Fractional dynamics of the transmission phenomena of dengue infection with vaccination

Dengue infection brings unimaginable damage in low-income countries across the world to public health, social, and economical fields. Scientists rely on modeling to preferable understand the transmission phenomena of dengue in order to forecast some preventive measures and to give better data for the development of vaccines and medications. In present work, we construct a compartmental model for dengue infection via fractional derivatives to show the influence of memory. The suggested system's solution is investigated for existence as well as uniqueness with the help of fractional calculus fundamental characteristics. The model is analyzed and the reproduction number is obtained through Next-generation Matrix technique, moreover, the sensitivity of the reproduction number is determined using the partial rank correlation coefficient (PRCC) method. We have shown that if document R₀, the disease-free steady-state of the dengue model is locally asymptotically stable (LAS) and globally asymptotically stable (GAS) in the absence of vaccine. In particular case, we have shown that the infection of dengue persists uniformly in the system for document R₀ document greater than one. Furthermore, we quantitatively showed memory's impact on document R₀ document by fluctuation of different factors. Our result predicted that the biting frequency, mosquito recruiting rate, and memory index are the most sensitive aspects in efficiently controlling new dengue illnesses, according to our findings. The effect of vaccination on the suggested system's threshold is also investigated. Novel numerical schemes are presented to conceptualize the time series of the system in different scenarios. The findings suggested that more accurate and precious results are obtained through non-integer derivative and that memory plays a beneficial role in the management of dengue disease. We demonstrated that manipulating the index of memory in the system may manage the system reproduction number and endemic level of dengue infection.