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Mathematical analysis of multi-compartmental malaria transmission model with reinfection

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  • Rehman, Attiq ul
  • Singh, Ram
  • Singh, Jagdev

Abstract

In this investigation, a mathematical compartmental model of the malaria disease transmission dynamical process with an associated learning mechanism between vector-to-host and vice-versa with memory, relapse, and reinfection conditions is proposed and analysed. Stability analysis of the disease-free equilibrium (DFE) concerning the fractional-order derivative α and the reproductive number R0 is evaluated. We find the α that depends on R0, for which we have two cases: i if R0<1, then DFE is always locally asymptotically stable (LAS), ii if R0>1, then DFE is always unstable. The model is solved numerically by using the Corrector-Predictor numerical method. The numerical simulation is performed to verify the analytic results.

Suggested Citation

  • Rehman, Attiq ul & Singh, Ram & Singh, Jagdev, 2022. "Mathematical analysis of multi-compartmental malaria transmission model with reinfection," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    • Handle: RePEc:eee:chsofr:v:163:y:2022:i:c:s0960077922007263
    DOI: 10.1016/j.chaos.2022.112527
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    References listed on IDEAS

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    1. Rachel Waema Mbogo & Livingstone S. Luboobi & John W. Odhiambo, 2018. "A Stochastic Model for Malaria Transmission Dynamics," Journal of Applied Mathematics, Hindawi, vol. 2018, pages 1-13, February.
    2. Agarwal, Praveen & Singh, Ram & Rehman, Attiq ul, 2021. "Numerical solution of hybrid mathematical model of dengue transmission with relapse and memory via Adam–Bashforth–Moulton predictor-corrector scheme," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    3. Atangana, Abdon & İğret Araz, Seda, 2021. "New concept in calculus: Piecewise differential and integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    4. Agarwal, Praveen & Singh, Ram, 2020. "Modelling of transmission dynamics of Nipah virus (Niv): A fractional order Approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    5. Hai-Feng Huo & Guang-Ming Qiu, 2014. "Stability of a Mathematical Model of Malaria Transmission with Relapse," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, February.
    6. Lahrouz, A. & El Mahjour, H. & Settati, A. & Bernoussi, A., 2018. "Dynamics and optimal control of a non-linear epidemic model with relapse and cure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 299-317.
    7. Rehman, Attiq ul & Singh, Ram & Agarwal, Praveen, 2021. "Modeling, analysis and prediction of new variants of covid-19 and dengue co-infection on complex network," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
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