disease. Numerical simulation supports the analytical finding and shows the effectiveness of the impulse control strategies. [ABSTRACT FROM AUTHOR]

Abstract Background Hand, 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. Objective To predict and compare the incidence of HFMD under different vaccination scenarios in China. Methods We 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. Results We 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 R 0 for HFMD in 2015–2018 was 1.08, 1.10, 1.35 and 1.17. Conclusions Our 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.

Common air pollutants, such as ozone (O 3 O 3), sulfur dioxide (S O 2 S O 2) and nitrogen dioxide (N O 2 N O 2), can affect the spread of influenza. We propose a new non-autonomous impulsive differential equation model with the effects of ozone and vaccination in this paper. First, the basic reproduction number of the impulsive system is obtained, and the global asymptotic stability of the disease-free periodic solution is proved. Furthermore, the uniform persistence of the system is demonstrated. Second, the unknown parameters of the ozone dynamics model are obtained by fitting the ozone concentration data by the least square method and Bootstrap. The MCMC algorithm is used to fit influenza data in Gansu Province to identify the most suitable parameter values of the system. The basic reproduction number R 0 R 0 is estimated to be 1.2486 1.2486 (95 % C I : (1.2470 , 1.2501) 95 % C I : (1.2470 , 1.2501)). Then, a sensitivity analysis is performed on the system parameters. We find that the average annual incidence of seasonal influenza in Gansu Province is 31.3374 per 100,000 people. Influenza cases started to surge in 2016, rising by a factor of one and a half between 2014 and 2016, further increasing in 2019 (54.6909 per 100,000 population). The average incidence rate during the post-upsurge period (2017-2019) is one and a half times more than in the pre-upsurge period (2014-2016). In particular, we find that the peak ozone concentration appears 5–8 months in Gansu Province. A moderate negative correlation is seen between influenza cases and monthly ozone concentration (Pearson correlation coefficient: r r = -0.4427). Finally, our results show that increasing the vaccination rate and appropriately increasing the ozone concentration can effectively prevent and control the spread of influenza. [ABSTRACT FROM AUTHOR]

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 R0 as an index. We obtain that when R0 < 1, the disease-free equilibrium is globally asymptotically stable. While for R0 > 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 R0 of this system is given by utilizing the next generation operator. By the comparison theorem and persistent theory, we obtain that when R0 < 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. [ABSTRACT FROM AUTHOR]

Advanced prostate cancer (PCa) is usually treated with androgen deprivation therapy (ADT), which is initially effective but can lead to metastatic castration-resistant prostate cancer. The dendritic cell vaccine immunotherapy can enhance the antitumor immune responses to help fight cancer and has been shown to be effective. A stochastic impulsive PCa model incorporating ADT and immunotherapy is developed in this article to analyze the elimination of androgen-dependent and androgen-independent cancer cells under the noise interference. Besides the existence, uniqueness and boundedness of global positive solution of the model, some sufficient conditions of extinction and persistence in mean of PCa cells are also obtained by using the Itô's formula and the comparison theorem of stochastic differential equation. Our study illustrates that high-intensity noise perturbation can inhibit the development of PCa and verifies theoretically and numerically that frequent vaccination can improve the survival time of the patient with ADT. [ABSTRACT FROM AUTHOR]

Background: Hand, 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.Objective: To predict and compare the incidence of HFMD under different vaccination scenarios in China.Methods: We 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.Results: We 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.Conclusions: Our 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. [ABSTRACT FROM AUTHOR]

An alternative to the constant vaccination strategy could be the administration of a large number of doses on "immunization days" with the aim of maintaining the basic reproduction number to be below one. This strategy, known as pulse vaccination, has been successfully applied for the control of many diseases especially in low-income countries. In this paper, we analytically prove (without being computer-aided) the existence of chaotic dynamics in the classical SIR model with pulse vaccination. To the best of our knowledge, this is the first time in which a theoretical proof of chaotic dynamics is given for an epidemic model subject to pulse vaccination. In a realistic public health context, our analysis suggests that the combination of an insufficient vaccination coverage and high birth rates could produce chaotic dynamics and an increment of the number of infectious individuals. [ABSTRACT FROM AUTHOR]

We introduce a non-instantaneous pulse vaccination model. Non-instantaneous impulsive nonlinear differential equations provide an adequate biomathematical model of some medical problems. In this paper we study some basic properties such as the attractiveness of the infection-free periodic solution and the permanence of some sub-population for a vaccine model where a constant fraction of the susceptible population is vaccinated in some periodic way. Our model is a system of nonlinear differential equations with impulses. [ABSTRACT FROM AUTHOR]

A time-delayed SIR model with general nonlinear incidence rate, pulse vaccination and temporary immunity is developed. The basic reproduction number is derived and it is shown that the disease-free periodic solution generically undergoes a transcritical bifurcation to an endemic periodic solution as the vaccination coverage drops below a critical level. Using numerical continuation and a monodromy operator discretization scheme, we track the bifurcating endemic periodic solution as the vaccination coverage is decreased and a Hopf point is detected. This leads to a bifurcation to an attracting, invariant cylinder. As the vaccination coverage is further decreased, the geometry of the cylinder contracts along its length until it finally collapses to a periodic orbit when the vaccination coverage goes to zero. In the intermediate regime, phase locking on the cylinder is observed. [ABSTRACT FROM AUTHOR]

This paper considers the periodic pulse vaccination of susceptible and the isolation control of the infective，a SEIQR epidemic model is established. The sufficient condition for stability of disease-free periodic solution and permanence of disease are obtained by pulse equation theory.

