Modelling the spread of MonkeyPox in USA with vertical transmission and saturated treatment

Abstract In this study, we present a comprehensive mathematical model to investigate the dynamics of Susceptible-Infectious-Recovered (SIR) type infectious diseases. Our model incorporates various factors that play crucial roles in disease transmission and control, including saturated incidence, vertical transmission, inherited passive immunity in newborns of susceptible and recovered individuals, and treatment. We explore the interplay between these factors and their impact on disease spread and control measures using a reduced SI model. After ensuring the existence of the model, we obtain the stability of the system around the disease-free and endemic equilibria. Also, for comprehending the long-term dynamics of the system, we obtain the results of persistence and global stability. By varying the parameters, we observe various bifurcations in the reduced SI system such as backward, transcritical, saddle-node, and Hopf bifurcations. To understand the behavior of the medication rate, vertical transmission, and the measure of passive immunity of newborns in the S and R compartments, we conduct numerical simulations that investigate the existence of periodic solutions through Hopf bifurcation, elucidating multiple endemic bubbles in the bifurcation diagram. We also validate the proposed system for the zoonotic disease by analyzing the 2022 monkeypox outbreak in the USA using daily new infection data obtained from the official website of the Centers for Disease Control and Prevention (CDC). By demonstrating that our simulations of the reduced SI model is closely aligned with officially reported data and average daily cases, policymakers can have confidence in its predictive capabilities, enhancing their ability to anticipate and respond to future outbreaks effectively. We have followed the dual approach of validating analytical results both theoretically as well as empirically using real data. This dual approach distinguishes our work from existing studies, which typically focus on either modeling a specific disease or exploring hypothetical dynamics exclusively.