A Time-Delayed Mathematical Modeling for Monkeypox Transmission with Incubation Period

This paper proposes a time-delayed mathematical model designed to analyze the transmission dynamics of the monkeypox virus, explicitly incorporating the incubation period as a time delay. The disease-free and endemic equilibria of the time-delayed model are analyzed. The basic reproduction number determines the time delay caused by the incubation period. The disease-free equilibrium is locally asymptotically stable when the threshold is less than unity. The model parameters is then estimated using the least-squares fitting method based on monkeypox cases in the United States of America. Numerical simulations are performed with varying time-delay values, representing different lengths of the incubation period. The results reveal that a longer incubation period leads to slower spread of the disease. In other words, the longer the incubation period, the more gradual the increase in the number of infected individuals over time. The observed relationship between incubation period delays and disease spread rate highlights the crucial role of this delay factor in shaping the transmission patterns of monkeypox virus. These insights can inform disease control strategies, particularly those aimed at early detection and isolation during the incubation period.