Consequences of non-Markovian healing processes on epidemic models with recurrent infections on networks
Infectious diseases are marked by recovering time distributions which can be far from the exponential one associated with Markovian/Poisson processes, broadly applied in epidemic models. In the present work, we tackled this problem by investigating a susceptible-infected-recovered-susceptible model...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2025-01-01
|
| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ada795 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832593742733770752 |
|---|---|
| author | José Carlos M Silva Diogo H Silva Francisco A Rodrigues Silvio C Ferreira |
| author_facet | José Carlos M Silva Diogo H Silva Francisco A Rodrigues Silvio C Ferreira |
| author_sort | José Carlos M Silva |
| collection | DOAJ |
| description | Infectious diseases are marked by recovering time distributions which can be far from the exponential one associated with Markovian/Poisson processes, broadly applied in epidemic models. In the present work, we tackled this problem by investigating a susceptible-infected-recovered-susceptible model on networks with η independent infectious compartments (SI $_ {\eta}$ RS), each one with a Markovian dynamics, that leads to a Gamma-distributed recovering time. We analytically develop a theory for the epidemic lifespan on star graphs with a center and K leaves, which mimic hubs on networks, showing that the epidemic lifespan scales with a non-universal power-law. Compared with standard susceptible-infected-recovered-susceptible dynamics, the epidemic lifespan on star graphs is severely reduced as the number of stages increases. In particular, the case $\eta\rightarrow\infty$ leads to a finite lifespan. Numerical simulations support the approximated analytical calculations. We investigated the SI $_ {\eta}$ RS dynamics on random power-law networks. When the epidemic processes are ruled by a maximum k -core activation, either the epidemic threshold or the epidemic localization pattern are unaltered. When hub mutual activation is at work, the localization is reduced but not sufficiently to alter the threshold scaling with the network size. Therefore, the activation mechanisms remain the same as in the case of Markovian healing. |
| format | Article |
| id | doaj-art-d2f40a91a22d41cc8bac5044c6a6ccc6 |
| institution | Kabale University |
| issn | 1367-2630 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj-art-d2f40a91a22d41cc8bac5044c6a6ccc62025-01-20T09:05:58ZengIOP PublishingNew Journal of Physics1367-26302025-01-0127101300910.1088/1367-2630/ada795Consequences of non-Markovian healing processes on epidemic models with recurrent infections on networksJosé Carlos M Silva0https://orcid.org/0000-0002-9735-0108Diogo H Silva1https://orcid.org/0000-0001-6639-6413Francisco A Rodrigues2https://orcid.org/0000-0002-0145-5571Silvio C Ferreira3https://orcid.org/0000-0001-7159-2769Departamento de Física, Universidade Federal de Viçosa , 36570-900 Viçosa, Minas Gerais, BrazilInstituto de Ciências Matemáticas e de Computação, Universidade de São Paulo , São Carlos, SP 13566-590, BrazilInstituto de Ciências Matemáticas e de Computação, Universidade de São Paulo , São Carlos, SP 13566-590, BrazilDepartamento de Física, Universidade Federal de Viçosa , 36570-900 Viçosa, Minas Gerais, Brazil; National Institute of Science and Technology for Complex Systems , 22290-180 Rio de Janeiro, BrazilInfectious diseases are marked by recovering time distributions which can be far from the exponential one associated with Markovian/Poisson processes, broadly applied in epidemic models. In the present work, we tackled this problem by investigating a susceptible-infected-recovered-susceptible model on networks with η independent infectious compartments (SI $_ {\eta}$ RS), each one with a Markovian dynamics, that leads to a Gamma-distributed recovering time. We analytically develop a theory for the epidemic lifespan on star graphs with a center and K leaves, which mimic hubs on networks, showing that the epidemic lifespan scales with a non-universal power-law. Compared with standard susceptible-infected-recovered-susceptible dynamics, the epidemic lifespan on star graphs is severely reduced as the number of stages increases. In particular, the case $\eta\rightarrow\infty$ leads to a finite lifespan. Numerical simulations support the approximated analytical calculations. We investigated the SI $_ {\eta}$ RS dynamics on random power-law networks. When the epidemic processes are ruled by a maximum k -core activation, either the epidemic threshold or the epidemic localization pattern are unaltered. When hub mutual activation is at work, the localization is reduced but not sufficiently to alter the threshold scaling with the network size. Therefore, the activation mechanisms remain the same as in the case of Markovian healing.https://doi.org/10.1088/1367-2630/ada795complex networksepidemic processesnon-Markovian dynamics |
| spellingShingle | José Carlos M Silva Diogo H Silva Francisco A Rodrigues Silvio C Ferreira Consequences of non-Markovian healing processes on epidemic models with recurrent infections on networks New Journal of Physics complex networks epidemic processes non-Markovian dynamics |
| title | Consequences of non-Markovian healing processes on epidemic models with recurrent infections on networks |
| title_full | Consequences of non-Markovian healing processes on epidemic models with recurrent infections on networks |
| title_fullStr | Consequences of non-Markovian healing processes on epidemic models with recurrent infections on networks |
| title_full_unstemmed | Consequences of non-Markovian healing processes on epidemic models with recurrent infections on networks |
| title_short | Consequences of non-Markovian healing processes on epidemic models with recurrent infections on networks |
| title_sort | consequences of non markovian healing processes on epidemic models with recurrent infections on networks |
| topic | complex networks epidemic processes non-Markovian dynamics |
| url | https://doi.org/10.1088/1367-2630/ada795 |
| work_keys_str_mv | AT josecarlosmsilva consequencesofnonmarkovianhealingprocessesonepidemicmodelswithrecurrentinfectionsonnetworks AT diogohsilva consequencesofnonmarkovianhealingprocessesonepidemicmodelswithrecurrentinfectionsonnetworks AT franciscoarodrigues consequencesofnonmarkovianhealingprocessesonepidemicmodelswithrecurrentinfectionsonnetworks AT silviocferreira consequencesofnonmarkovianhealingprocessesonepidemicmodelswithrecurrentinfectionsonnetworks |