IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 17, Issue 4 Ser. II (Jul. – Aug. 2021), PP 29-32 www.iosrjournals.org DOI: 10.9790/5728-1704022932 www.iosrjournals.org 29 | Page Diffusion Epidemic model for Analysis the effects of six-day SSRI administration on diurnal cortisol secretion in healthy volunteers using non-linear partial differential equations A.Leema Rose 1 and A.Manickam 2 1,2 Research Scholar (FT), Department of Mathematics, Marudupandiyar College (Arts &Science), (Affiliated to Bharathidasan University, Tiruchirappalli-620 024), Vallam - Post, Thanjavur–613 403, Tamilnadu, India Abstract: In this paper, we investigated the dynamics of a reaction diffusion epidemic model with specific nonlinear incidence rate. This specific nonlinear incidence rate includes the traditional bilinear incidence rate, the bedding ton-De Angelis functional response, and Crowley Martin functional response. The local stability of the disease-free equilibrium and endemic equilibrium is obtained via characteristic equations. Eventually, we come to the conclusion that medical solutions had obtained and evaluated the relevant mathematical findings. Ultimately, we conclude that the application part coincides with a mathematical model and the result is linked to the medical report. In the future, this paper will be beneficial in the medical field. Keywords - Cortisol, Epidemic model, Partial differential equation, HPA axis, Depression Mathematical subject classification:        --------------------------------------------------------------------------------------------------------------------------------------- Date of Submission: 24-07-2021 Date of Acceptance: 09-08-2021 --------------------------------------------------------------------------------------------------------------------------------------- I. Introduction In this article, we check out the following SIR disease model with a particular nonlinear occurrence rate as stated below                                 (1)       Where S, I, and R are susceptible, infectious, and recovered classes, respectively. is the enrolment pace of the people,  is the normal population mortality rate, d is the mortality levels due to sickness, r is the retrieval levels for Infectious Persons,  is the disease coefficient, and          is the event rate, where        are constants. It is very important to note that this Beddington-DeAngelis functional response introduced in [1,2] and used in [3] when     and Crowley- Martin functional response presented in [4-6] if        Moreover, the function          satisfies the hypothesis(H1), (H2), and (H3) of general incidence rate presented by Hattaf et al[7]. II. Mathematical Model And Assumptions In traditional disease models, this rate was believed to be linear with the number of vulnerable and contaminated persons. This assumption is based on a rule of mass intervention that is more suitable for transmittable illnesses, but not for highly contagious diseases such as HIV/AIDS. The following SIR disease model with a particular non-linear occurrence rate and spatial diffusion is considered:                                            - (                 (2)