An infectious disease model with asymptomatic transmission and waning immunity

Abstract

Infectious diseases present persistent challenges to global public health, demanding a comprehensive understanding of their dynamics to develop effective prevention and control strategies. The presence of asymptomatic carriers, individuals capable of transmitting pathogens without displaying symptoms, challenges conventional containment approaches focused on symptomatic cases. Waning immunity, the decline in protective response following natural recovery or vaccination, introduces further complexity to disease dynamics. In this paper, we developed a mathematical model to investigate the interplay between these factors, aiming to inform strategies for the management of infectious diseases. We derived the basic reproduction number for the model and showed that the disease would die out when this number falls below 1. We obtained a formula to estimate the relative contributions of asymptomatic and symptomatic transmission to the basic reproduction number, which remains unchanged when vaccination is included in the model. Through computer simulations with parameter values tailored for COVID-19 and sensitivity analysis, we demonstrated that population susceptibility significantly impacts the timing and magnitude of infection peaks. Populations with lower susceptibility experience delayed and less severe outbreaks. Vaccination was shown to play a crucial role in disease control, with an increased vaccination rate, extended immunity, and heightened vaccine efficacy proving pivotal. However, the effectiveness of these strategies hinges on maintaining a low vaccine escape proportion. Taken together, this study underscores the need for multifaceted, adaptable approaches to infectious disease management, highlighting the central role of vaccination in mitigating disease spread. Further research and validation with disease-specific data will enhance parameter estimates, improve model predictions, and inform evidence-based disease control strategies.