Research ArticlesNo Access

A reliable numerical analysis for stochastic gonorrhea epidemic model with treatment effect

Department of Mathematics, Stochastic Analysis and Optimization Research Group, Air University, PAF Complex E-9, Islamabad 44000, Fedral, Pakistan

E-mail Address: 160865@students.au.edu.pk

Corresponding author.

Search for more papers by this author

Muhammad Shoaib Arif

Department of Mathematics, Stochastic Analysis and Optimization Research Group, Air University, PAF Complex E-9, Islamabad 44000, Fedral, Pakistan

E-mail Address: shoaib.arif@mail.au.edu.pk

Search for more papers by this author

, and

Muhammad Rafiq

Faculty of Engineering, University of Central Punjab, Lahore 54000, Punjab, Pakistan

E-mail Address: m.rafiq@ucp.edu.pk

Search for more papers by this author

https://doi.org/10.1142/S1793524519500724Cited by:28 (Source: Crossref)

Abstract

The phenomena of disease spread are unpredictable in nature due to random mixing of individuals in a population. It is of more significance to include this randomness while modeling infectious diseases. Modeling epidemics including their stochastic behavior could be a more realistic approach in many situations. In this paper, a stochastic gonorrhea epidemic model with treatment effect has been analyzed numerically. Numerical solution of stochastic model is presented in comparison with its deterministic part. The dynamics of the gonorrhea disease is governed by a threshold quantity $A_{1}$ $A_{1}$ called basic reproductive number. If $A_{1} < 1$ $A_{1} < 1$ , then disease eventually dies out while $A_{1} > 1$ $A_{1} > 1$ shows the persistence of disease in population. The standard numerical schemes like Euler Maruyama, stochastic Euler and stochastic Runge–Kutta are highly dependent on step size and do not behave well in certain scenarios. A competitive non-standard finite difference numerical scheme in stochastic setting is proposed, which is independent of step size and remains consistent with the corresponding deterministic model.

Keywords:

AMSC: 34-01, 34-04, 65C30, 46N40, 47N40

Remember to check out the Most Cited Articles in IJB!

Check out new Biomathematics books in our Mathematics 2018 catalogue!
Featuring author Frederic Y M Wan and more!

