Annealed mean-field epidemiological model on scale-free networks with a mitigating factor
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916571285291008 |
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| author | Kim, K. M. Hase, M. O. |
| author_facet | Kim, K. M. Hase, M. O. |
| contents | An annealed version of the quenched mean-field model for epidemic spread is introduced and investigated analytically and assisted by numerical calculations. The interaction between individuals follows a prescription that is used to generate a scale-free network, and we have adjusted the number of connections to produce a sparse network. Specifically, the model's behavior near the infection threshold is examined, as well as the behavior of the stationary prevalence and the probability that a connection between individuals encounters an infected one. We found that these functions display a monotonically increasing dependence on the infection rate. Subsequently, a modification that mimics the mitigation in the probability of encountering an infected individual is introduced, following an old idea rooted in the Malthus-Verhulst model. We found that this modification drastically changes the probability that a connection meets an infected individual. However, despite this change, it does not alter the monotonically increasing behavior of the stationary prevalence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07706 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Annealed mean-field epidemiological model on scale-free networks with a mitigating factor Kim, K. M. Hase, M. O. Populations and Evolution Statistical Mechanics An annealed version of the quenched mean-field model for epidemic spread is introduced and investigated analytically and assisted by numerical calculations. The interaction between individuals follows a prescription that is used to generate a scale-free network, and we have adjusted the number of connections to produce a sparse network. Specifically, the model's behavior near the infection threshold is examined, as well as the behavior of the stationary prevalence and the probability that a connection between individuals encounters an infected one. We found that these functions display a monotonically increasing dependence on the infection rate. Subsequently, a modification that mimics the mitigation in the probability of encountering an infected individual is introduced, following an old idea rooted in the Malthus-Verhulst model. We found that this modification drastically changes the probability that a connection meets an infected individual. However, despite this change, it does not alter the monotonically increasing behavior of the stationary prevalence. |
| title | Annealed mean-field epidemiological model on scale-free networks with a mitigating factor |
| topic | Populations and Evolution Statistical Mechanics |
| url | https://arxiv.org/abs/2501.07706 |