A dynamically consistent discrete-time model for monkeypox transmission with implications for quarantine policies

Monkeypox is a zoonotic viral infection with significant public health implications. Since epidemiological data are typically reported in discrete time intervals and public health interventions are implemented at specific decision points, discrete-time models provide a natural and policy-relevant modeling framework. Although numerous mathematical models for Mpox have been developed using differential equations, discrete-time approaches remain relatively unexplored, despite their practical importance. In this study, we introduce a discrete-time framework for Mpox by constructing a nonstandard finite difference (NSFD) scheme that preserves the key dynamical properties of the corresponding continuous model. The preservation of positivity, boundedness, and equilibrium behavior is particularly important for decision-support models, as numerical artifacts may otherwise lead to misleading interpretations in applied health and policy contexts. The basic reproduction number R₀ is explicitly computed and shown to depend on the human and animal reproduction numbers, denoted by R₀ʰ and R₀ᵃ, respectively. Three equilibrium states are identified, and both the local and global dynamics of the system around these equilibria are rigorously analyzed. It is demonstrated that the condition R₀<1 alone may not be sufficient to guarantee disease eradication. Furthermore, it is proven that the condition R₀ᵃ>1 is sufficient for the persistence of the disease in both human and animal populations. A sensitivity analysis is also performed to quantify the impact of model parameters on disease transmission dynamics. This analysis provides a clear interpretation of how quarantine measures and contact-reduction strategies influence disease persistence in human and animal populations. Numerical simulations confirm the theoretical findings and provide a comparative assessment of the proposed NSFD scheme against standard methods such as Euler and Runge-Kutta. The time-step-independent nature of the proposed framework ensures robust numerical outcomes and provides a reliable tool for supporting evidence-based public health decision-making and the evaluation of quarantine-oriented intervention strategies.