A Mathematical Study on Coronavirus Model with Two Infectious States


  • V.S.V. Naga Soundarya Lakshmi Department of Mathematics, Auxilium College, Vellore 632 006, Tamilnadu
  • A. Sabarmathi Department of Mathematics, Auxilium College, Vellore 632 006, Tamilnadu




COVID-19, Stability, SIR model, Basic reproduction number, Siddha, Allopathy


A SIR model is formulated for COVID-19 with initial and secondary states. Existence and uniqueness of solutions, stability of the model and basic reproduction number were derived. In this article, the vulnerability of COVID-19 in Tirupathur district, Tamilnadu, India is discussed to exhibit the flow of variables of the model using numerical simulations. Also, analysis of recovered is explored for Siddha and allopathy treatments.


Download data is not yet available.


C. J. Burrell and F. A. Murphy, Coronaviruses, Fenner and White's Medical Virology, 5th edition, Springer (2017).

T.-M. Chen, J. Rui, Q.-P. Wang, Z.-Y. Zhao, J.-A. Cui and L. Yin, A mathematical model for simulating the phase-based transmissibility of a novel coronavirus, Infectious Diseases of Poverty 9 (2020), Article number: 24, DOI: 10.1186/s40249-020-00640-3.

O. Diekmann, J. A. P. Heesterbeek and M. G. Roberts, The construction of next-generation matrices for compartmental epidemic models, Journal of the Royal Society Interface 7 (2010), 873 – 885, DOI: 10.1098/rsif.2009.0386.

A. Dighe, T. Jombart, M. Van Kerkhove and N. Ferguson, A mathematical model of the transmission of middle East respiratory syndrome coronavirus in dromedary camels (Camelus dromedaries), International Journal of Infectious Diseases 79(1) (2019), 1 – 150, DOI: 10.1016/j.ijid.2018.11.023.

B. Ivorra, M. R. Ferrández, M. Vela-Pérez and A. M. Ramos, Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections, the case of China, Communications in Nonlinear Science and Numerical Simulation 88 (2020), ID 105303, DOI: 10.1016/j.cnsns.2020.105303.

S. H. A. Khoshnaw, R. H. Salih and S. Sulaimany, Mathematical modelling for Coronavirus disease (Covid-19) in predicting future behaviours and sensitivity analysis, Mathematical Modelling of Natural Phenomena 15 (2020), DOI: 10.1051/mmnp/2020020.

Y. Li, B. Wang, R. Peng, C. Zhou, Y. Zhan, Z. Liu, X. Jiang and B. Zhao, Mathematical modeling and epidemic prediction of COVID-19 and its significance to epidemic prevention and control measures, Annals of Infectious Disease and Epidemiology 5(1) (2020), https://www.remedypublications.com/annals-of-infectious-disease-and-epidemiology-abstract.php?aid=5755.

K. Maity, Introduction to Differential Equations, Nasora Publishing House, New Delhi (2017).

F. K. Mbabazi, J. Y. T. Mugisha and M. Kimathi, Hopf-bifurcation analysis of pneumococcal pneumonia with time delays, Abstract and Applied Analysis 2019 (2019), Article ID 3757036, DOI: 10.1155/2019/3757036.

A. V. Okhuese, Estimation of the probability of reinfection with COVID-19 by the susceptibleexposed-infectious-removed-undetectable-susceptible model, JMIR Public Health and Surveillance 6(2) (2020), e19097, DOI: 10.2196/19097.

D. Otoo, P. Opoku, S. Charles and A. P. Kingsley, Deterministic epidemic model for (SVCSYCASY IR) Pneumonia dynamics with vaccination and temporal immunity, Infectious Disease Modelling 5 (2020), 42 – 60, DOI: 10.1016/j.idm.2019.11.001.

C. Yang and J. Wang, A mathematical model for the novel Coronavirus epidemic in Wuhan, China, Mathematical Biosciences and Engineering 17 (3) (2020), 2708 – 2724, DOI: 10.3934/mbe.2020148.

A. Zeb, E. Alzahrani, V. S. Erturk and G. Zaman, Mathematical model for Coronavirus Disease 2019 (COVID-19) containing isolation class, BioMed Research International, 2020 (2020), Article ID 3452402, DOI: 10.1155/2020/3452402.

O. C. Zephaniah, U.-I. R. Nwaugonma, I. S. Chioma and O. Adrew, A mathematical model and analysis of an SVEIR model for streptococcus pneumonia with saturated incidence force of infection, Mathematical Modelling and Applications 5(1) (2020), 16 – 38, DOI: 10.11648/j.mma.20200501.13.




How to Cite

Lakshmi, V. N. S., & Sabarmathi, A. (2021). A Mathematical Study on Coronavirus Model with Two Infectious States. Journal of Informatics and Mathematical Sciences, 13(2), 71–81. https://doi.org/10.26713/jims.v13i2.1555



Research Articles