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Modeling the transmission dynamics of malaria with saturated treatment: a case study of India

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Abstract

Malaria is a life-threatening mosquito-borne disease. It is transmitted through the bite of an infected Anopheles mosquito. Malaria may be fatal if not treated promptly. Malaria is a major public health problem in India. Here we propose an SIRS model to study the transmission dynamics of malaria with saturated treatment. We assume that the mosquito population is growing logistically in the environment. Here we include a saturated type treatment function which is more suitable for the regions with limited resources. We discuss the existence and stability of different equilibria of the proposed model. We also compute the basic reproduction number \(R_0\) which plays an important role in existence and stability of equilibria of the model. For \(R_0 < 1\), backward bifurcation occurs, which suggests that lowering \(R_0\) below one is not enough to eliminate the disease from the population. We estimate the key parameter corresponding to transmission of malaria using real data from different states of India by least square method. We also perform sensitivity analysis using PRCC to identify the key parameters which influence the infection prevalence of the disease and the basic reproduction number. Numerical simulations are presented to illustrate the analytic findings. Our numerical results suggest that infected population should get proper treatment and increase in the death rate of mosquito can also help to eradicate the malaria disease from the population.

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Acknowledgements

The authors thank the handling editor and anonymous referees for their valuable comments and suggestions that led to an improvement of our original manuscript. This research was supported by the research grants of DST, Govt. of India, via a sponsored research project: FILE NO. EMR/2017/003139.

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  1. Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, India

    Akhil Kumar Srivastav & Mini Ghosh

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  1. Akhil Kumar Srivastav
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Correspondence to Mini Ghosh.

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Srivastav, A.K., Ghosh, M. Modeling the transmission dynamics of malaria with saturated treatment: a case study of India. J. Appl. Math. Comput. 67, 519–540 (2021). https://doi.org/10.1007/s12190-020-01469-7

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  • DOI: https://doi.org/10.1007/s12190-020-01469-7

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