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. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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 R 0 , we show that if R 0 < 1 , the disease-free periodic solution is globally asymptotically stable; If R 0 > 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 R 0 = 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. • For the COVID-19 model with pulse vaccination: If the basic reproduction number R 0 < 1, the disease-free periodic solution is globally asymptotically stable. • For the COVID-19 model with pulse vaccination: If the basic reproduction number R 0 > 1, the model is permanent. • For the COVID-19 model with pulse vaccination: If the basic reproduction number R 0 = 1, the model has a supercritical bifurcation. • For the COVID-19 model with pulse vaccination: By analyzing the parameters, we obtain that drugs for COVID-19 is more important. [ABSTRACT FROM AUTHOR]

In this paper, we have considered a dynamical model of Chlamydia disease with varying total population size, bilinear incidence rate, and pulse vaccination strategy in a random environment. It has been shown that the Chlamydia epidemic model has global positive solutions and, under some conditions, it admits a unique positive periodic disease-free solution, which is globally exponentially stable in mean square. We have defined two positive numbers R1 and R2 ( 1. Our analytical findings are explained through numerical simulation, which show the reliability of our model from the epidemiological point of view.

In this paper, we establish two new stochastic switched epidemic models with continuous and impulsive control. The stochastic perturbations are considered for the natural death rate in each equation of the models. Firstly, a stochastic switched S I L I model with continuous control schemes is investigated. By using Lyapunov–Razumikhin method, the sufficient conditions for extinction in mean are established. Our result shows that the disease could be die out theoretically if threshold value R is less than one, regardless of whether the disease-free solutions of the corresponding subsystems are stable or unstable. Then, a stochastic switched S I L I model with continuous control schemes and pulse vaccination is studied. The threshold value R is derived. The global attractivity of the model is also obtained. At last, numerical simulations are carried out to support our results. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Harbin University of Science & Technology is the property of Journal of Harbin University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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., Competing Interests: The authors declare that they have no competing interests., (© 2023 The Authors.)

In this paper, we have considered a dynamical model of diseases that spread by droplet infection and also through direct contact with varying total population size and discrete time delay to become infectious. It is assumed that there is a latent period of the disease and an immune period of the recovered individuals. Pulse vaccination is an effective and important strategy for the elimination of infectious diseases and so we have analysed this model with pulse vaccination and saturation incidence rate. It is also assumed that the time lag due to lose of immunity of recovered individuals is equal to the interval between two pulses. We have defined two positive numbersand. It is proved that there exists an infection-free periodic solution which is globally attractive ifand the disease is permanent ifThe important mathematical findings for the dynamical behaviour of the model are also numerically verified using MATLAB. Finally epidemiological implications of our analytical findings are addressed critically. [ABSTRACT FROM AUTHOR]

Pulse vaccination is an important strategy to eradicate an infectious disease. In this paper, we investigate an SIR epidemic model with stage structure and pulse vaccination. By using the discrete dynamical system determined by stroboscopic map, we obtain the conditions for the global asymptotical stability of the infection-free periodic solution of the studied system. The permanent conditions of the investigated system are also given. The results indicate that a large pulse vaccination rate is a sufficient condition to eradicate the disease. It provides a reliable tactic basis for preventing the epidemic outbreak. [ABSTRACT FROM AUTHOR]

The possibility of periodic routine vaccination campaigns (PRVCs) is introduced in the context of a search for optimal oral poliovirus vaccine (OPV) administration strategies. Like the usual continuous routine vaccination campaign (CRVC), PRVCs target only newborns. However, they are not necessarily implemented continuously in time. Using a dynamic and compartmental polio transmission model in a stochastic context, it is shown that some PRVCs can achieve much greater efficiency than CRVC in terms of probability of wild poliovirus (WPV) eradication, even though they never outperform CRVC in terms of total number of paralytic infections. Moreover, these PRVCs results can be obtained at a lower price than CRVC. It is also shown that, even though PRVCs do not perform better than pulse vaccination campaigns (PVCs) when only epidemiological outputs are valued, they can do so when a cost–benefit analysis is preferred. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the dynamic of two SEIVS models, which incorporate an imperfect vaccination compartment. In this paper, we focus on the psychological inhibition effect of vaccinated individuals and the efficacy of vaccine on the spread of disease. For the susceptible individuals, we consider the psychological inhibition effect through the nonmonotone incidence rate. We find the disease-free and the disease persistent conditions. We also give some numerical simulations to demonstrate the effect of behavioral change of the vaccinated individuals and the efficiency of vaccine. [ABSTRACT FROM AUTHOR]

