Modeling hepatitis B infection dynamics with a novel mathematical model incorporating convex incidence rate and real data

In this study, we present a novel mathematical model that comprehensively addresses the mechanics of hepatitis B infection propagation, caused by the hepatitis B virus, which represents a significant global health concern. This viral infection encompasses various stages, including chronic and acute carrier phases, each playing a pivotal role in the progression and transmission of hepatitis B. Notably, individuals in the chronic phase, despite being asymptomatic, can still transmit the virus, posing a substantial public health challenge. Our study develops an endemic model with a nonlinear incidence rate to better understand the infectiousness of hepatitis B at various phases of the illness. To achieve this, we refine the infectious group into two distinct subclasses: those acutely infected and chronic carriers, both capable of transmitting the virus both horizontally and vertically. We provide an in-depth description of the fundamental characteristics of the proposed model. Furthermore, in order to determine the reproduction number R0, we use the next-generation matrix approach. We study the biological relevance of the threshold state in great detail shedding light on its implications for disease control and spread. We also establish criteria for analyzing all potential equilibria of the model based on the fundamental reproduction number. To assess the sensitivity of the model’s outcomes to various parameters, we conduct a comprehensive sensitivity analysis, identifying the most influential factors. Estimation of parameter values is achieved using robust least square curve-fitting techniques, further enhancing the model’s practical applicability. Additionally, we complement our analytical findings with numerical simulations to gain deeper insights into the dynamics of hepatitis B transmission. Furthermore, we extend our investigation by formulating a fractional-order model, employing the Atangana–Baleanu derivative. Finally, we establish the existence and uniqueness of the model by employing the ABC fractional-order derivative, contributing to a more comprehensive understanding of the model’s behavior.