Measles dynamics on network models with optimal control strategies
Yuyi Xue1, Xiaoe Ruan1, Yanni Xiao1
1School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, P.R. China.
Abstract:
To investigate the influences of heterogeneity and waning immunity on measles transmission, we formulate a network model with periodic transmission rate, and theoretically examine the threshold dynamics. We numerically find that the waning of immunity can lead to an increase in the basic reproduction number and the density of infected individuals. Moreover, there exists a critical level for average degree above which increases quicker in the scale-free network than in the random network. To design the effective control strategies for the subpopulations with different activities, we examine the optimal control problem of the heterogeneous model. Numerical studies suggest us no matter what the network is, we should implement control measures as soon as possible once the outbreak takes off, and particularly, the subpopulation with high connectivity should require high intensity of interventions. However, with delayed initiation of controls, relatively strong control measures should be given to groups with medium degrees. Furthermore, the allocation of costs (or resources) should coincide with their contact patterns.
Insights
Waning immunity increases measles spread, especially in high-activity networks. Early, targeted interventions are crucial for effective measles control, prioritizing highly connected groups.
Area of Science:
- Epidemiology
- Network Science
- Mathematical Biology
Background:
- Measles transmission dynamics are influenced by population heterogeneity and immunity duration.
- Understanding these factors is key to effective disease control strategies.
Purpose of the Study:
- To investigate how population heterogeneity and waning immunity affect measles transmission.
- To determine optimal control strategies for measles outbreaks in complex networks.
Main Methods:
- Formulation of a network model with periodic transmission rates.
- Theoretical examination of threshold dynamics.
- Numerical analysis of an optimal control problem for heterogeneous models.
Main Results:
- Waning immunity can increase the basic reproduction number and infected individual density.
- Scale-free networks show faster increases in the basic reproduction number above a critical average degree compared to random networks.
- Early implementation of control measures is vital, with higher intensity for highly connected subpopulations.
Conclusions:
- Heterogeneity and waning immunity significantly impact measles transmission dynamics.
- Timely and targeted interventions, considering network structure and contact patterns, are essential for controlling measles outbreaks.
- Resource allocation should align with population contact patterns for maximum intervention effectiveness.
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