Epidemic dynamics of influenza-like diseases spreading in complex networks
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ORIGINAL PAPER
Epidemic dynamics of influenza-like diseases spreading in complex networks Yi Wang · Zhouchao Wei · Jinde Cao
Received: 25 April 2020 / Accepted: 30 July 2020 © Springer Nature B.V. 2020
Abstract Population contact pattern plays an important role in the spread of an infectious disease. This can be described in the framework of a complex network approach. In this paper network epidemic models for influenza-like diseases that may have infectious force in incubative or asymptomatic stage are formulated and studied. Two general types of network models are considered: the annealed and the quenched networks. The next-generation matrix approach is employed to compute the basic reproduction number of our networkbased models. The implicit equations for the final epidemic size are derived, and the existence and uniqueness of solutions for implicit equations are studied by rewriting implicit equations as suitable fixedpoint problems. In particular, for networks with no degree correlation, low-dimensional systems of nonlinear ordinary differential model are derived by employing an edge-based compartmental approach. Due to their low dimension, a gap between the parameter identification problem for influenza-like diseases or network inference and network epidemic models may be Y. Wang · Z. Wei (B) School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China e-mail: [email protected] Y. Wang e-mail: [email protected] Y. Wang · J. Cao School of Mathematics, Southeast University, Nanjing 210096, China e-mail: [email protected]
built through our results. The analysis is applied to an example of influenza epidemic based on the final epidemic size, from which the transmission rate and the basic reproduction number can be estimated. Keywords Influenza-like diseases · Basic reproduction number · Implicit final size equations · Complex networks · Transmission rate
1 Introduction Seasonal influenza, caused by influenza viruses, is an acute respiratory infection circulating in all parts of the world. There are four types (A, B, C, and D) of seasonal influenza viruses, among which type A and B viruses are mainly responsible for the circulation and cause of seasonal epidemics [1]. Seasonal influenza poses a huge health threat to human, with the World Health Organization (WHO) estimation of 3–5 million infected cases every year killing up to 650,000 people [2]. In modern history, one of the most catastrophic public health crises is the 1918 influenza pandemic, known colloquially as “Spanish flu”, infecting onethird of the global population and resulting in millions of deaths. On 11 March 2019, WHO released a Global Influenza Strategy for 2019–2030 to protect people in all countries from the threat of influenza [3]. Based on the classical susceptible-infectious-recovered (SIR) model, first formulated by Kermack and McKendrick [4], many scholars have extended it to
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investigate the spread and control of influenza (see, e.g., [5–14]). Before introducing the models in detail,
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