Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, and Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR-CONICET), Deán Funes 3350, 7600 Mar del Plata, Argentina.
Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.
Phys Rev E. 2019 Jan;99(1-1):012302. doi: 10.1103/PhysRevE.99.012302.
In this work we propose and investigate a strategy of vaccination which we call "dynamic vaccination." In our model, susceptible people become aware that one or more of their contacts are infected and thereby get vaccinated with probability ω, before having physical contact with any infected patient. Then the nonvaccinated individuals will be infected with probability β. We apply the strategy to the susceptible-infected-recovered epidemic model in a multiplex network composed by two networks, where a fraction q of the nodes acts in both networks. We map this model of dynamic vaccination into bond percolation model and use the generating functions framework to predict theoretically the behavior of the relevant magnitudes of the system at the steady state. We find a perfect agreement between the solutions of the theoretical equations and the results of stochastic simulations. In addition, we find an interesting phase diagram in the plane β-ω, which is composed of an epidemic and a nonepidemic phase, separated by a critical threshold line β_{c}, which depends on q. As q decreases, β_{c} increases, i.e., as the overlap decreases, the system is more disconnected, and therefore more virulent diseases are needed to spread epidemics. Surprisingly, we find that, for all values of q, a region in the diagram where the vaccination is so efficient that, regardless of the virulence of the disease, it never becomes an epidemic. We compare our strategy with random immunization and find that, using the same amount of vaccines for both scenarios, we obtain that the spread of disease is much lower in the case of dynamic vaccination when compared to random immunization. Furthermore, we also compare our strategy with targeted immunization and we find that, depending on ω, dynamic vaccination will perform significantly better and in some cases will stop the disease before it becomes an epidemic.
在这项工作中，我们提出并研究了一种我们称之为“动态接种”的接种策略。在我们的模型中，易感人群意识到他们的一个或多个接触者感染了病毒，因此在与任何感染患者进行身体接触之前，他们有概率ω接种疫苗。然后，未接种疫苗的个体将以概率β感染。我们将该策略应用于由两个网络组成的复合格子网络中的易感-感染-恢复传染病模型中，其中一部分节点 q 在两个网络中都起作用。我们将这种动态接种模型映射到键渗流模型上，并使用生成函数框架来理论预测系统在稳态时的相关量的行为。我们发现理论方程的解与随机模拟的结果之间存在完美的一致性。此外，我们在β-ω平面上发现了一个有趣的相图，它由传染病和非传染病相组成，由临界阈值线β c 分隔，β c 取决于 q。随着 q 的减小，β c 增大，即随着重叠的减小，系统的连接性越差，因此需要更具毒性的疾病才能传播流行病。令人惊讶的是，我们发现，对于 q 的所有值，图中都存在一个区域，其中接种疫苗的效率如此之高，无论疾病的毒性如何，它都永远不会成为流行病。我们将我们的策略与随机免疫进行比较，发现对于两种情况，使用相同数量的疫苗，与随机免疫相比，动态接种可以大大降低疾病的传播。此外，我们还将我们的策略与靶向免疫进行了比较，发现取决于ω，动态接种将表现得更好，在某些情况下，甚至可以在疾病成为流行病之前阻止它。
