title: Stability analysis and optimal control of an epidemic model with awareness programs by media.
abstract: The impact of awareness campaigns and behavioral responses on epidemic outbreaks has been reported at times. However, to what extent does the provision of awareness and behavioral changes affect the epidemic trajectory is unknown, but important from the public health standpoint. To address this question, we formulate a mathematical model to study the effect of awareness campaigns by media on the outbreak of an epidemic. The awareness campaigns are treated as an intervention for the emergent disease. These awareness campaigns divide the whole populations into two subpopulation; aware and unaware, by inducing behavioral changes amongst them. The awareness campaigns are included explicitly as a separate dynamic variable in the modeling process. The model is analyzed qualitatively using stability theory of differential equations. We have also identified an optimal implementation rate of awareness campaigns so that disease can be controlled with minimal possible expenditure on awareness campaigns, using optimal control theory. The control setting is investigated analytically using optimal control theory, and the numerical solutions illustrating the optimal regimens under various assumptions are also shown.
authors.affiliation: Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi 221 005, India. Electronic address: akmisra_knp@yahoo.com.
authors.forename: A K
authors.initials: AK
authors.lastname: Misra
authors.affiliation: Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi 221 005, India. Electronic address: anupama_bhu@yahoo.com.
authors.forename: Anupama
authors.initials: A
authors.lastname: Sharma
authors.affiliation: BIT, BIIFR&D, Bhabha Group of Institutions, Kanpur 209 204, India. Electronic address: jbs@iik.ac.in.
authors.forename: J B
authors.initials: JB
authors.lastname: Shukla
mesh_terms: D003140:Communicable Disease Control / Q000379:methods / Q000706:statistics & numerical data*; D003141:Communicable Diseases / Q000401:mortality*; D054626:Consumer Health Information / Q000706:statistics & numerical data*; D007722:Health Knowledge, Attitudes, Practice; D006293:Health Promotion / Q000706:statistics & numerical data*; D006801:Humans; D015994:Incidence; D033181:Information Dissemination / Q000379:methods; D008402:Mass Media / Q000706:statistics & numerical data*; D012307:Risk Factors; D015996:Survival Rate
keywords: Awareness campaigns; Epidemic model; Media; Optimal control; Stability