Continuous Vaccination Strategy Research Articles

Random dynamics of an SIV epidemic model

Vaccines train the immune system to create antibodies when it has been exposed to a disease. They protect against many different diseases, including Hepatitis B, Influenza, Polio, etc. This paper considers the vaccination process by including individuals who have started the vaccination process in the transmission model. By the non-parametric perturbation technique, we shall formulate the stochastic SIV model. The examination of the deterministic model relies on the global Lipschitz condition, a crucial factor in guaranteeing the uniqueness and stability of solutions to the model’s differential equation. In contrast, our scrutiny of the stochastic model is rooted in the local Lipschitz condition, which proves to be more applicable and realistic in the context of real-world scenarios. Analysis of the stochastic models may be superior to the analysis of the deterministic models. In many cases, surprisingly, analysis of the stochastic models may provide results that are close to the results obtained from the analysis of the deterministic models. However, it comes with a cost, namely, we might not predict the pattern or the random probability distribution of the stochastic system, moreover, the necessary conditions for the extinction of the disease are weaker compared to the deterministic model. The impact of the continuous vaccination strategy on disease spread is demonstrated. Our results reveal that the vaccination process is very helpful and useful in eradicating the disease. Using MATHEMATICA software and MATLAB software, stability regions of the disease-free equilibrium are presented.

Pathwise methods for the integration of a stochastic SVIR model

We propose an approach for the precise numerical integration of a stochastic SVIR model defined by a stochastic differential equation (SDE) with non‐globally Lipschitz continuous coefficients and multiplicative noise. This equation, based on a compartmental epidemic model, describes a continuous vaccination strategy with environmental noise effects. By means of an appropriate invertible continuous transformation, we link the solution to the stochastic SVIR model to the solution of an auxiliary random differential equation (RDE) that has an Ornstein–Uhlenbeck process as the only input parameter of the system. In this way, based on this explicit conjugacy between both equations, new pathwise numerical schemes are constructed for the SVIR model. In particular, we propose an exponential method that outperforms other integrators in the literature and is able to approximate, with high stability, meaningful probabilistic features of the continuous system, including its stationary distribution and ergodicity. A simulation study is presented to illustrate the practical performance of the introduced methods, and a comparative analysis with other integrators commonly used for the simulation of epidemiological models is performed.

Epidemic Dynamics and Adaptive Vaccination Strategy: Renewal Equation Approach.

We use analytical methods to investigate a continuous vaccination strategy's effects on the infectious disease dynamics in a closed population and a demographically open population. The methodology and key assumptions are based on Breda et al. (J Biol Dyn 6(Sup2):103-117, 2012). We show that the cumulative force of infection for the closed population and the endemic force of infection in the demographically open population can be reduced significantly by combining two factors: the vaccine effectiveness and the vaccination rate. The impact of these factors on the force of infection can transform an endemic steady state into a disease-free state.

Analysis of an SVIC model with age-dependent infection and asymptomatic carriers

In this paper,we formulated an age-dependent model for the transmission dynamics of HBV with vaccination. The class of acutely infectious individuals,asymptomatic carrier of host population is stratified by age. Mathematically, we established that basic reproduction number can govern the global stability of equilibria. Biologically, we verify the impacts of the asymptomatic carriers and the effectiveness of vaccination on the disease transmission through numerical simulation. Our results indicated that the more number of infectious individuals specific to frequently progressed to asymptomatic carriers, the more likely the disease can be eradicated by continuous vaccination strategies.

Comparative effectiveness of different strategies of oral cholera vaccination in bangladesh: a modeling study.

