A Vaccination Model for Transmission Dynamics of Influenza

Despite the availability of preventive vaccines and public health vaccination programs, influenza inflicts substantial morbidity, mortality, and socio-economic costs and remains a major public health problem. This is largely because the protection conferred by current vaccines is dependent on the immune status of the individual, ranging between 70%--90% in healthy young adults and 30%--40% among the elderly and others with weakened immune systems. Whether a strategic use of such partially effective vaccines can control the spread of influenza within a certain population is unknown but of great public health interest. To address this question, we construct a deterministic mathematical model to study the transmission dynamics of influenza. The model is analyzed qualitatively to determine criteria for control of an influenza epidemic and is used to compute the threshold vaccination rate necessary for community-wide control of influenza. Using two specific populations of similar size, an office and a personal care home, our model shows that the spread of influenza can be controlled if the combined effect of the vaccine efficacy and vaccination rate reaches a threshold determined by the duration of infectiousness and the rate of contact between infected and susceptible individuals.