<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathfrak {R}_0\)</EquationSource> </InlineEquation> is explicitly computed and shown to depend on the human and animal reproduction numbers, denoted by <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathfrak {R}_0^h\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathfrak {R}_0^a\)</EquationSource> </InlineEquation>, 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 <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathfrak {R}_0<1\)</EquationSource> </InlineEquation> alone may not be sufficient to guarantee disease eradication. Furthermore, it is proven that the condition <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathfrak {R}_0^a>1\)</EquationSource> </InlineEquation> 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.</p>

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

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2026年4月16日

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Kemal Türk,
Mehmet Gümüş

摘要

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 \(\mathfrak {R}_0\) is explicitly computed and shown to depend on the human and animal reproduction numbers, denoted by \(\mathfrak {R}_0^h\) and \(\mathfrak {R}_0^a\) , 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 \(\mathfrak {R}_0<1\) alone may not be sufficient to guarantee disease eradication. Furthermore, it is proven that the condition \(\mathfrak {R}_0^a>1\) 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.