Estimation of Parameters in the SIR Epidemic Model Using Particle Swarm Optimization
Supriadi Putra,
Khozin Mu'tamar,
Zulkarnain
Issue:
Volume 4, Issue 4, December 2019
Pages:
83-93
Received:
30 September 2019
Accepted:
25 October 2019
Published:
30 October 2019
Abstract: Susceptible, Infected and Resistant (SIR) models are used to observe the spread of infection from infected populations into healthy populations. Stability analysis of the model is done using the Routh-Hurwitz criteria, basic reproduction number or the Lyapunov Stability. For stability analysis, parameters value are needed and these values are usually assumed. Given data cannot be used to determine the parameter values of SIR model because analytic solution of system of nonlinear differential equation cannot be determined. In this article, we determine the parameters of the exponential growth model, logistic model and SIR models using the Particle Swarm Optimization (PSO) algorithm. The SIR model is solved numerically using the Euler method based on the parameter values determined by PSO. The simulation results show that the PSO algorithm is good enough in determining the parameters of the three models compared to analytical methods and the Gauss-Newton’s method. Based on the average hypothesis test the relative error obtained from the PSO algorithm to determine the parameters is less than 3% with a significance level of 1%.
Abstract: Susceptible, Infected and Resistant (SIR) models are used to observe the spread of infection from infected populations into healthy populations. Stability analysis of the model is done using the Routh-Hurwitz criteria, basic reproduction number or the Lyapunov Stability. For stability analysis, parameters value are needed and these values are usual...
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The Matching Energy of Random Multipartite Graphs
Caibing Chang,
Bo Deng,
Haizhen Ren,
Feng Fu
Issue:
Volume 4, Issue 4, December 2019
Pages:
94-98
Received:
22 September 2019
Accepted:
2 December 2019
Published:
7 December 2019
Abstract: Let Gn be a simple graph with n vertices. Gutman and Wagner founded the theory of random graphs, they introduced the matching energy of the graph Gn, which was defined as the sum of the absolute values of the eigenvalues of the matching polynomial of the graph Gn. For the Erdös-Rényi type random graph Gn,p of order n with a fixed probability p, where p is a real number greater than zero and less than 1, that is, the graph G on n vertices by connecting two vertices with probability p(e), and each edge is independent of other one. Chen, Li and Lian solved a conjecture proposed by Gutman and Wagner, that is, the expectation of the matching energy of Gn,p converges to a certain number associated with n and p almost surely. But they only did the result for random bipartite graphs. In this paper, we give some lower bounds for the matching energy of random bipartite graphs. And then we will use Chen et al’s method to generalize this conclusion to any random multipartite graphs.
Abstract: Let Gn be a simple graph with n vertices. Gutman and Wagner founded the theory of random graphs, they introduced the matching energy of the graph Gn, which was defined as the sum of the absolute values of the eigenvalues of the matching polynomial of the graph Gn. For the Erdös-Rényi type random graph Gn,p of order n with a fixed probability p, whe...
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