Modeling and analysis of the transmission of avian spirochetosis with non-singular and non-local kernel

Abstract

An acute bacterial infection called avian spirochetosis is spread by ticks to a variety of birds. Clinical symptoms can vary greatly and are frequently non-specific. To diagnose a condition, the infectious spirochete must be detected. Here, we structure an epidemic model for the transmission of avian spirochetosis to visualize the interaction between tick and bird populations. The recommended dynamics of avian spirochetosis is illustrated with the help of fractional framework. We inspected the steady-states of the system of the avian spirochetosis for the stability analysis. The next-generation technique is used to evaluate the model’s reproduction parameter ${\mathrm{R}}_0.$ The infection-free and endemic steady-state of avian spirochetosis were shown to be locally asymptotically stable under the specified conditions. Through mathematical skills, the positivity of solutions is determined. Additionally, evidence supporting the existence and uniqueness of the avian spirochetosis framework solution has been shown. We conduct modified simulations of the suggested avian spirochetosis system with different input factors to study the complex phenomena of avian spirochetosis under the effect of numerous input parameters. Our outcomes illustrate the significance and plausibility of fractional parameter, and they also suggest that this input parameter may adequately account for these kinds of observations.

Keywords:

• Numerical technique
• avian spirochetosis
• Atangana–Baleanu derivative
• fractional dynamics
• dynamical behaviour
• fixed-point theory

Disclosure statement

No conflict of interest regarding this work.

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Funding

The author(s) reported there is no funding associated with the work featured in this article.