SIRS Epidemic Model Based On State Transition Probability

In the real world, the spreading of the biological viruses, computer viruses, rumors gives rise to enormous losses. Complex networks is regard as a cutting-edge interdisciplinary. Researchers can describe the computer, biological, and social systems by the appropriate complex networks and apply complex network theory to study the propagation and features deeply. In this paper, we build the model with the state transition probability method and microscopically depicts the probability of each node at each moment in each state. Using this method we accurately describe the virus propagation process and analyze the spreading threshold and the steady-state value.Then the results were verified by Monte Carlo simulations. In this paper, my specific work and contribution include the following aspects:First,based on the SIRS(Susceptible-Infected-Removed-Susceptible) epidemic model, we use the method of state transition probability to study the SIRS epidemic process by calculating the probability in each state over time. First, we establish state probability equations to describe the probability in susceptible state, infection state and immune state of each node at each moment,then, derive the epidemic threshold by the theory of steady state analysis. Through Monte Carlo method, we analyze and simulate the epidemic threshold in both homogeneous network and heterogeneous network. Compared with the traditional mean-field method, the results here show that the threshold obtained by the state probability equations is much closer to real Monte Carlo value and have no relations with the immune deficiency rate.Second, based on the SIRS virus propagation model, we derive the maximum steady-state probability of infection by state probability equations and obtain the maximum infection density of the whole network. Then we analyze it in fully connected network, ER random network, WS small-world network, BA scale-free network and verify the maximum steady-state value by Monte Carlo simulation. The results show that the network steady-value of infection density is close to the maximum steady-state probability derived by equations when the degree of the network is big enough.Third,taking into account the mobile behavior of individuals in the real system, in this paper we study and propose SIRS virus propagation model in which nodes move randomly. We analyze and simulate the effects of node moving speed, network density, radius of the infected node by Monte Carlo method. The results show that the network steady-value of infection density is close tothe maximum steady-state probability derived by equations when the node moving speed, network density or the radius of the infected node increases.