A hierarchical intervention scheme based on epidemic severity in a community network

As there are no targeted medicines or vaccines for newly emerging infectious diseases, isolation among communities (villages, cities, or countries) is one of the most effective intervention measures. As such, the number of intercommunity edges ([Formula: see text]) becomes one of the most important factor in isolating a place since it is closely related to normal life. Unfortunately, how [Formula: see text] affects epidemic spread is still poorly understood. In this paper, we quantitatively analyzed the impact of [Formula: see text] on infectious disease transmission by establishing a four-dimensional [Formula: see text] edge-based compartmental model with two communities. The basic reproduction number [Formula: see text] is explicitly obtained subject to [Formula: see text] [Formula: see text]. Furthermore, according to [Formula: see text] with zero [Formula: see text], epidemics spread could be classified into two cases. When [Formula: see text] for the case 2, epidemics occur with at least one of the reproduction numbers within communities greater than one, and otherwise when [Formula: see text] for case 1, both reproduction numbers within communities are less than one. Remarkably, in case 1, whether epidemics break out strongly depends on intercommunity edges. Then, the outbreak threshold in regard to [Formula: see text] is also explicitly obtained, below which epidemics vanish, and otherwise break out. The above two cases form a severity-based hierarchical intervention scheme for epidemics. It is then applied to the SARS outbreak in Singapore, verifying the validity of our scheme. In addition, the final size of the system is gained by demonstrating the existence of positive equilibrium in a four-dimensional coupled system. Theoretical results are also validated through numerical simulation in networks with the Poisson and Power law distributions, respectively. Our results provide a new insight into controlling epidemics.

Modelling epidemics with fractional-dose vaccination in response to limited vaccine supply

The control strategies of emergency infectious diseases are constrained by limited medical resources. The fractional dose vaccination strategy as one of feasible strategies was proposed in response to global shortages of vaccine stockpiles. Although a variety of epidemic models have been developed under the circumstances of limited resources in treatment, few models particularly investigated vaccination strategies in resource-limited settings. In this paper, we develop a two-group SIR model with incorporation of proportionate mixing patterns and n-fold fractional dose vaccination related parameters to evaluate the efficiency of fractional dose vaccination on disease control at the population level. The existence and uniqueness of the final size of the two-group SIR epidemic model, the formulation of the basic reproduction number and the relationship between them are established. Moreover, numerical simulations are performed based on this two-group vector-free model to investigate the effectiveness of n-fold fractional dose vaccination by using the emergency outbreaks of yellow fever in Angola in 2016. By employing linear and nonlinear dose-response relationships, we compare the resulting fluctuations of four characteristics of the epidemics, which are the outbreak size, the peak time of the outbreak, the basic reproduction number and the infection attack rate (IAR). For both types of dose-response relationships, dose-fractionation takes positive effects in lowering the outbreak size, delay the peak time of the outbreak, reducing the basic reproduction number and the IAR of yellow fever only when the vaccine efficacy is high enough. Moreover, five-fold fractional dose vaccination strategy may not be the optimal vaccination strategy as proposed by the World Health Organization if the dose-response relationship is nonlinear.