Measles dynamics on network models with optimal control strategies

Xue, Yuyi; Ruan, Xiaoe; Xiao, Yanni

doi:10.1186/s13662-021-03306-y

“…Recently, a mathematical model was developed by Rahmayani et al [1] on measles transmission with vaccination and treatment intervention. In a similar manner, the model developed by Xue et al [18] on the measles dynamics of network model tries to emphasize a transmission rate and theoretically examine the threshold dynamics to investigate the infuence of heterogeneity and waning immunity of measles transmission dynamics. Pokharel et al [19] recently developed a novel transmission dynamics model to evaluate the efects of monitored vaccination programs to control and eliminate measles.…”

Section: Introductionmentioning

confidence: 99%

Modelling, Analysis, and Simulation of Measles Disease Transmission Dynamics

Alemneh

¹

,

Belay

²

2023

Discrete Dynamics in Nature and Society

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Measles is one of the top communicable diseases, which is still responsible for 2.6 million deaths every year. Due to this reason, the paper focuses on measles transmission dynamics concerning the impact of indirect contact rate (transmitted from the host of the virus to the healthy individual) and improving the SEVIR model into the SVIRP model. From the model, we first estimated the disease-free equilibrium, calculated the effective reproduction number R E f f , and established the stability analysis. The Castillo–Chavez stability criterion is used to demonstrate the global stability of the disease-free equilibrium point, while the linearization method is used to justify its local stability analysis and gives a result R E f f < 1 . The stability analysis of endemic equilibrium point is explained by defining a Lyapunov function, and its global stability exists when R E f f > 1 . To identify the effect of parameters on the transmission dynamics, we performed sensitivity index and numerical simulation. From the result, we obtained that the indirect contact rate has the highest impact in maximizing the transmission dynamics of measles. Also, we found that working on prevention and treatment strategies brings a significant contribution in reducing the disease effect in the community.

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“…Together with a more localized approach to finding sub‐populations with low coverage, 15 which can be obscured by coverage estimates in larger population groups, 16 modeling can help inform routine immunization (RI) policy (eg, recommended vaccination ages) and interventions to improve RI coverage, as well as optimization of the timing of supplemental immunization activities 17 . There have been extensive efforts to model measles disease transmission and vaccination impacts over time, 18‐34 spanning from the use of deterministic and stochastic models, time series analyses, and logit functions to metapopulation, agent‐based, and network approaches. Literature surveys have followed these developments that started in the 1960s 35‐37 .…”

Section: Introductionmentioning

confidence: 99%

Analysis of the yearly transition function in measles disease modeling

Davila‐Payan,

Hill,

Kayembe

et al. 2023

Statistics in Medicine

1

0

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Globally, there were an estimated 9.8 million measles cases and 207 500 measles deaths in 2019. As the effort to eliminate measles around the world continues, modeling remains a valuable tool for public health decision‐makers and program implementers. This study presents a novel approach to the use of a yearly transition function that formulates mathematically the vaccine schedules for different age groups while accounting for the effects of the age of vaccination, the timing of vaccination, and disease seasonality on the yearly number of measles cases in a country. The methodology presented adds to an existing modeling framework and expands its analysis, making its utilization more adjustable for the user and contributing to its conceptual clarity. This article also adjusts for the temporal interaction between vaccination and exposure to disease, applying adjustments to estimated yearly counts of cases and the number of vaccines administered that increase population immunity. These new model features provide the ability to forecast and compare the effects of different vaccination timing scenarios and seasonality of transmission on the expected disease incidence. Although the work presented is applied to the example of measles, it has potential relevance to modeling other vaccine‐preventable diseases.

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“…The study involved an investigation into the conditions ensuring the positivity of solutions, the invariant region of the solution, the existence and stability of equilibrium points in the model, and the sensitivity analysis of the model 27 . A network model with periodic transmission rate was developed to analyze the effects of heterogeneity and waning immunity on measles transmission and to theoretically examine the threshold dynamics 28 . Mathematical modeling of infectious disease is studied a lot in recent times 29 – 35 , for example.…”

Section: Introductionmentioning

confidence: 99%

A reliable numerical investigation of an SEIR model of measles disease dynamics with fuzzy criteria

Dayan,

Ahmed,

Rafiq

et al. 2023

Sci Rep

0

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The terms susceptibility, exposure, infectiousness, and recovered all have some inherent ambiguity because different population members have different susceptibility levels, exposure levels, infectiousness levels, and recovery patterns. This uncertainty becomes more pronounced when examining population subgroups characterized by distinct behaviors, cultural norms, and varying degrees of resilience across different age brackets, thereby introducing the possibility of fluctuations. There is a need for more accurate models that take into account the various levels of susceptibility, exposure, infectiousness, and recovery of the individuals. A fuzzy SEIR model of the dynamics of the measles disease is discussed in this article. The rates of disease transmission and recovery are treated as fuzzy sets. Three distinct numerical approaches, the forward Euler, fourth-order Runge-Kutta, and nonstandard finite difference (NSFD) are employed for the resolution of this fuzzy SEIR model. Next, the outcomes of the three methods are examined. The results of the simulation demonstrate that the NSFD method adeptly portrays convergent solutions across various time step sizes. Conversely, the conventional Euler and RK-4 methods only exhibit positivity and convergence solutions when handling smaller step sizes. Even when considering larger step sizes, the NSFD method maintains its consistency, showcasing its efficacy. This demonstrates the NSFD technique’s superior reliability when compared to the other two methods, while maintaining all essential aspects of a continuous dynamical system. Additionally, the results from numerical and simulation studies offer solid proof that the suggested NSFD technique is a reliable and effective tool for controlling these kinds of dynamical systems.The convergence and consistency analysis of the NSFD method are also studied.

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Measles dynamics on network models with optimal control strategies

Cited by 5 publications

References 40 publications

Modelling, Analysis, and Simulation of Measles Disease Transmission Dynamics

Modelling, Analysis, and Simulation of Measles Disease Transmission Dynamics

Analysis of the yearly transition function in measles disease modeling

A reliable numerical investigation of an SEIR model of measles disease dynamics with fuzzy criteria

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