This document discusses the implementation of a triangular probabilistic distribution to optimize recovery rates in the SEIR model, particularly in the context of disease spread post-COVID-19. It highlights the potential for improved modeling by using distributed delays and presents a modified SEIR model based on previous research. The study includes details on the parameters for the triangular distribution and acknowledges contributions from the author's advisor.

1. Implementation of a triangular probabilistic
distribution for optimal parameterization of the
SEIR model recovery rates with delay
Mustafa Senturk,
Computational Science and Engineering Program,
Institute of Graduate Studies,
Piri Reis University, Tuzla, Istanbul, 34940,

2. Introduction
The study of how diseases spread, especially after the Covid-19
pandemic, has grabbed a lot of attention. While most focus has
been on picking the right model to understand and predict how
diseases spread, there's still a lot we can learn by digging deeper
into the hidden dynamics. This study offers that models can be
improved by using triangular probabilistic distributions as
distributed delays.

3. Introduction
Daily novel cases and daily recovered numbers, S.Korea

4. Recovery as a Distributed Delay
Triangular Distribution

5. Triangular Distribution

6. Model
the modified SEIR model proposed by Kok Yew Ng et al. in DDE form.

7. Implementation of Distributed Delay

8. Implementation of Distributed Delay
In discrete form (Trapezoidal Rule):

11. Optimization
Determination of Triangular Parameters

12. Parameters of Triangular Distribution
T = {x0, c,L | x0 ∈ Z +, c ∈ Z +,L ∈ Z +}
x0 : time delay or the starting point (ta) of the triangular
distribution,
c : mode of the triangular distribution,
L: period of the triangular distribution.

13. Parameters of Triangular Distribution
Germany, optimized in short period

14. Parameters of Triangular Distribution
S. Korea, optimized in short period

15. Thank you
Special Thanks to my advisor professeur
O. Ö. Aybar, Ph.D.