International Journal of Scientific & Technology Research

Home About Us Scope Editorial Board Blog/Latest News Contact Us
10th percentile
Powered by  Scopus
Scopus coverage:
Nov 2018 to May 2020


IJSTR >> Volume 8 - Issue 7, July 2019 Edition

International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616

Impact Of Treatment On Droplet Infection: Age Structured Mathematical Model

[Full Text]



Chanda Purushwani, Poonam Sinha



Droplet infection; SITR Model; Basic Reproduction Number; Stability analysis; Sensitivity Analysis; Optimal controls



Droplet infection is a widespread disease of all age groups. Consciousness about prevention and treatment can reduce the risk of infection. Infected population of any age group can avail a common treatment. In this paper, we have proposed age structured SITR model along with droplet infection. To analyse the model, we have evaluated disease free equilibrium point, endemic equilibrium point and basis reproduction number (R0).It is found that disease free equilibrium point always exists and model is stable around it when R0 <1. Similarly endemic equilibrium point exists and model is stable around it when R0 >1. Sensitivity analysis for basic reproduction number is performed to see the influence of parameters on disease spread. Optimal controls are measured to minimize infected population and produced droplets, using Pontryagin's minimum Principle. Numerical simulation is done to observe the dynamic behaviour of all population in model. Suitable graphs are illustrated to support the results.



[1] https://medicaldictionary.thefreedictionary.com/droplet+infection.
[2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3311988/.
[3] https://www.accesscontinuingeducation.com/ACE1000-10/c2/index.htm.
[4] G. P. Samanta, P. Sen and A. Maiti,” A delayed epidemic model of diseases through droplet infection and direct contact with saturation incidence and pulse vaccination,”Systems Science & Control Engineering, 4(1), (2016), 320-333.
[5] O. P. Misra and D. K. Mishra,” Modelling the effect of booster vaccination on the transmission dynamics of diseases that spread by droplet infection,”Nonlinear Analysis: Hybrid Systems, 3(4), (2009), 657–665.
[6] P. Pongsumpun, and I. M. Tang,” Transmission of dengue hemorrhagic fever in an age structured population,”Mathematical and Computer Modelling, 37(9-10), (2003), 949–961.
[7] E. Beretta, V. Capasso and D. G. Garao,”A mathematical model for malaria transmission with asymptomatic carriers and two age groups in the human population,” Mathematical Biosciences, 300, (2018), 87–101.
[8] T. Kajiwara, T. Sasaki and Y. Otani,” Global stability of an age-structured modelfor pathogen–immune interaction,”Journal of Applied Mathematics and Computing, (2018).
[9] P. Rani, D. Jain and V. P. Saxena,”Stability Analysis of HIV/AIDS Transmission with Treatment and Role of Female Sex Workers.,”IJNSNS, DE GRUYTER. (2017).
[10] J. M. Hefferman, R. J. Smith and L. M. Wahi,”Perspective on the basic reproductive ratio,” J. R. Soc. Interface, 2, (2005), 281-293.
[11] K. Park,”Preventive and social Medicine,” (2002), M/S BanarsiDas Bhanot publishers. Jabalpur, India.
[12] K. Park, “Essentials of Community Health Nursing,” (2004), M/S BanarsiDas Bhanot publishers Jabalpur, India.
[13] P. D. Driessche,” Reproduction numbers of infectious disease models,” Infectious Disease Modelling, 2(3), (2017), 288-303.
[14] P. Rani, D. Jain, V. P. Saxena and D. S. Hooda, “Age-structured mathematical model for HIV/AIDS in a two-dimensional heterogeneous population,”Communications Math. Biol. Neurosci, (2015), 1–20.
[15] Marsudi and A. Andari, “Sensitivity analysis of effect of screening and HIV therapy on the dynamics of spread of HIV,” Appl. Math. Sci, 8, (2014), 7749–7763.