Fractional-view analysis of the transmission dynamics of a bacterial infection with nonlocal and nonsingular kernel

Abstract An enormous cost is placed on people, communities, and healthcare systems by bacterial infections. Measures of the burden of bacterial infections include morbidity, mortality, economic expenditures, and overall effects on public health. Campylobacteriosis is a bacterial infection imposes a significant economic burden on both individuals and societies due to its prevalence, healthcare costs, and the associated loss of productivity. In our research, we develop a model to analyze the transmission of campylobacteriosis infection, taking into account factors such as vaccination and treatment. We also examine the fundamental characteristics of fractional calculus to understand the model better. The equilibria of the model are studied, and we calculate the reproduction parameter denoted as $$\mathcal{R}_{0}$$ R 0 . Furthermore, we provide proof of stability for the equilibria of the system. Lastly, we conduct numerical investigations to explore the variation of the system’s reproduction parameter with different input parameters. We have established the necessary conditions to ensure the existence and uniqueness of solutions for the proposed model of campylobacteriosis infection. To better understand the complex dynamics of campylobacteriosis infection, we conduct various simulations of the suggested model while modifying the input factors. These simulations allow us to investigate the effects of different input parameters on the dynamics of campylobacteriosis infection. We analyze the dynamic behavior of the system to develop efficient control strategies for managing the infection. Notable improvements have been observed by reducing the order of the fractional derivative. Based on our findings, we propose various factors to the policy makers in the community to mitigate the spread of campylobacteriosis infection.