In the case of an epidemic, the government (or population itself) can use protection for reducing the epidemic. This research investigates the global dynamics of a delayed epidemic model with partial susceptible protection. A threshold dynamics is obtained in terms of the basic reproduction number, where for $ R_0 < 1 $ the infection will extinct from the population. But, for $ R_0 > 1 $ it has been shown that the disease will persist, and the unique positive equilibrium is globally asymptotically stable. The principal purpose of this research is to determine a relation between the isolation rate and the basic reproduction number in such a way we can eliminate the infection from the population. Moreover, we will determine the minimal protection force to eliminate the infection for the population. A comparative analysis with the classical SIR model is provided. The results are supported by some numerical illustrations with their epidemiological relevance.
Citation: Abdelheq Mezouaghi, Salih Djillali, Anwar Zeb, Kottakkaran Sooppy Nisar. Global proprieties of a delayed epidemic model with partial susceptible protection[J]. Mathematical Biosciences and Engineering, 2022, 19(1): 209-224. doi: 10.3934/mbe.2022011
In the case of an epidemic, the government (or population itself) can use protection for reducing the epidemic. This research investigates the global dynamics of a delayed epidemic model with partial susceptible protection. A threshold dynamics is obtained in terms of the basic reproduction number, where for $ R_0 < 1 $ the infection will extinct from the population. But, for $ R_0 > 1 $ it has been shown that the disease will persist, and the unique positive equilibrium is globally asymptotically stable. The principal purpose of this research is to determine a relation between the isolation rate and the basic reproduction number in such a way we can eliminate the infection from the population. Moreover, we will determine the minimal protection force to eliminate the infection for the population. A comparative analysis with the classical SIR model is provided. The results are supported by some numerical illustrations with their epidemiological relevance.
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Abdelheq Mezouaghi, Salih Djillali, Anwar Zeb, Kottakkaran Sooppy Nisar. Global proprieties of a delayed epidemic model with partial susceptible protection[J]. Mathematical Biosciences and Engineering, 2022, 19(1): 209-224. doi: 10.3934/mbe.2022011
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