# MATHEMATICAL MODELLING OF PRIMARY INFECTION TUBERCULOSIS WITH ASTHMA AS A SECOND INFECTION

• Tri Sri Noor Asih Department of Mathematics, Semarang State University, Indonesia
• Nurul Fadhilah Department of Mathematics, Semarang State University, Indonesia
Keywords: Tuberculosis, Asthma, Second Infection, Mathematical Modeling

### Abstract

Tuberculosis is an infectious disease caused by Mycobacterium Tuberculosis. Tuberculosis patients undergoing long-term tuberculosis treatment have a high risk to get asthma as a second infection. A person suffering from asthma cannot recover. Asthma therapy is only to control the development of asthma so that asthma does not get worse. In this study we discusses the spread of tuberculosis with asthma as a secondary infection. We perform the model into system of non- linear differential equation that consist of  six equation because the population divided into six sub-population which are susceptible, infected by tuberculosis, undergoing tuberculosis treatment, infected by asthma, undergoing asthma treatment and recovered from tuberculosis. From the model that has been formed, we perform the analysis to obtain the equilibrium point and the basic reproduction number. Then we show the local stability of the equilibrium point and perform simulations to provide an illustration. From the analytical result, we got that the spread influence by recruitment rate, infection rate, natural death rate, tuberculosis treatment rate and death rate because of tuberculosis.

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Published
2023-12-18
How to Cite
[1]
T. S. N. Asih and N. Fadhilah, “MATHEMATICAL MODELLING OF PRIMARY INFECTION TUBERCULOSIS WITH ASTHMA AS A SECOND INFECTION”, BAREKENG: J. Math. & App., vol. 17, no. 4, pp. 1855-1864, Dec. 2023.
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Articles