Abstract
The complex network theory constitutes a natural support for the study of a disease propagation. In this work, we present a study of an infectious disease spread with the use of this theory in combination with the Individual Based Model. More specifically, we use several complex network models widely known in the literature to verify their topological effects in the propagation of the disease. In general, complex networks with different properties result in curves of infected individuals with different behaviors, and thus, the growth of a given disease is highly sensitive to the network model used. The disease eradication is observed when the vaccination strategy of 10% of the population is used in combination with the random, small world or modular network models, which opens an important space for control actions that focus on changing the topology of a complex network as a form of reduction or even elimination of an infectious disease.
Highlights
Infectious or transmissible diseases are caused by biological agents, such as viruses or bacteria
With the use of Equation (5.1), it is possible to build the equivalence between the SIR models and the Individual Based Model (IBM), in such way that, on average, their solutions will present similar behaviors [27]
The disease eradication is observed when the vaccination strategy of 10% of the population is used in combination with the random, small world or modular network models
Summary
Infectious or transmissible diseases are caused by biological agents, such as viruses or bacteria. Instead of working directly with a complex network, the technique is based on producing a similar model based on differential equations to approximate the mean-field behavior of the complex network Works in this direction can be seen in [28, 30, 31]. The novelty of this study is the establishment of a direct relationship between the mean jump length, the disease spread and the number of infected individuals This perspective opens an important space for control actions that focus on changing the topology of complex networks as a form of reduction or even eradication of infectious diseases. The classic SIR model, defined by a continuous system of three ordinary differential equations, considers that the distribution of individuals is spatially and temporally homogeneous This model (Eq (2.1)), describes the temporal evolution of each epidemiological class, that is: dS = dt μ.
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