Abstract
Cryptosporidium is associated with waterborne transmission mechanism through the faecal–oral path in many recreational water facilities. We investigate the probable approximate solution of integer and noninteger systems of nonlinear ordinary differential equations representing cryptosporidiosis dynamics. The approximate or estimate solution is derived through recent developed analytic method, the homotopy decomposition method (HDM). The algorithm is systemically explained and demonstrated with some numerical examples. The numerical results indicate that the approximate solution is of continuous function form in the light of noninteger-order derivative. The integer-order numerical solution of parameters values varied and investigated which show similar solution in each case. The method employed to obtain the solution to this problem is robust, easy, reliable and quick in terms of time.
Highlights
Human cryptosporidiosis is caused by cryptosporidium protozoan and constitutes a large number of gastrointestinal disease usually connected with recreational water use as the case in Australia [1, 2] as well as other parts of the world [see e.g. [3,4,5,6] and references therein]
Cryptosporidium is well identified with waterborne transmission mechanism via the faecal–oral path in many recreational water facilities
The purpose of this paper is to present approximate analytical solutions for the standard form and fractional aspect of (1) in addition to (2) using the relative new analytical method called homotopy decomposition method (HDM)
Summary
Human cryptosporidiosis is caused by cryptosporidium protozoan and constitutes a large number of gastrointestinal disease usually connected with recreational water use as the case in Australia [1, 2] as well as other parts of the world [see e.g. [3,4,5,6] and references therein]. The rate of cryptosporidiosis infected to the environment is denoted by π. Mathematical models, in general, are highly nonlinear, and obtaining the exact solution usually becomes a challenge.
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