### Mathematical Biosciences and Engineering

2022, Issue 11: 11047-11070. doi: 10.3934/mbe.2022515
Research article

# Global stability of an age-structured infection model in vivo with two compartments and two routes

• Received: 11 January 2022 Revised: 21 June 2022 Accepted: 23 June 2022 Published: 02 August 2022
• In this paper, for an infection age model with two routes, virus-to-cell and cell-to-cell, and with two compartments, we show that the basic reproduction ratio $R_0$ gives the threshold of the stability. If $R_0 > 1$, the interior equilibrium is unique and globally stable, and if $R_0 \le 1$, the disease free equilibrium is globally stable. Some stability results are obtained in previous research, but, for example, a complete proof of the global stability of the disease equilibrium was not shown. We give the proof for all the cases, and show that we can use a type reproduction number for this model.

Citation: Tsuyoshi Kajiwara, Toru Sasaki, Yoji Otani. Global stability of an age-structured infection model in vivo with two compartments and two routes[J]. Mathematical Biosciences and Engineering, 2022, 19(11): 11047-11070. doi: 10.3934/mbe.2022515

### Related Papers:

• In this paper, for an infection age model with two routes, virus-to-cell and cell-to-cell, and with two compartments, we show that the basic reproduction ratio $R_0$ gives the threshold of the stability. If $R_0 > 1$, the interior equilibrium is unique and globally stable, and if $R_0 \le 1$, the disease free equilibrium is globally stable. Some stability results are obtained in previous research, but, for example, a complete proof of the global stability of the disease equilibrium was not shown. We give the proof for all the cases, and show that we can use a type reproduction number for this model.

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