Bifurcation analysis for a COVID-19 cell model with passive antibody treatment control strategy

We present a mathematical model that describes the cellular dynamics of COVID-19 infection and antibody response. We improve upon existing mathematical models by adding detailed evidence-based assumptions and proving key features of solutions, such as the existence of unique, positive, and bounded solutions. Our susceptible–exposed–infected–virus particle–antibody (SEIVA) model divides the cell population into three compartments: susceptible ( S ) , latent/exposed ( E ), and infectious ( I ). In addition, it incorporates virus particles ( V ) and antibody compartments ( A ) with neutralizing interactions. We identify both the disease-free and the endemic equilibrium states, and we use the next-generation matrix approach to determine that the most important measure for understanding the severity of the infection is the basic reproduction number ( R 0 ) . Using the normalized sensitivity index technique, we identify the pivotal parameters that influence R 0 . We establish the conditions for the stability of the proposed model at the aforementioned equilibrium points. We also analyze bifurcation and chaos in the dynamics of the proposed COVID-19 cell model to the infection rate and determine its critical value. We further extend this model with an additional control parameter that represents passive antibody treatment and examine the model’s responsiveness to various control strategies. Overall, this work presents a comprehensive modeling approach for analyzing and controlling the disease at the cellular level, combining advanced mathematical techniques with practical insights for disease management.