Inference of a Susceptible–Infectious stochastic model
We considered a time-inhomogeneous diffusion process able to describe the dynamics of infected people in a susceptible-infectious (SI) epidemic model in which the transmission intensity function was time-dependent. Such a model was well suited to describe some classes of micro-parasitic infections i...
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AIMS Press
2024-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2024310 |
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| author | Giuseppina Albano Virginia Giorno Francisco Torres-Ruiz |
| author_facet | Giuseppina Albano Virginia Giorno Francisco Torres-Ruiz |
| author_sort | Giuseppina Albano |
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| description | We considered a time-inhomogeneous diffusion process able to describe the dynamics of infected people in a susceptible-infectious (SI) epidemic model in which the transmission intensity function was time-dependent. Such a model was well suited to describe some classes of micro-parasitic infections in which individuals never acquired lasting immunity and over the course of the epidemic everyone eventually became infected. The stochastic process related to the deterministic model was transformable into a nonhomogeneous Wiener process so the probability distribution could be obtained. Here we focused on the inference for such a process, by providing an estimation procedure for the involved parameters. We pointed out that the time dependence in the infinitesimal moments of the diffusion process made classical inference methods inapplicable. The proposed procedure were based on the generalized method of moments in order to find a suitable estimate for the infinitesimal drift and variance of the transformed process. Several simulation studies are conduced to test the procedure, these include the time homogeneous case, for which a comparison with the results obtained by applying the maximum likelihood estimation was made, and cases in which the intensity function were time dependent with particular attention to periodic cases. Finally, we applied the estimation procedure to a real dataset. |
| format | Article |
| id | doaj-art-503ce9a93f654b9581ca25277ec25512 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | AIMS Press |
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| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-503ce9a93f654b9581ca25277ec255122025-01-23T07:47:53ZengAIMS PressMathematical Biosciences and Engineering1551-00182024-09-012197067708310.3934/mbe.2024310Inference of a Susceptible–Infectious stochastic modelGiuseppina Albano0Virginia Giorno1Francisco Torres-Ruiz2Dipartimento di Studi Politici e Sociali, Università degli Studi di Salerno, Via Giovanni Paolo Ⅱ, 84084 Fisciano (SA), ItalyDipartimento di Informatica, Università degli Studi di Salerno, Via Giovanni Paolo Ⅱ, 84084 Fisciano (SA), ItalyDepartamento de Estadística e I.O., Universidad de Granada, Avenida de Fuente Nueva s/n, 18071, Granada, SpainWe considered a time-inhomogeneous diffusion process able to describe the dynamics of infected people in a susceptible-infectious (SI) epidemic model in which the transmission intensity function was time-dependent. Such a model was well suited to describe some classes of micro-parasitic infections in which individuals never acquired lasting immunity and over the course of the epidemic everyone eventually became infected. The stochastic process related to the deterministic model was transformable into a nonhomogeneous Wiener process so the probability distribution could be obtained. Here we focused on the inference for such a process, by providing an estimation procedure for the involved parameters. We pointed out that the time dependence in the infinitesimal moments of the diffusion process made classical inference methods inapplicable. The proposed procedure were based on the generalized method of moments in order to find a suitable estimate for the infinitesimal drift and variance of the transformed process. Several simulation studies are conduced to test the procedure, these include the time homogeneous case, for which a comparison with the results obtained by applying the maximum likelihood estimation was made, and cases in which the intensity function were time dependent with particular attention to periodic cases. Finally, we applied the estimation procedure to a real dataset.https://www.aimspress.com/article/doi/10.3934/mbe.2024310time inhomogeneous wiener processestimating proceduregeneralized method of moments |
| spellingShingle | Giuseppina Albano Virginia Giorno Francisco Torres-Ruiz Inference of a Susceptible–Infectious stochastic model Mathematical Biosciences and Engineering time inhomogeneous wiener process estimating procedure generalized method of moments |
| title | Inference of a Susceptible–Infectious stochastic model |
| title_full | Inference of a Susceptible–Infectious stochastic model |
| title_fullStr | Inference of a Susceptible–Infectious stochastic model |
| title_full_unstemmed | Inference of a Susceptible–Infectious stochastic model |
| title_short | Inference of a Susceptible–Infectious stochastic model |
| title_sort | inference of a susceptible infectious stochastic model |
| topic | time inhomogeneous wiener process estimating procedure generalized method of moments |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2024310 |
| work_keys_str_mv | AT giuseppinaalbano inferenceofasusceptibleinfectiousstochasticmodel AT virginiagiorno inferenceofasusceptibleinfectiousstochasticmodel AT franciscotorresruiz inferenceofasusceptibleinfectiousstochasticmodel |