Impact of heterogeneous vaccination on epidemic dynamics in metapopulation networks

Vaccination has undoubtedly been one of the most effective strategies to mitigate outbreaks of many infectious diseases. However, vaccination rates in different cities exhibit heterogeneity due to various factors. In order to explore the impacts of heterogeneous vaccination on epidemic spreading, we propose a discrete-time Markov-chain epidemic model (of SVIR type) with heterogeneous vaccination on Erdős-Rényi (ER) and Barabási-Albert like (BA-like) metapopulation networks. First, the epidemic threshold of the model is derived. It is found that there is a negative and linear correlation between the epidemic threshold and the max population size when the mobility probability is small, while this relationship becomes weaker and disappears when the mobility probability increases to a certain level. Then numerical simulations on different metapopulation networks are performed. It shows that the population mobility plays an important role in influencing the effects of vaccination strategies on epidemic spreading. Preferential vaccination on patches with larger population can significantly enlarge the epidemic threshold when the mobility probability is small on both ER and BA-like metapopulation networks, while random vaccination on the whole metapopulation network is more efficient when the mobility probability approaches 1 on BA-like metapopulation network. Besides, numerical results suggest that reducing the population size of large patches and decreasing population mobility from low-degree patches to high-degree patches are effective strategies to suppress epidemic spreading on the whole metapopulation network. Our findings help guide the precise allocation and deployment of vaccination resources, improve the efficiency of medical services and reduce unnecessary costs in infectious disease prevention and control.