A new model of dengue fever in terms of fractional derivative

Fatmawati, Rashid Jan, Muhammad Altaf Khan, Yasir Khan, Saif Ullah

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)

Abstract

It is eminent that the epidemiological patterns of dengue are threatening for both the global economy and human health. The experts in the field are always in search to have better mathematician models in order to understand the transmission dynamics of epidemics models and to suggest possible control or the minimization of the infection from the community. In this research, we construct a new fractional-order system for dengue infection with carrier and partially immune classes to visualize the intricate dynamics of dengue. By using the basics of fractional theory, we determine the fundamental results of the proposed fractional-order dengue model. We obtain the basic reproduction number R0 by next generation method and present the results based on it. The stability results are established for the infection-free state of the system. Moreover, sensitivity of R0 is analyzed through partial rank correlation coefficient(PRCC) method to show the importance of different parameters in R0. The influence of different input factors is shown on the output of basic reproduction number R0 numerically. Our result showed that the threshold parameter R0 can be decreased by increasing vaccination and treatment in the system. Finally, we illustrate the solution of the suggested dengue system through a numerical scheme to notice the influence of the fractional-order ϑ on the system. We observed that the fractional-order dynamics can explain the complex system of dengue infection more precisely and accurately rather than the integer-order dynamics. In addition, we noticed that the index of memory and biting rate of vector can play a significant part in the prevention of the infection.

Original languageEnglish
Pages (from-to)5267-5287
Number of pages21
JournalMathematical Biosciences and Engineering
Volume17
Issue number5
DOIs
Publication statusPublished - 2020

Keywords

  • Dengue disease
  • Fractional derivative
  • Mathematical model
  • Numerical simulations
  • Sensitivity analysis

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