https://doi.org/10.1140/epjp/s13360-025-06367-0
Regular Article
Mathematical modeling of psittacosis: guiding effective interventions and public health policy
1 Department of Mathematics, National College of Business Administration and Economics, 54660, Lahore, Pakistan
2 Department of Physical Sciences, The University of Chenab, 507001, Gujrat, Pakistan
3 Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal
4 Department of Zoology, University of Sialkot, 51310, Sialkot, Pakistan
5 Department of Mathematics and Statistics, College of Science, King Faisal University, P. O. Box 400, 31982, Al-Ahsa, Saudi Arabia
6 Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P. O. Box 84428, Riyadh, Saudi Arabia
a
ali.raza@uevora.pt
, alimustasamcheema@gmail.com
, ali@phs.uchenab.edu.pk
Received:
24
February
2025
Accepted:
25
April
2025
Published online: 24 May 2025
Psittacosis is a disease that primarily affects humans and is linked to pet birds like cockatiels and parrots as well as livestock like ducks and turkeys. According to the World Health Organization, the European region (Austria, Denmark, Germany, Sweden and The Netherlands) observed an odd and unanticipated rise in psittacosis cases reported. These reported cases developed pneumonia and resulted in hospitalization, and even fatality. For awareness of all living communities and the significance of psittacosis, its modeling has been done in the present study. There are four divisions within humans’ population: susceptible S𝒽(t) , exposed E𝒽(t) , infected I𝒽(t) and recovered R𝒽(t) , and the subpopulation of turkey is susceptible S𝓅(t) , exposed E𝓅(t) , infected I𝓅(t) and recovered R𝓅(t) with artificial delay term. Model steady states, reproduction number, positivity and boundedness are among the feasible properties studied rigorously. Also, the stochastic formulation of the model is presented in two ways with transition probabilities and nonparametric perturbation with the effective use of decay term. Due to the complexity of the system, the Euler Maruyama, stochastic Euler and stochastic Runge–Kutta were used to model the behavior of human and turkey populations. Unfortunately, these numerical methods are not realistic and could not restore the dynamical properties of the model like positivity, boundedness, consistency and convergence of the solution. The nonstandard finite difference method is an effective agreement to solve the system of stochastic delay differential equations in the light of dynamical properties. Results from traditional stochastic methods either converge conditionally or diverge over time. The NSFD method converges unconditionally to the true steady states of the model. In conclusion, this study increases our understanding of psittacosis infection dynamics by employing stochastic with delay techniques and offers new paths for psittacosis infection dynamics investigation. Also, the plotting is done for the visualization of results in comparative profiles of new solutions and interactions.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
