In this work,we first propose a mathematical model to study the impact of awareness programs on dengue transmission.The basic reproduction number Ro is derived.The existence and stability of equilibria are investigate...In this work,we first propose a mathematical model to study the impact of awareness programs on dengue transmission.The basic reproduction number Ro is derived.The existence and stability of equilibria are investigated.The uniform persistence is established when Ro is larger than one.Our results suggest that awareness programs have significant impacts on dengue transmission dynamics although they cannot affect Ro.When o is less than one,awareness programs can shorten the prevailing time effectively.When Ro is larger than one,awareness programs may destabilize the unique interior equilibrium and a stable periodic solution appears due to Hopf bifurcation.In particular,we find that the occurrence of Hopf bifurcation depends not only on the intensity of awareness programs but also on the level of Ro.Besides,large fuctuations in the number of infected individuals caused by the stable periodic solution may bring pressure on limited medical resources.Therefore,different from intuitive ideas,blindly increasing the intensity of awareness programs is not necessarily conducive to control the transmission of dengue.The decision-making department should decide to adopt different publicity strategies according to the current level of Ro.Finally,we consider the optimal control problem of the model and find the optimal control strategy corresponding to awareness programs by Pontryagin's Maximum Principle.The results manifest that the optimal control strategy can effectively mitigate the transmission of dengue.展开更多
基金the National Natural Science Foundation of China(Nos.11971240,61973166 and 12001282)the Natural Science Foundation for Young Scholars of Jiangsu Province(No.SBK2020041626)the Natural Science Research Foundation of Jiangsu Higher Education Institutions(No.20KJB110024).
文摘In this work,we first propose a mathematical model to study the impact of awareness programs on dengue transmission.The basic reproduction number Ro is derived.The existence and stability of equilibria are investigated.The uniform persistence is established when Ro is larger than one.Our results suggest that awareness programs have significant impacts on dengue transmission dynamics although they cannot affect Ro.When o is less than one,awareness programs can shorten the prevailing time effectively.When Ro is larger than one,awareness programs may destabilize the unique interior equilibrium and a stable periodic solution appears due to Hopf bifurcation.In particular,we find that the occurrence of Hopf bifurcation depends not only on the intensity of awareness programs but also on the level of Ro.Besides,large fuctuations in the number of infected individuals caused by the stable periodic solution may bring pressure on limited medical resources.Therefore,different from intuitive ideas,blindly increasing the intensity of awareness programs is not necessarily conducive to control the transmission of dengue.The decision-making department should decide to adopt different publicity strategies according to the current level of Ro.Finally,we consider the optimal control problem of the model and find the optimal control strategy corresponding to awareness programs by Pontryagin's Maximum Principle.The results manifest that the optimal control strategy can effectively mitigate the transmission of dengue.
