A MATHEMATICAL MODELLING FRAMEWORK FOR EPIDEMIC DYNAMICS UNDER QUARANTINE AND MEDIA-INDUCED AWARENESS USING AN SIQRM FRAMEWORK
Keywords:
Dengue modelling, SIQRM model, Lyapunov stability, Disease-free equilibrium, Endemic equilibrium, Nonlinear epidemic systemsAbstract
Dengue control remains challenging due to the complex interaction between disease transmission, intervention effectiveness, and human behavioural responses. This study develops a human-host SIQRM mathematical model incorporating quarantine and infection-induced media awareness to investigate their combined influence on epidemic dynamics. In this reduced human-host formulation, mosquito-mediated transmission is represented implicitly through the effective transmission process rather than through explicit mosquito compartments. The model consists of susceptible, infectious, quarantined, recovered, and media-awareness compartments and is analysed through positivity, boundedness, equilibrium analysis, reproduction number estimation, sensitivity analysis, and numerical simulations. The analytical results establish the conditions governing disease invasion and persistence, with the baseline parameter set yielding , indicating the potential for epidemic growth. Numerical simulations over 365 days show that media awareness reduces epidemic burden. Without media feedback, the infectious population reached approximately 1726.30 individuals, whereas the inclusion of media awareness reduced the peak infectious population to 670.88 individuals, corresponding to a 61.14% reduction. Furthermore, cumulative infections decreased from 19,618.10 to 12,321.56, representing a 37.19% reduction. Increasing media-generation intensity further reduced epidemic magnitude and delayed the infection peak. Sensitivity analysis revealed that transmission intensity and residual infectiousness during quarantine positively influenced epidemic persistence, whereas quarantine and recovery rates contributed to transmission reduction. The results indicate that quarantine effectiveness depends strongly on limiting infectious contact after isolation, while media awareness provides an additional mechanism for reducing epidemic severity. The proposed framework highlights the importance of integrating behavioural-information dynamics with conventional intervention strategies for improved epidemic control.
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