Constant Vaccination Strategy Research Articles

Global approximate solution of SIR epidemic model with constant vaccination strategy

Providing a global semi-analytical method has the advantage of offering a global and accurate solution to the epidemic model, which can help in studying and controlling the spread of the disease. Unlike numerical methods such as the Runge–Kutta–Fehlberg method, global semi-analytical methods can provide an explicit expression of the solution over the entire time period, including obtaining the peak time, which is crucial information for understanding disease spread. In this paper, a global semi-analytical method based on the two-point Padé approximants for solving the SIR epidemic model of childhood diseases is presented. The objective of this study is to examine the temporal dynamics of a childhood disease when a preventive vaccine is present. For this purpose, we have first derived the solution of the SIR model of childhood diseases in terms of series expansions for small and large values. Then, the theory of two-point Padé approximations is used to provide the global approximate solution. The peak time related to this model is also obtained via these global approximants. Furthermore, in order to show the efficiency of our study, some graphs have been given to compare our results with those obtained using the classical Padé approximations and the numerical Runge–Kutta–Fehlberg method.

Variational iteration and successive approximation methods for a SIR epidemic model with constant vaccination strategy

We consider a SIR epidemic model with constant vaccination strategy. An existing variational iteration method for solving the model is recalled. We provide a successive approximation method for this model. We prove that the existing variational iteration method is identical with the successive approximation method. Unfortunately, the existing variational iteration method (that is, the successive approximation method) is not accurate for large domains. Therefore, we propose an improvement to the existing variational iteration method and show that the improved variational iteration method is much more accurate than the existing one.

Paradoxical phenomena and chaotic dynamics in epidemic models subject to vaccination

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.

Competitive analysis for stochastic influenza model with constant vaccination strategy.

This manuscript discusses a competitive analysis of stochastic influenza model with constant vaccination strategy. The stochastic influenza model is comparatively more pragmatic versus the deterministic influenza model. The effect of influenza generation number holds in the stochastic model. If the value of this number is less than one, this situation will help us to control the disease in a population. A greater than one value of this threshold number shows the persistence of disease to become endemic. The proposed structure for the stochastic influenza model as stochastic non-standard finite difference scheme conserve all vital characteristics like positivity, boundedness and dynamical consistency defined by Mickens.

Modelling the Spread of Dengue in a Human Population In National Capital Region (Ncr), Philippines using the Sir (Susceptible-Infected-Recovered), Seir (Susceptible-Exposed Infected-Recovered), and Sir with Vertical Transmission Models

The unimpeded growth of urban population has unfortunately paved way to spreading multiple infectious diseases that greatly puts a population the risk of incurring an outbreak had the spread of disease not been managed well. Dengue is a major contagious disease that has been plaguing the world ever since, and epidemic outbreaks trying to be mitigated and minimized by researchers. One way to predict the pattern of the disease on a macro scale is to use mathematical models to understand the dynamics of the epidemics caused by the disease. This study uses the SIR, SEIR, and SIR with Vertical Transmission to model the spread of dengue in NCR, Philippines within the year 2010. Afterwards, each model was then used to simulate two disease control methods: Constant Vaccination Strategy (CVS) and Quarantine, which controls the infection and recovery rate parameters with SIR with linear parameters having the highest accuracy among all the models the R 2 value being 0.99683. The created models are accurate hence can be used to simulate dengue dynamics in NCR. CVS and Quarantine substantially decreased the peak of the epidemic for all models, confirming those methods as effective deterrents dengue incidence

On the Dynamical Complexity of a Seasonally Forced Discrete SIR Epidemic Model with a Constant Vaccination Strategy

