Resumen de Exploring Discrete-Time Epidemic Behavior Based on Saturated Incidence Rate and Multiple Transmission Pathways

Preeti Deolia, Vijay Shankar Sharma, Anuraj Singh

• The viral shedding is crucial for understanding the transmission of infectious diseases via contaminated surfaces. In this work, a discrete-time SIR-type mathematical model incorporating pathogen shedding is investigated. The basic reproduction number (R0) is used to determine the conditions for the local stability of the fixed points of the discrete-time model. The existence of co-dimension one bifurcations particularly, transcritical (BP) and period-doubling (PD) bifurcations, along with co-dimension two bifurcations namely, generalized period doubling (GPD), and limit point period doubling (LPPD) bifurcations are discussed. The presence of these bifurcations is detected using algebraic criterion methods. These methods are based on the properties of the coefficients of the characteristic polynomial instead of the eigenvalues of the Jacobian matrix. The sensitivity indices of R0 are calculated via the normalized forward sensitivity method with respect to significant parameters. The performed numerical simulation supports the analytical findings of the model. The existence of several bifurcations in the discrete-time epidemic model reflects a situation where a slight adjustment in some specific parameters can significantly impact the model outcomes.