Dynamic Systems for Signaling Parasite-Host from Differential Equations

Mathematical models, using ordinary differential equations with integer order, have been proven valuable in understanding the dynamics of biological systems. However, the behavior of most biological systems has memory or aftereffects. The modelling of these systems by fractional-order differential equations has more advantages than classical integer-order mathematical modeling, in which such effects are neglected. The topic of fractional calculus (theory of integration and differentiation of an arbitrary order) was started over 300 years ago. Recently, fractional differential equations have attracted many scientists and researchers due to the tremendous use in Mathematical Biology. The reason of using fractional-order differential equations (FOD) is that FOD are naturally related to systems with memory which exists in most biological systems. Also they are closely related to fractals which are abundant in biological systems. The results derived of the fractional system are of a more general nature.

Parasite-Host
Parasite-Host Equations

Respectively, solutions of FOD spread at a faster rate than the classical differential equations, and may exhibit asymmetry. Theory of differential equations in the formation process, the solution of differential equations there have been many methods, such as separation of variables, variable substitution method, constant variation, and integral factor method. Especially the integral factor method is the latest and the biggest role which is the essence of differential equation into appropriate solution which is easy to draw, so we can easily obtain the solution of differential equations. Therefore, the integral factor method is the key to solution of different equations.

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