Fractional-order delayed Ross–Macdonald model for malaria transmission
- 22 January 2022
- journal article
- research article
- Published by Springer Science and Business Media LLC in Nonlinear Dynamics
- Vol. 107 (3), 3155-3173
- https://doi.org/10.1007/s11071-021-07114-7
Abstract
This paper proposes a novel fractional-order delayed Ross–Macdonald model for malaria transmission. This paper aims to systematically investigate the effect of both the incubation periods of Plasmodium and the order on the dynamic behavior of diseases. Utilizing inequality techniques, contraction mapping theory, fractional linear stability theorem, and bifurcation theory, several sufficient conditions for the existence and uniqueness of solutions, the local stability of the positive equilibrium point, and the existence of fractional-order Hopf bifurcation are obtained under different time delays cases. The results show that time delay can change the stability of system. System becomes unstable and generates a Hopf bifurcation when the delay increases to a certain value. Besides, the value of order influences the stability interval size. Thus, incubation periods and the order have a major effect on the dynamic behavior of the model. The effectiveness of the theoretical results is shown through numerical simulations.Keywords
Funding Information
- National Natural Science Foundation of China (61673094)
This publication has 27 references indexed in Scilit:
- Stability and bifurcation analysis of a vector-bias model of malaria transmissionMathematical Biosciences, 2013
- Stability and Hopf Bifurcations of nonlinear delay malaria epidemic modelNonlinear Analysis: Real World Applications, 2010
- Dynamical models of happiness with fractional orderCommunications in Nonlinear Science and Numerical Simulation, 2010
- A model for the transmission of malariaDiscrete & Continuous Dynamical Systems - B, 2009
- A mathematical analysis of the effects of control strategies on the transmission dynamics of malariaApplied Mathematics and Computation, 2008
- On the Delayed Ross–Macdonald Model for Malaria TransmissionBulletin of Mathematical Biology, 2008
- Remarks on fractional derivativesApplied Mathematics and Computation, 2007
- The epidemiology of Plasmodium falciparum gametocytes: weapons of mass dispersionTrends in Parasitology, 2006
- MALARIA PARASITE DEVELOPMENT IN MOSQUITOESAnnual Review of Entomology, 1998
- ELECTRIC CONDUCTANCE OF BIOLOGICAL SYSTEMSCold Spring Harbor Symposia on Quantitative Biology, 1933