BackgroundKilled, oral cholera vaccines have proven safe and effective, and several large-scale mass cholera vaccination efforts have demonstrated the feasibility of widespread deployment. This study uses a mathematical model of cholera transmission in Bangladesh to examine the effectiveness of potential vaccination strategies.Methods & FindingsWe developed an age-structured mathematical model of cholera transmission and calibrated it to reproduce the dynamics of cholera in Matlab, Bangladesh. We used the model to predict the effectiveness of different cholera vaccination strategies over a period of 20 years. We explored vaccination programs that targeted one of three increasingly focused age groups (the entire vaccine-eligible population of age one year and older, children of ages 1 to 14 years, or preschoolers of ages 1 to 4 years) and that could occur either as campaigns recurring every five years or as continuous ongoing vaccination efforts. Our modeling results suggest that vaccinating 70% of the population would avert 90% of cholera cases in the first year but that campaign and continuous vaccination strategies differ in effectiveness over 20 years. Maintaining 70% coverage of the population would be sufficient to prevent sustained transmission of endemic cholera in Matlab, while vaccinating periodically every five years is less effective. Selectively vaccinating children 1–14 years old would prevent the most cholera cases per vaccine administered in both campaign and continuous strategies.ConclusionsWe conclude that continuous mass vaccination would be more effective against endemic cholera than periodic campaigns. Vaccinating children averts more cases per dose than vaccinating all age groups, although vaccinating only children is unlikely to control endemic cholera in Bangladesh. Careful consideration must be made before generalizing these results to other regions.

STABILITY OF SVIR SYSTEM WITH RANDOM PERTURBATIONS

In this paper, the SVIR epidemic models with continuous vaccination strategies investigated by Liu, Takeuchi and Iwamo, [SVIR epidemic models with vaccination strategies, J. Theor. Biol.253 (2008) 1–11], allowing random fluctuation around the endemic equilibrium and the transmission rate β are analyzed. The equilibrium state of the model with random perturbation is locally asymptotically stable as shown by a Lyapunov stability analysis.

SVIR epidemic models with vaccination strategies

Vaccination is important for the elimination of infectious diseases. To finish a vaccination process, doses usually should be taken several times and there must be some fixed time intervals between two doses. The vaccinees (susceptible individuals who have started the vaccination process) are different from both susceptible and recovered individuals. Considering the time for them to obtain immunity and the possibility for them to be infected before this, two SVIR models are established to describe continuous vaccination strategy and pulse vaccination strategy (PVS), respectively. It is shown that both systems exhibit strict threshold dynamics which depend on the basic reproduction number. If this number is below unity, the disease can be eradicated. And if it is above unity, the disease is endemic in the sense of global asymptotical stability of a positive equilibrium for continuous vaccination strategy and disease permanence for PVS. Mathematical results suggest that vaccination is helpful for disease control by decreasing the basic reproduction number. However, there is a necessary condition for successful elimination of disease. If the time for the vaccinees to obtain immunity or the possibility for them to be infected before this is neglected, this condition disappears and the disease can always be eradicated by some suitable vaccination strategies. This may lead to over-evaluating the effect of vaccination.

Mixed pulse vaccination strategy in epidemic model with realistically distributed infectious and latent times

In this paper we study the use of a pulse vaccination strategy to eradicate infectious diseases modelable by epidemic model having gamma distributed infectious and latent time. We demonstrate the global asymptotic stability of the eradication solution for a general model in which co-presence of a continuous vaccination strategy, the non-permanent duration of the immunization and the emerging problem of the vaccine failures are considered.

Stability properties of pulse vaccination strategy in SEIR epidemic model

The problem of the applicability of the pulse vaccination strategy (PVS) for the stable eradication of some relevant general class of infectious diseases is analyzed in terms of study of local asymptotic stability (LAS) and global asymptotic stability (GAS) of the periodic eradication solution for the SEIR epidemic model in which is included the PVS. Demographic variations due or not to diseased-related fatalities are also considered. Due to the non-triviality of the Floquet's matrix associate to the studied model, the LAS is studied numerically and in this way it is found a simple approximate (but analytical) sufficient criterion which is an extension of the LAS constraint for the stability of the trivial equilibrium in SEIR model without vaccination. The numerical simulations also seem to suggest that the PVS is slightly more efficient than the continuous vaccination strategy. Analytically, the GAS of the eradication solutions is studied and it is demonstrated that the above criteria for the LAS guarantee also the GAS.