References

1. A. Lajmanvovich and J. A. Yorke, A deterministic model for gonorrhea in a non-homogeneous population, Math. Biosci. 28 (1976) 221–236. Google Scholar
2. A. Raza, M. S. Arif and M. Rafiq, A reliable numerical analysis for stochastic dengue epidemic model with incubation period of virus, Adv. Difference Equ. 32 (2019) 1–19. Google Scholar
3. A. Slomski, Novel antibiotic efficacious in treating gonorrhea, Jama Netw. 4 (2019) 321–335. Google Scholar
4. S. N. Taylor et al., Gepotidacin for the treatment of uncomplicated urogenital gonorrhea a Phase 2, randomized, dose-ranging, single-oral dose evaluation, Clin. Infect. Dis. 67 (2018) 504–512. Web of Science, Google Scholar
5. J. Piszezk, R. S. Jean and Y. Khaliq, Gonorrhea treatment update for an increasingly resistant organism, Can. Pharm. J. 148 (2015) 82–89. Google Scholar
6. C. Balmelli and H. F. Gunthard, Gonococci tonsillar infection a case report and literature review, Infection 31 (2003) 362–365. Web of Science, Google Scholar
7. M. R. Chacko, C. M. Wiemann and P. B. Smith, Chlamydia and gonorrhea screening in asymptomatic young women, J. Pediatr. Adolesc. Gynecol. 17 (2004) 165–178. Google Scholar
8. A. R. Katz et al., False positive gonorrhea test result with a nuclei amplification test the impact of how prevalence on positive predictive value, Clin. Infect. Dis. 38 (2004) 814–819. Web of Science, Google Scholar
9. J. R. Schwebke, C. Rivers and J. Lee, Prevalence of Gardnerella vaginalis in male sexual partners of women with and without bacterial vaginosis, Sex. Transm. Dis. 36 (2009) 92–95. Web of Science, Google Scholar
10. C. Bignell and M. Umemo, European guideline on diagnosis and treatment of gonorrhea in adult, Int. J. STD. AIDS. 24 (2013) 85–92. Web of Science, Google Scholar
11. M. S. Arif et al., A reliable stochastic numerical analysis for typhoid fever incorporating with protection against infection, Comput. Mater. Con. 59 (2019) 787–804. Web of Science, Google Scholar
12. T. G. Benedek, Gonorrhea and the beginning of clinical research ethics, Perspect. Biol. Med. 48 (2005) 54–73. Web of Science, Google Scholar
13. M. Tibebu, A. Shibabaw, G. Medhin and A. Kassu, Neisseria gonorrhoeae non-susceptible to cephalosporins and quinolones in Northwest Ethiopia, BMC Infect. Dis. 13 (2013) 1–6. Web of Science, Google Scholar
14. M. Bala, Antimicrobial resistance in Neisseria gonorrhea South East Asia, Reg. Health. Forum 15 (2011) 63–73. Google Scholar
15. Z. Zafar, K. Rehan and M. Mushtaq, Fractional-order scheme for bovine babesiosis disease and tick populations, Adv. Difference. Equ. 86 (2017) 1–9. Google Scholar
16. Z. Zafar et al., Numerical treatment for nonlinear Brusselator chemical model, J. Differ. Equ. Appl. 23 (2017) 521–538. Web of Science, Google Scholar
17. Z. Zafar, K. Rehan and M. Mushtaq, HIV/AIDS epidemic fractional-order model, J. Differ. Equ. Appl. 23 (2017) 1298–1315. Web of Science, Google Scholar
18. P. E. Kloeden, Numerical Solution of SDE Through Computer Experiments (Springer, Berlin, 1994). Google Scholar
19. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations (Springer, Berlin, 1992). Google Scholar
20. B. Oksendal, Stochastic Differential Equations (Springer, Berlin, 2003). Google Scholar
21. E. Platen, An introduction to numerical methods for stochastic differential equations, Acta. Numer. 8 (1999) 197–246. Google Scholar
22. J. Cresson and F. Pierret, Nonstandard finite difference scheme preserving dynamical properties, preprint (2014), arXiv:1410.6661. Google Scholar
23. R. E. Mickens, Nonstandard Finite Difference Models of Differential Equations (World Scientific, River Edge, 1994). Google Scholar
24. R. E. Mickens, Advances in Applications of Nonstandard Finite Difference Schemes (World Scientific, Hackensack, 2005). Link, Google Scholar
25. R. E. Mickens, A fundamental principle for constructing nonstandard finite difference schemes for differential equations, J. Differ. Equ. Appl. 11 (2005) 645–653. Web of Science, Google Scholar
26. T. C. Gard, Introduction to Stochastic Differential Equations (Dekker, New York, 1988). Google Scholar
27. I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus (Springer, Berlin, 1998). Google Scholar
28. L. J. S. Allen and A. Burgin, Comparison of deterministic and stochastic SIS and SIR models in discrete time, Math. Biosci. 163 (2000) 1–33. Web of Science, Google Scholar
29. E. J. Allen, Modeling with Ito Stochastic Differential Equations (Springer, Dordrecht, 2007). Google Scholar
30. T. Britton, Stochastic epidemic models a survey, Math. Biosci. 225 (2010) 24–35. Web of Science, Google Scholar
31. E. J. Allen et al., Construction of equivalent stochastic differential equation models, Stoch. Anal. Appl. 26 (2008) 274–297. Web of Science, Google Scholar
32. M. J. Keeling and P. Rohani, Modeling Infectious Diseases in Humans and Animals (Princeton University Press, Princeton, 2008). Google Scholar
33. I. Shoji and T. Ozaki, Comparative study of estimation methods for continuous time stochastic processes, J. Time Ser. Anal. 18 (1997) 485–506. Google Scholar
34. M. Bayram, T. Partal and G. O. Buyukoz, Numerical methods for simulation of stochastic differential equations, Adv. Difference Equ. 17 (2018) 1–10. Google Scholar
35. G. Maruyama, Continuous Markov processes and stochastic equations, Rend. Circ. Mat. Palermo 4 (1955) 48–90. Google Scholar
36. A. Jajarmi and D. Baleanu, A new fractional analysis on the interaction of HIV with CD4+ T-cells, Chaos Solitons Fractals 113 (2018) 221–229. Web of Science, Google Scholar
37. D. Baleanu et al., New aspects of poor nutrition in the life cycle within the fractional calculus, Adv. Difference Equ. 23 (2018) 1–14. Google Scholar
38. E. H. Doha et al., Approximate solutions for solving nonlinear variable-order fractional Riccati differential equations, Nonlinear Anal. Model. Control 24 (2019) 176–188. Web of Science, Google Scholar