Abstract
Mathematical modeling represents a useful instrument to describe epidemic spread and to propose useful control actions, such as vaccination scheduling, quarantine, informative campaign, and therapy, especially in the realistic hypothesis of resources limitations. Moreover, the same representation could efficiently describe different epidemic scenarios, involving, for example, computer viruses spreading in the network. In this paper, a new model describing an infectious disease and a possible complication is proposed; after deep-model analysis discussing the role of the reproduction number, an optimal control problem is formulated and solved to reduce the number of dead patients, minimizing the control effort. The results show the reasonability of the proposed model and the effectiveness of the control action, aiming at an efficient resource allocation; the model also describes the different reactions of a population with respect to an epidemic disease depending on the economic and social original conditions. The optimal control theory applied to the proposed new epidemic model provides a sensible reduction in the number of dead patients, also suggesting the suitable scheduling of the vaccination control. Future work will be devoted to the identification of the model parameters referring to specific epidemic disease and complications, also taking into account the geographic and social scenario.
Highlights
In the last few years, the importance of epidemic modeling and control has increased in respect of their capability to describe infectious disease and proposing suitable control strategies [1,2,3,4,5,6,7,8]; the power of epidemic modeling has been used in different fields, such as to study the propagation effects of a virus outbreak on a network [9,10].The scenario discussed in this paper considers a unique population in which an epidemic disease is spreading and a second non-infectious disease is present
The results show the reasonability of the proposed model and the effectiveness of the control action, aiming at an efficient resource allocation; the model describes the different reactions of a population with respect to an epidemic disease depending on the economic and social original conditions
The problem of the containment of an epidemic spread could be efficiently solved by the framework of optimal control theory; in this case, particular attention is devoted to patients with the two pathologies
Summary
In the last few years, the importance of epidemic modeling and control has increased in respect of their capability to describe infectious disease and proposing suitable control strategies [1,2,3,4,5,6,7,8]; the power of epidemic modeling has been used in different fields, such as to study the propagation effects of a virus outbreak on a network [9,10]. The scenario discussed in this paper considers a unique population in which an epidemic disease is spreading and a second non-infectious disease is present. While the former yields an immunity, the latter could be caught repeatedly This is a very common scenario, and happens, for example, in measles and for the HIV/AIDS; if one thinks of an age-structured model, a similar context occurs if referring to elderly subjects who could be at risk when a complication is added to an infectious disease. A unique population with two pathologies is considered: the first one is the dangerous disease that may be transmitted only by contact with infected patients, and the second one may be fatal only if it becomes a complication of the first The former yields an immunity, whereas the second one could be caught repeatedly.
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