In this paper, we have considered a dynamical model of hand-foot-mouth disease (HFMD) with varying total population size, saturation incidence rate and discrete time delay to become infectious. It is assumed that there is a latent period of the disease and an immune period of the recovered individuals. It is reported that the first vaccine to protect children against enterovirus 71 or EV71 has been invented (Zhang and Teng, J Biol Dyn 2(1):64-84, ). Pulse vaccination is an effective and important strategy for the elimination of infectious diseases and so we have analyzed this model with pulse vaccination. It is also assumed that the time lag due to lose of immunity of recovered individuals is equal to the interval between two pulses. We have defined two positive numbers $$R_{1}$$ and $$R_{2}$$ . It is proved that there exists an infection-free periodic solution which is globally attractive if $$R_{1}<1$$ and the disease is permanent if $$R_{2}>1$$ . It is derived that the infectious population extinct if the pulse vaccination rate is larger than a critical vaccination proportion. Our analysis indicates that a small pulse vaccination rate will rise the permanence of the disease. The important mathematical findings for the dynamical behaviour of the HFMD model are also numerically verified using MATLAB. Finally epidemiological implications of our analytical findings are addressed critically. [ABSTRACT FROM AUTHOR]

This paper analyzes a new model of the vector-borne disease chikungunya by considering time-varying parameters and impulsive control. In particular, the birth rate of the mosquito population varies between rainy season and dry season, and the contact rate between mosquito and human changes in time. Mechanical control of breeding sites and reduced contact rate strategies are studied. Motivated by a potential commercial vaccine in the future, pulse vaccination with vaccine failure is considered. Sufficient conditions are established which guarantee disease eradication or persistence of the disease in the endemic case. [ABSTRACT FROM AUTHOR]

In this paper, we have considered a dynamical model of Chlamydia disease with varying total population size, bilinear incidence rate and pulse vaccination strategy. We have defined two positive numbers $$R_{0}$$ and $$R_{1}(\le R_{0})$$ . It is proved that there exists an infection-free periodic solution which is globally attractive if $$R_{0}<1$$ and the disease is permanent if $$R_{1}>1.$$ The important mathematical findings for the dynamical behaviour of the Chlamydia disease model are also numerically verified using MATLAB. Finally epidemiological implications of our analytical findings are addressed critically. [ABSTRACT FROM AUTHOR]

We investigate an SIVS model with pulse vaccination strategy. First we compute the disease free periodic solution and prove its global asymptotic stability in the disease free subspace. We identify the corresponding control reproduction number Rc and prove that the disease free periodic solution is locally asymptotically stable if Rc<1, and under some additional conditions it is globally asymptotically stable as well. For Rc>1 we prove the uniform persistence of the disease. Our main result is that nontrivial endemic periodic solutions are bifurcating from the disease free periodic solution as Rc is passing through the threshold value one. A complete bifurcation analysis is provided for the associated nonlinear fixed point equation. We show that backward bifurcation of periodic orbits is possible for suitable parameter values, and give explicit conditions to determine whether the bifurcation is backward or forward. The main mathematical tools are comparison principles and Lyapunov-Schmidt reduction. Finally, we compare the pulse vaccination strategy with continuous vaccination, and illustrate that backward bifurcation occurs in more realistic models as well when pulse vaccination is applied. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates an SIS model with seasonal changes in disease transmission. The model is formulated as a switched system and its long-term behavior is analyzed. A constant treatment strategy is then applied to a switched SIS model which takes media coverage into account. A pulse vaccination control strategy with vaccine failure is also considered. Throughout the paper, the stability of the disease-free solution is analyzed and threshold criteria involving the basic reproduction number are established which guarantee disease eradication. Sufficient conditions are also given for the endemic case. [Copyright &y& Elsevier]

Abstract: In this paper, we have considered a dynamical model of Chlamydia disease with varying total population size, saturation incidence rate and discrete time delay to become infectious. It is assumed that there is a time lag (τ) to account for the fact that an individual infected with bacterium Chlamydia trachomatis is not infectious until after some time after exposure. The probability that an individual remains in the latency period (exposed class) at least t time units before becoming infectious is given by a step function with value 1 for and value zero for . The probability that an individual in the latency period has survived is given by , where μ denotes the natural mortality rate in all epidemiological classes. Pulse vaccination is an effective and important strategy for the elimination of infectious diseases and so we have analyzed this model with pulse vaccination. We have defined two positive numbers and . It is proved that there exists an infection-free periodic solution which is globally attractive if and the disease is permanent if . Our analytical findings are illustrated through computer simulation using MATLAB, which show the reliability of our model from the epidemiological point of view. [Copyright &y& Elsevier]