https://doi.org/10.1140/epjs/s11734-025-02122-9
Regular Article
Epidemic model with seasonality for avian influenza waves in humans
1
Postgraduate Program in Sciences, State University of Ponta Grossa, 84030-900, Ponta Grossa, PR, Brazil
2
Physics Institute, University of São Paulo, 05508-090, São Paulo, SP, Brazil
3
Municipal Secretary of Education of Ponta Grossa, Municipal Government, 84030-320, Ponta Grossa, PR, Brazil
4
Department of Mathematics and Statistics, State University of Ponta Grossa, 84030-900, Ponta Grossa, PR, Brazil
5
University Center UNIFATEB, 84266-010, Telêmaco Borba, PR, Brazil
6
Potsdam Institute for Climate Impact Research, 14473, Potsdam, Germany
7
Department of Physics, Humboldt University Berlin, 12489, Berlin, Germany
a
antoniomarcosbatista@gmail.com
Received:
12
August
2025
Accepted:
26
December
2025
Published online:
7
January
2026
Control strategies and prevention of infectious illnesses are challenges faced by the healthcare systems. Infectious diseases are caused by organisms and can be transmitted through different ways, such as contact between individuals of the same species or interspecies (zoonotic diseases). One contagious viral disease is the avian influenza, known as bird flu, that infects wild birds, as well as domestic poultry. It can also contaminate some mammalian species and was detected in humans. Epidemiologic models have been used to study the transmission dynamics of bird flu. In this work, we analyse a model that describes the spread of a avian influenza from birds to humans. We consider a compartmental model in which the bird system is divided into susceptible and infected birds (SI), whilst the human system is separated into susceptible, infected and recovered (SIR). In addition, we substantially extend this model by including seasonal effects in the transmission rate of the system and investigate the behaviour of the model through the waves of infection. We uncover that depending on the parameters and initial conditions, the number of disease cases can be kept under control, as well as it is possible to observe even disease-free state. Our results show that the initial conditions play a crucial role in the number of avian influenza waves. Furthermore, we demonstrate that the seasonal forcing increases the infection numbers and induces a more complex dynamical behaviour.
© The Author(s) 2026
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
