IJPAM: Volume 115, No. 4 (2017)

Title

ASSESSING THE POTENTIAL OF MEDICAL-MASK
AND DRUG-TREATMENT IN CONTROLLING
INFLUENZA DISEASE

Authors

M. Rohmah$^1$, B.D. Handari$^2$, D. Aldila$^3$
$^{1,2,3}$Department of Mathematics
Universitas Indonesia
Kampus UI Depok
Depok 16424, INDONESIA

Abstract

A classical SIS model for influenza disease with two intervention strategies such as medical mask and drug treatment from deterministic framework was extended in this paper into a stochastic differential equation (SDE). The SDE model was constructed by introducing a random perturbation in successful contact rate parameter. The concern of this study is focused in to two aspects based on from mathematical and epidemiological point of view. From mathematical point of view, the basic reproduction number from deterministic framework (known as $R_0$) was analyzed and compared with the stochastic threshold parameter (we call it as $\rho_0$). As well as $R_0$ in deterministic model, the $\rho_0$ also linked into the extinction and persistence condition of endemic equilibrium. If $\rho_0<1$, then the SDE system will reach the extinction of influenza disease with probability one. Otherwise, if $\rho_0>1$ then influenza disease will persist. However, we found a situation where $\rho_0$ gives a contrast result compared to $R_0$ as a consequence of random perturbation in successful contact rate parameter. From epidemiological point of view, we found that medical mask and drug treatment intervention and successful contact rate influence the dynamic of influenza spread in our model, which can give us a direction about the best strategy to regulate influenza spreads. Some numerical simulations were generated to support the analytical results.

History

Received: January 14, 2017
Revised: April 26, 2017
Published: August 10, 2017

AMS Classification, Key Words

AMS Subject Classification: 92B05
Key Words and Phrases: influenza, deterministic, stochastic differential equations, medical mask, drug treatment, basic reproductive ratio, stochastic threshold parameter

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How to Cite?

DOI: 10.12732/ijpam.v115i4.7 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 115
Issue: 4
Pages: 731 - 746


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