In this article, taking into account distributed delay and multidimensional L\'evy disturbances, wepresent an exhaustive study on the dynamic of the Susceptible-Infected-Removed (SIR ) model . We aim to ameliorate the mathematical tools to obtain the long-run characteristics of the perturbed delayed model. Within this scope, we give sufficient conditions for two interesting asymptotic proprieties: extinction and the mean persistence of the epidemic. Numerical simulations on different L\'evy disturbances are carried out to verify the obtained theoretical results .
Recently, emerging epidemics like COVID-19 and its variants require predictive mathematical models to implement suitable responses in order to limit their negative and profound impact on society. The SIR (Susceptible-InfectedRemoved) system is a straightforward mathematical formulation to model the dissemination of many infectious diseases. The present paper reports novel theoretical and analytical results for a perturbed version of an SIR model with Gamma-distributed delay. Notably, our epidemic model is represented by It\^o-L'evy stochastic differential equations in order to simulate sudden and unexpected external phenomena. By using some new and ameliorated mathematical approaches, we study the long-run characteristics of the perturbed delayed model. Within this scope, we give sufficient conditions for two interesting asymptotic proprieties: extinction and persistence of the epidemic. One of the most interesting results is that the dynamics of the stochastic model are closely related to the intensities of white noises and L'evy jumps, which can give us a good insight into the evolution of the epidemic in some unexpected situations. Our work complements the results of some previous investigations and provides a new approach to predict and analyze the dynamic behavior of epidemics with distributed delay. For illustrative purposes, numerical examples are presented for checking the theoretical study
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In this article, taking into account distributed delay and multidimensional L\'evy disturbances, wepresent an exhaustive study on
Recently, emerging epidemics like COVID-19 and its variants require predictive mathematical models to implement suitable responses in order to limit their negative and profound impact on society. The SIR (Susceptible-InfectedRemoved) system is a straightforward mathematical formulation to model the dissemination of many infectious diseases. The present paper reports novel theoretical and analytical results for a perturbed version of an SIR model with Gamma-distributed delay. Notably, our epidemic model is represented by It\^o-L'evy stochastic differential equations in order to simulate sudden and unexpected external phenomena. By using some new and ameliorated mathematical approaches, we study
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dynamic of the Susceptible-Infected-Removed (SIR ) model . We aim to ameliorate the mathematical tools to obtain the
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the mean
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Numerical simulations on different L\'evy disturbances are carried out to verify the obtained theoretical results .
One of the most interesting results is that the dynamics of the stochastic model are closely related to the intensities of white noises and L'evy jumps, which can give us a good insight into the evolution of the epidemic in some unexpected situations. Our work complements the results of some previous investigations and provides a new approach to predict and analyze the dynamic behavior of epidemics with distributed delay. For illustrative purposes, numerical examples are presented for checking the theoretical study