Mathematical modeling of psittacosis: guiding effective interventions and public health policy

Abstract

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 \({S}_{\mathcalligra{h}}\left(t\right)\), exposed \({E}_{\mathcalligra{h}}\left(t\right)\), infected \({I}_{\mathcalligra{h}}\left(t\right)\) and recovered \({R}_{\mathcalligra{h}}\left(t\right)\), and the subpopulation of turkey is susceptible \({S}_{\mathcalligra{p}}\left(t\right)\), exposed \({E}_{\mathcalligra{p}}\left(t\right)\), infected \({I}_{\mathcalligra{p}}\left(t\right)\) and recovered \({R}_{\mathcalligra{p}}\left(t\right)\) 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.