In this article, we consider the discretized classical Susceptible‐Infected‐Recovered (SIR) forced epidemic model to investigate the consequences of the introduction of different transmission rates and the effect of a constant vaccination strategy, providing new numerical and topological insights into the complex dynamics of recurrent diseases. Starting with a constant contact (or transmission) rate, the computation of the spectrum of Lyapunov exponents allows us to identify different chaotic regimes. Studying the evolution of the dynamical variables, a family of unimodal‐type iterated maps with a striking biological meaning is detected among those dynamical regimes of the densities of the susceptibles. Using the theory of symbolic dynamics, these iterated maps are characterized based on the computation of an important numerical invariant, the topological entropy. The introduction of a degree (or amplitude) of seasonality, ε, is responsible for inducing complexity into the population dynamics. The resulting dynamical behaviors are studied using some of the previous tools for particular values of the strength of the seasonality forcing, ε. Finally, we carry out a study of the discrete SIR epidemic model under a planned constant vaccination strategy. We examine what effect this vaccination regime will have on the periodic and chaotic dynamics originated by seasonally forced epidemics.

An NSFD scheme for SIR epidemic models of childhood diseases with constant vaccination strategy

Abstract In this paper, we construct a nonstandard finite difference (NSFD) scheme for an SIR epidemic model of childhood disease with constant strategy. The dynamics of the obtained discrete model is investigated. First we show that the discrete model has equilibria which are exactly the same as those of the continuous model. Furthermore, we prove that the conditions for those equilibria to be globally asymptotically stable are consistent with the continuous model for any size of numerical time-step. The analytical results are confirmed by some numerical simulations.

Optimal control of vaccination dynamics during an influenza epidemic.

For emerging diseases like pandemic influenza, several factors could impact the outcome of vaccination programs, including a delay in vaccine availability, imperfect vaccine-induced protection, and inadequate number of vaccines to sufficiently lower the susceptibility of the population by raising the level of herd immunity. We sought to investigate the effect of these factors in determining optimal vaccination strategies during an emerging influenza infection for which the population is entirely susceptible. We developed a population dynamical model of disease transmission and vaccination, and analyzed the control problem associated with an adaptive time-dependent vaccination strategy, in which the rate of vaccine distribution is optimally determined with time for minimizing the total number of infections (i.e., the epidemic final size). We simulated the model and compared the outcomes with a constant vaccination strategy in which the rate of vaccine distribution is time-independent. When vaccines are available at the onset of epidemic, our findings show that for a sufficiently high vaccine efficacy, the adaptive and constant vaccination strategies lead to comparable outcomes in terms of the epidemic final size. However, the adaptive vaccination requires a vaccine coverage higher than (or equivalent to) the constant vaccination regardless of the rate of vaccine distribution, suggesting that the latter is a more cost-effective strategy. When the vaccine efficacy is below a certain threshold, the adaptive vaccination could substantially outperform the constant vaccination, and the impact of adaptive strategy becomes more pronounced as the rate of vaccine distribution increases. We observed similar results when vaccines become available with a delay during the epidemic; however, the adaptive strategy may require a significantly higher vaccine coverage to outperform the constant vaccination strategy. The findings indicate that the vaccine efficacy is a key parameter that affects optimal control of vaccination dynamics during an epidemic, raising an important question on the trade-off between effectiveness and cost-effectiveness of vaccination policies in the context of limited vaccine quantities.

Optimal Vaccination Strategies in an SIR Epidemic Model with Time Scales

Childhood related diseases such as measles are characterised by short periodic outbreaks lasting about 2 weeks. This means therefore that the timescale at which such diseases operate is much shorter than the time scale of the human population dynamics. We analyse a compartmental model of the SIR type with periodic coefficients and different time scales for 1) disease dynamics and 2) human population dynamics. Interest is to determine the optimal vaccination strategy for such diseases. In a model with time scales, Singular Perturbation theory is used to determine stability condition for the disease free state. The stability condition is here referred to as instantaneous stability condition, and implies vaccination is done only when an instantaneous threshold condition is met. We make a comparison of disease control using the instantaneous condition to two other scenarios: one where vaccination is done constantly over time (constant vaccination strategy) and another where vaccination is done when a periodic threshold condition is satisfied (orbital stability from Floquet theory). Results show that when time scales of the disease and human population match, we see a difference in the performance of the vaccination strategies and above all, both the two threshold strategies outperform a constant vaccination strategy.

