Dynamical analysis of scabies delayed epidemic model with second-order global stability

Abstract

Scabies is a highly transmitted skin disease that can affect people of all ages, especially children. According to the World Health Organization (WHO), South Asia and sub-Saharan Africa are the regions most affected. For the study of the dynamics of scabies in the population, the mathematical model is designed with delay differential equations (DDEs) for four subpopulations: unvaccinated individuals, vaccinated individuals, infected individuals, and recovered individuals. The fundamental properties of the model, such as positivity, boundedness, existence, and uniqueness, are proved. The equilibria, reproduction number, sensitivity analysis, and (Local and Global) stabilities for the second order are studied rigorously. The numerical simulations were performed to confirm the validity of their theoretical results. The study's findings suggest delay-based modeling of scabies and the advanced stability analysis provides a better understanding of epidemic management and disease dynamics over time.

Fig 1. Model diagram.

Fig 2. Sensitivity index of parameters.

Fig 3. Subpopulations denote the sizes of various groups within the population over time.

In this instance, the subpopulations pertain to the dimensions of the scabies-free equilibrium within the model when τ = 0.

Fig 4. Time plots of each subpopulation at Scabies existing equilibrium when

$\tau =0$.

Fig 5. The behaviour of subpopulations at Scabies existing equilibrium when the value of delay parameter is

$\tau =0.5$.

Fig 6. The behaviour of subpopulations at Scabies existing equilibrium when the value of delay parameter is

$\tau =1.$.

Fig 7. The effect of delay parameters on the infected individuals.

Fig 8. The effect of delay parameters on the unvaccinated susceptible individuals.

Fig 9. Comparison of the reproduction number with a delay parameter.