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Mathematical modeling and analysis for controlling the spread of infectious diseases

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  • Tyagi, Swati
  • Martha, Subash C.
  • Abbas, Syed
  • Debbouche, Amar

Abstract

In this work, we present and discuss the approaches, that are used for modeling and surveillance of dynamics of infectious diseases by considering the early stage asymptomatic and later stage symptomatic infections. We highlight the conceptual ideas and mathematical tools needed for such infectious disease modeling. We compute the basic reproduction number of the proposed model and investigate the qualitative behaviours of the infectious disease model such as, local and global stability of equilibria for the non-delayed as well as delayed system. At the end, we perform numerical simulations to validate the effectiveness of the derived results.

Suggested Citation

  • Tyagi, Swati & Martha, Subash C. & Abbas, Syed & Debbouche, Amar, 2021. "Mathematical modeling and analysis for controlling the spread of infectious diseases," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000606
    DOI: 10.1016/j.chaos.2021.110707
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    References listed on IDEAS

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    1. Nazir, Ghazala & Shah, Kamal & Debbouche, Amar & Khan, Rahmat Ali, 2020. "Study of HIV mathematical model under nonsingular kernel type derivative of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Sajjadi, Samaneh Sadat & Baleanu, Dumitru & Jajarmi, Amin & Pirouz, Hassan Mohammadi, 2020. "A new adaptive synchronization and hyperchaos control of a biological snap oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Naik, Parvaiz Ahmad & Zu, Jian & Owolabi, Kolade M., 2020. "Modeling the mechanics of viral kinetics under immune control during primary infection of HIV-1 with treatment in fractional order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    4. Goyal, Manish & Baskonus, Haci Mehmet & Prakash, Amit, 2020. "Regarding new positive, bounded and convergent numerical solution of nonlinear time fractional HIV/AIDS transmission model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Carol Y. Lin, 2008. "Modeling Infectious Diseases in Humans and Animals by KEELING, M. J. and ROHANI, P," Biometrics, The International Biometric Society, vol. 64(3), pages 993-993, September.
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    Cited by:

    1. Boukhobza, Meriem & Debbouche, Amar & Shangerganesh, Lingeshwaran & Torres, Delfim F.M., 2024. "Modeling the dynamics of the Hepatitis B virus via a variable-order discrete system," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    2. Zhu, Linhe & Chen, Siyi & Shen, Shuling, 2024. "Pattern dynamics analysis of a reaction–diffusion network propagation model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 425-444.
    3. Koutou, Ousmane & Diabaté, Abou Bakari & Sangaré, Boureima, 2023. "Mathematical analysis of the impact of the media coverage in mitigating the outbreak of COVID-19," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 600-618.
    4. Anand, Monalisa & Danumjaya, P. & Rao, P. Raja Sekhara, 2023. "A nonlinear mathematical model on the Covid-19 transmission pattern among diabetic and non-diabetic population," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 346-369.
    5. Meriem Boukhobza & Amar Debbouche & Lingeshwaran Shangerganesh & Juan J. Nieto, 2024. "The Stability of Solutions of the Variable-Order Fractional Optimal Control Model for the COVID-19 Epidemic in Discrete Time," Mathematics, MDPI, vol. 12(8), pages 1-24, April.
    6. Yadav, Pramod Kumar & Goel, Palak, 2023. "Treatment seeking dilemma for tuberculosis as timed strategic prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).

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