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Effect Of Treatment And Protection Measures On The Outbreak Of Infectious Disease Using An Sir Epidemic Model With Two Delays, Discrete And Distributed

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  • MOHAMMED AMINE MENOUER

    (��Laboratoire d’Analyse Non Linéaire et Mathématiques Appliquées, Université de Tlemcen, Tlemcen, Algeria‡Mathematic Department, University of Abou Bekr Belkaid, Tlemcen 13000, Algeria)

  • NADIA GUL

    (Department of Mathematics, Shaheed Benazir Bhutto Women University, Peshawar, 25000 Khyber Pakhtunkhwa, Pakistan)

  • SALIH DJILALI

    (��Laboratoire d’Analyse Non Linéaire et Mathématiques Appliquées, Université de Tlemcen, Tlemcen, Algeria∥Department of Mathematics, Faculty of Exact Sciences and Computer Science, Hassiba Benbouali University, Chlef 02000, Algeria)

  • ANWAR ZEB

    (�Department of Mathematics, COMSATS University Islamabad, Abbottabad, 22060 Khyber Pakhtunkhwa, Pakistan)

  • ZAREEN A. KHAN

    (�Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P. O. Box 84428, Riyadh 11671 Saudi Arabia)

Abstract

In this paper, we aim to analyze the effect of treatment and protection measures on the spread of infectious disease. Therefore, we formulate a delayed mathematical which contains a discrete delay which stands for the duration of protection and distributed delay that represents the repulsed individuals from treatment. The main result is to show that the model has threshold behavior governed by ℜ0. For ℜ0 < 1, it is shown that the disease-free equilibrium is globally stable. However, for ℜ0 > 1, it is proved that the semiflow is uniformly persistent, and the endemic equilibrium is globally stable. Another purpose is fixed in this paper, which consists of studying the effect of treatment and protection measures on the spread of the disease, and to distinguish the minimal protection and treatment measure for reducing the basic reproduction number below one. The results are supported numerically using numerical simulations.

Suggested Citation

  • Mohammed Amine Menouer & Nadia Gul & Salih Djilali & Anwar Zeb & Zareen A. Khan, 2022. "Effect Of Treatment And Protection Measures On The Outbreak Of Infectious Disease Using An Sir Epidemic Model With Two Delays, Discrete And Distributed," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(08), pages 1-14, December.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:08:n:s0218348x2240223x
    DOI: 10.1142/S0218348X2240223X
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    Keywords

    Delay; Protection; Treatment;
    All these keywords.

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