A model of hepatitis B virus with random interference infection rate

Dong-Me Li; Bing Chai; Qi Wang; Dong-Me Li; Bing Chai; Qi Wang

doi:10.3934/mbe.2021410

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 6: 8257-8297. doi: 10.3934/mbe.2021410

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A model of hepatitis B virus with random interference infection rate

1.
College of Science, Harbin University of Science and Technology, Harbin 150080, China
2.
Heilongjiang Hospital, Harbin 150036, China

Received: 25 June 2021 Accepted: 16 September 2021 Published: 22 September 2021

According to the mechanism of drug inhibition of hepatitis B virus and the analysis of clinical data, it is found that random factors in long-term treatment produced uncertainty and resistance to hepatitis B virus infection rate, a model of hepatitis B virus with random interference infection rate is established. By constructing Lyapunov function and using Ito's formula, it is proved that the stochastic hepatitis B model has a unique global positive solution. The sufficient conditions for the asymptotic behavior of solution are given. The relationship between noise intensity and oscillation amplitude is obtained. The effects of noise intensity on the asymptotic behavior of the model and antiviral therapy are simulated, and the conclusion of the theorem is verified. An interesting phenomenon is also found that with the increase of noise intensity, the number of drug-resistant viruses will decrease, which will affect the accuracy of a single test of HBV DNA. Therefore, it is suggested to increase the frequency and interval of tests.
- drug resistance,
- stochastic virus dynamics model,
- asymptotic behavior,
- the numerical simulation
Citation: Dong-Me Li, Bing Chai, Qi Wang. A model of hepatitis B virus with random interference infection rate[J]. Mathematical Biosciences and Engineering, 2021, 18(6): 8257-8297. doi: 10.3934/mbe.2021410

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Abstract

According to the mechanism of drug inhibition of hepatitis B virus and the analysis of clinical data, it is found that random factors in long-term treatment produced uncertainty and resistance to hepatitis B virus infection rate, a model of hepatitis B virus with random interference infection rate is established. By constructing Lyapunov function and using Ito's formula, it is proved that the stochastic hepatitis B model has a unique global positive solution. The sufficient conditions for the asymptotic behavior of solution are given. The relationship between noise intensity and oscillation amplitude is obtained. The effects of noise intensity on the asymptotic behavior of the model and antiviral therapy are simulated, and the conclusion of the theorem is verified. An interesting phenomenon is also found that with the increase of noise intensity, the number of drug-resistant viruses will decrease, which will affect the accuracy of a single test of HBV DNA. Therefore, it is suggested to increase the frequency and interval of tests.

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