Efficiency of Different Vaccination Strategies for Childhood Diseases: A Simulation Study

Vaccination strategies are designed and applied to control or eradicate an infection from the population. This paper studies three different vaccination strategies used worldwide for many infectious diseases including childhood diseases. These strategies are the conventional constant vaccination strategy, the periodic step (pulse) vaccination strategy and finally the mixed vaccination strategy of both the constant and the periodic one. Simulation of the different vaccination programs is conducted using three parameter sets of measles, chickenpox and rubella. The Poincaré section is playing as a filter of our simulation results to show a wide range of possible behavior of our model. Critical vaccination level is been estimated from the results to prevent severe epidemics.

Solutions of Fractional Order Model of Childhood diseases with Constant Vaccination Strategy

Childhood vaccination programs have had a dramatic impact on child morbidity and mortality. Protecting children from diseases that can be prevented by vaccination is a primary goal of health administrators. A SIR model that monitors the temporal dynamics of a childhood disease in the presence of preventive vaccine is presented in this paper. We introduce fractional-order into the presented model. Homotopy analysis method (HAM) is considered in this paper to obtain an analytic approximate solution of this model. The results obtained by HAM are compared with the classical fourth order Runge-Kutta method (RK4) to gauge its effectiveness. The obtained results proved that the disease will persist within the population if the vaccination coverage level is below a certain threshold.

The effect of constant and pulse vaccination on an SIR epidemic model with infectious period

In this paper, we investigate two delayed SIR models with vaccination and a generalized nonlinear incidence and obtain sufficient conditions for eradication and permanence of the disease, respectively. Our results indicate that a larger vaccination rate will lead to the eradication of a disease. Furthermore, theoretical results show that constant vaccination strategy can lead to disease eradication at relatively low values of vaccination than pulse vaccination strategy, which is different from the results in [1]. In addition, numerical simulations indicate that pulse vaccination strategy or a longer infectious period will make a larger fraction of population infected by disease.

Analytical approximate solution of a SIR epidemic model with constant vaccination strategy by homotopy perturbation method

PurposeThe purpose of this paper is to introduce an efficient method for solving susceptible‐infected‐removed (SIR) epidemic model. A SIR model that monitors the temporal dynamics of a childhood disease in the presence of preventive vaccine. The qualitative analysis reveals the vaccination reproductive number for disease control and eradication. It introduces homotopy perturbation method (HPM) to overcome these problems.Design/methodology/approachThe paper considers HPM to solve differential system which describes SIR epidemic model. The essential idea of this method is to introduce a homotopy parameter, say p, which takes values from 0 to 1. When p=0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p is gradually increased to 1, the system goes through a sequence of deformations, the solution for each of which is close to that at the previous stage of deformation. One of the most remarkable features of the HPM is that usually just few perturbation terms are sufficient for obtaining a reasonably accurate solution.FindingsHPM is employed to compute an approximation to the solution of the non‐linear system of differential equations governing the problem.Originality/valueThe paper is of value in presenting, via some tables and figures, some numerical experiments which resulted from applying new methods on test problem.

Adomian decomposition approach to a SIR epidemic model with constant vaccination strategy

Over the years, diligent vaccination campaigns have resulted in high levels of permanent immunity against the childhood disease among the population. In this article, a SIR model that monitors the temporal dynamics of a childhood disease in the presence of preventive vaccine is developed. The qualitative analysis reveals the vaccination reproductive number for disease control and eradication. Adomian decomposition method is also employed to compute an approximation to the solution of the non-linear system of differential equations governing the problem. Maple is used to carry out the computations. Graphical results are presented and discussed quantitatively to illustrate the solution.