## Modeling Pediculosis Transmission with Infection Awareness for Control

Published: 2024-03-02

Page: 104-117

A. S. Wunuji *

Department of Mathematics and Statistics, Federal University, Wukari, Taraba State, Nigeria.

D. A. Amayindi

Department of Mathematical Science, Taraba State University, Jalingo, Nigeria.

Joseph Navokhi

Department of Mathematics and Statistics, Taraba State Polytechnic, Jalingo, Nigeria.

*Author to whom correspondence should be addressed.

### Abstract

In this paper, a mathematical model for pediculosis infection was developed and analysed. The model was designed by dividing the system into six compactments leading to a system of ordinary differential equations. The model is built on the assumption that some of those with pediculosis infection are aware of the disease while others are not. Conditions are derived for the positivity of the solution, and the existence of disease free and endemic equilibria. It shows that the disease can be eliminated under certain conditions. The model equation was solved using the homotopy perturbation method and numerical simulation were carried out to investigate the effects of some of the transmission parameters on the dynamics of the infection. The results showed that with effective treatment, pediculosis can be eradicated from a human population.

Keywords: Pediculosis disease, mathematical model, awareness infection, transmission dynamics and homotopy pertbation method (HPM)

#### How to Cite

Wunuji, A. S., Amayindi, D. A., & Navokhi , J. (2024). Modeling Pediculosis Transmission with Infection Awareness for Control. Asian Journal of Pure and Applied Mathematics, 6(1), 104–117. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1958

### References

Castelletti N, Maria VB. Deterministic approaches for head lice infestation and treatments: Infectious Disease Modelling. 2020;5(2020):386-404.

DOI: ORG/10.1016/J.IDM.2020.05.002

Jessica EL, Julie MA, Lauren ML, Tamar EC, Lisa B, Ganbold S, Didier R and David L. Geographic Distribution and origins of Human Head Lice (Pediculus Humanus Capitis). Journal of Parasitology. University of Florida. 2007;94(6):1275-1281.

Shekelle PG, Woolf SH, Eccles M, Grimshaw J. Clinical guidelines: Developing guidelines. BMJ (Clinical researched.). 1999;318(7183):593-596.

DOI:org/10.1136/bmj.318.7183.593

Dirk ME. In principles and practice of pediatric infectious diseases (5th ed). Elsevier; 2018.

DOI: org/10.1016/C2013-0-19020-4

Brouqui P, Raoult D. Arthropod-borne diseases in homeless. Annals of the New York Academy of Sciences. 2006;1078(1):223-235.

DOI: org/10.1196/ANNALS.1374.041

Dagrosa AT, Elston DM. what’s eating you? Head lice (Pediculus humanus capitis). Cutis. 2017;100(6):389-392.

Cetinkaya U, Sahin S, Ulatabanca RO. The Epidemiology of Scabies and Pediculosis in Kayseri. Turkish Society for Parasitology. 2018;42(2):134-137.

DOI: org/10.5152/TPD.2018.5602

Van-den Driessche P, Watmough J. Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission. Journal of Mathematical Bioscience. 2002;180(2):29-48.

DOI: org/10.1016/s0025-5564

Dickmann O, Heesterbeek JAP, Melz JAJ. Mathematical Epidemology of infection diseases and the computation of the Basic Reproductive Number R0in models of infection Diseases in Hetrogeneous Populations. Journal of mathematical Biology.,1990;28:365-380

Chukwu FI. A Mathematical Model on the transmission dynamics of pediculosis Infection, Unpublished M.Sc. Thesis, University of Nigeria, Nsukka. 2020;57.