Stability analysis and optimal control strategies of direct and indirect transmission dynamics of conjunctivitis

This article concerns the S–E–I–R (Susceptible–Exposed–Infected–Recovered) mathematical model formulation describing the dynamics of the spread of conjunctivitis predominant in human host population. The model considered possesses two equilibrium points, namely, the conjunctivitis‐free and conjuncti...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical methods in the applied sciences 2020-12, Vol.43 (18), p.10619-10636
Main Author: Ogunmiloro, Oluwatayo Michael
Format: Article
Language:English
Subjects:
Asymptotic properties
Conjunctivitis
Control stability
Dynamic stability
Hygiene
Mathematical models
Optimal control
Optimization
Runge-Kutta method
Sensitivity analysis
Stability analysis
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This article concerns the S–E–I–R (Susceptible–Exposed–Infected–Recovered) mathematical model formulation describing the dynamics of the spread of conjunctivitis predominant in human host population. The model considered possesses two equilibrium points, namely, the conjunctivitis‐free and conjunctivitis‐present equilibrium, which are dependent on the basic reproduction number (Rco). The local and global stabilities of derived model system were investigated at the equilibrium solutions, and it was found that if Rco  1, the conjunctivitis‐present equilibrium is globally asymptotically stable. The sensitivity analysis of Rco is performed, and the corresponding graphical results are presented to examine the relative importance of conjunctivitis model parameters as to conjunctivitis prevalence. The model is reformulated by applying control measures of isolation and hygiene compliance to minimize conjunctivitis infection and irritants concentration as well as the cost associated with it. An optimality system is derived and numerically solved with and without controls using the forward–backward Runge–Kutta scheme via computational software MATLAB. The graphical results obtained showed that each of the control strategies has its own importance for conjunctivitis elimination. Further graphical descriptions reveal that the combination of isolation and hygiene compliance strategies are more effective in curtailing conjunctivitis prevalence in human and environmental host community.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6756