A Complete Model of Crimean-Congo Hemorrhagic Fever (CCHF) Transmission Cycle with Nonlocal Fractional Derivative

Abstract

Crimean-Congo hemorrhagic fever is a common disease between humans and animals that is transmitted to humans through infected ticks, contact with infected animals, and infected humans. In this paper, we present a boxed model for the transmission of Crimean-Congo fever virus. With the help of the fixed-point theory, our proposed system model is investigated in detail to prove its unique solution. Given that the Caputo fractional-order derivative preserves the system’s historical memory, we use this fractional derivative in our modeling. The equilibrium points of the proposed system and their stability conditions are determined. Using the Euler method for the Caputo fractional-order derivative, we calculate the approximate solutions of the fractional system, and then, we present a numerical simulation for the transmission of Crimean-Congo hemorrhagic fever.

Spatial and temporal dynamics of SARS‐CoV‐2: Modeling, analysis and simulation

“…Compared with some earlier related and useful studies without considering the spatial factor of SARS-CoV-2 infection [35] , [36] , [37] , [38] , our results give rise to the following implications: (1) It is clear to see an important impact of spatial heterogeneity on SARS-CoV-2 infection within the host. Based on the theoretical results, as the threshold parameter of dynamical behaviors plays a crucial role in SARS-CoV-2 infections.…”

Chaos of calcium diffusion in Parkinson s infectious disease model and treatment mechanism via Hilfer fractional derivative

“…The fractional calculus is a generalization of the integer-order calculus and it provides more accurate results as compared to classical calculus. Hence, it is widely used in mathematical modelling of science and engineering, medical, and almost all area of education [39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60]. Nowadays, numbers of the fractional derivative are available to deal with real-world problems such as Caputo derivative, Caputo-Fabrizio derivative, Atangana-Baleneu derivative, Hilfer derivative, Weyl derivative, Conformable derivative and many more.…”

Dynamics of the worm transmission in wireless sensor network in the framework of fractional derivatives

“…Applications of these derivatives in understanding various phenomena of mathematical biology and their interdisciplinary fields can be found in the works of 30–38 (see also other related applications in previous works 39,40 ). In this connection, mathematical epidemiologists have also started exploring the classical order epidemiological models by incorporating various fractional derivatives 19,41–44 …”

“…In this connection, mathematical epidemiologists have also started exploring the classical order epidemiological models by incorporating various fractional derivatives. 19,[41][42][43][44] Due to the increasing dependency on computer networks and risk of worm attacks on the security and functionality of WSNs, there is a necessity of studying this subject in the perspective of fractional derivatives. In this study, we have analyzed the interaction of susceptible, exposed, infected, recovered, and vaccinated nodes in a WSN in the framework of the Caputo fractional derivative.…”