Dynamic Analysis of a VSEIR Model with Vaccination Efficacy and Immune Decline

Han, Xiaotao; Hua, Loo-Keng; Lin, Xiaofen; Wei, Yueguang; Ma, Mengyu

doi:10.1155/2022/7596164

Cited by 3 publications

(2 citation statements)

References 40 publications

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“…We consider the asymptomatic infection stage, symptomatic infection stage, and persistent infection stage [4]. Additionally, we take into account the vaccine effectiveness to more accurately capture the pathological changes of HPV [5]. We partition the entire population ( ) N t into six compartments: vaccinated individuals ( ) V t , susceptible individuals ( ) S t , asymptomatic infectious individuals ( ) E t , symptomatic infectious individuals 1 ( ) I t , persistent infectious individuals 2 ( ) I t , and recovered individuals ( ) R t at time t .…”

Section: Introductionmentioning

confidence: 99%

Sensitivity analysis and numerical simulation of a human papillomavirus infection model

Liu,

Zhu

et al. 2024

Third International Conference on Biomedical and Intelligent Systems (IC-BIS 2024)

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Human Papillomavirus (HPV) is a prevalent sexually transmitted virus and skin-to-mucous membrane contact transmitted virus that infects a significant proportion of the global population. In this paper, we propose a mathematical model based on the pathology development of HPV to explain the difference in HPV viral load among patients in different stages of infection results in variations in infectivity. Compute the disease-free equilibrium point and basic reproduction number utilizing the next generation approach. We performed the normalized forward sensitivity index and LHS-PRCCs to analyze the basic reproduction number, determine the key factors influencing HPV transmission. The results indicate that immune decline and the rate of recovery related to host immune response as well as vaccination plays a significant role in suppressing HPV transmission. Based on this, the effective control of transmission strategies and suggestions for enhancing protective measures are proposed to suppress the spread of HPV.

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Section: Introductionmentioning

confidence: 99%

Sensitivity analysis and numerical simulation of a human papillomavirus infection model

Liu,

Zhu

et al. 2024

Third International Conference on Biomedical and Intelligent Systems (IC-BIS 2024)

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“…A series of mathematical models for the coronavirus epidemic, studying their bifurcation and local and global asymptotical dynamics, have been discussed in [13,14]. The study of the vaccination model under vaccine immunization and their efficacy have been discussed in detail in [15].…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of COVID-19 with Vaccination Using Fractional Derivative: A Case Study

et al. 2023

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Vaccination against any infectious disease is considered to be an effective way of controlling it. This paper studies a fractional order model with vaccine efficacy and waning immunity. We present the model’s dynamics under vaccine efficacy, the impact of immunization, and the waning of the vaccine on coronavirus infection disease. We analyze the model under their equilibrium points. The model under the equilibrium points is discussed and proven that it is locally asymptotically stable if Rv is lesser than unity. We present the backward bifurcation hypothesis of the model and show that there is a parameter β2 that causes the backward bifurcation in the imperfect vaccine model. We show certain assumptions when ψ=1 for the imperfect vaccine case; the model is both stable globally asymptotically at the disease-free (R0≤1) and endemic cases (R0>1). By using infected cases from the recent wave throughout Pakistan, we shall estimate the model parameters and calculate the numerical value of the basic reproductive number R0≈1.2591. We present the comprehensive graphical results for the realistic parameter values and show many useful suggestions regarding the elimination of the infection from society. The vaccination efficacy that provides an important role in disease elimination is discussed in detail.

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Global stability and optimal vaccination control of SVIR models

Zhu,

Liu,

Lin

et al. 2024

MATH

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<abstract> <p>Vaccination is widely acknowledged as an affordable and cost-effective approach to guard against infectious diseases. It is important to take vaccination rate, vaccine effectiveness, and vaccine-induced immune decline into account in epidemic dynamical modeling. In this paper, an epidemic dynamical model of vaccination is developed. This model provides a framework of the infectious disease transmission dynamics model through qualitative and quantitative analysis. The result shows that the system may have multiple equilibria. We used the next-generation operator approach to calculate the maximum spectral radius, that is, basic reproduction number $ {R_{vac}} $. Next, by dividing the model into infected and uninfected subjects, we can prove that the disease-free equilibrium is globally asymptotically stable when $ {R_{vac}} < 1 $, provided certain assumptions are satisfied. When $ {R_{vac}} > 1 $, there exists a unique endemic equilibrium. Using geometric methods, we calculate the second compound matrix and demonstrate the Lozinskii measure $ \bar q \leqslant 0 $, which is equivalent to the unique endemic equilibrium, which is globally asymptotically stable. Then, using center manifold theory, we justify the existence of forward bifurcation. As the vaccination rate decreases, the likelihood of forward bifurcation increases. We also theoretically show the presence of Hopf bifurcation. Then, we performed sensitivity analysis and found that increasing the vaccine effectiveness rate can curb the propagation of disease effectively. To examine the influence of vaccination on disease control, we chose the vaccination rate as the optimal vaccination control parameter, using the Pontryagin maximum principle, and we found that increasing vaccination rates reduces the number of infected individuals. Finally, we ran a numerical simulation to finalize the theoretical results.</p> </abstract>

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Dynamic Analysis of a VSEIR Model with Vaccination Efficacy and Immune Decline

Cited by 3 publications

References 40 publications

Sensitivity analysis and numerical simulation of a human papillomavirus infection model

Sensitivity analysis and numerical simulation of a human papillomavirus infection model

Mathematical Modeling of COVID-19 with Vaccination Using Fractional Derivative: A Case Study

Global stability and optimal vaccination control of SVIR models

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