### Abstract

Coinfection of hosts with multiple strains or serotypes of the same agent, such as different influenza virus strains, different human papilloma virus strains, and different dengue virus serotypes, is not only a very serious public health issue but also a very challenging mathematical modeling problem. In this paper, we study a time-periodic two-strain SIS epidemic model with diffusion and latent period. We first define the basic reproduction number R_{0} ^{i} and introduce the invasion number Rˆ_{0} ^{i} for each strain i(i=1,2), which can determine the ability of each strain to invade the other single-strain. The main question that we investigate is the threshold dynamics of the model. It is shown that if R_{0} ^{i}⩽1(i=1,2), then the disease-free periodic solution is globally attractive; if R_{0} ^{i}>1⩾R_{0} ^{j}(i≠j,i,j=1,2), then competitive exclusion, where the jth strain dies out and the ith strain persists, is a possible outcome; and if Rˆ_{0} ^{i}>1(i=1,2), then the disease persists uniformly. Finally we present the basic framework of threshold dynamics of the system by using numerical simulations, some of which are different from that of the corresponding multi-strain SIS ODE models.

Original language | English (US) |
---|---|

Article number | 102966 |

Journal | Nonlinear Analysis: Real World Applications |

Volume | 51 |

DOIs | |

State | Published - Feb 1 2020 |

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### Keywords

- Basic reproduction number
- Competitive exclusion
- SIS epidemic model
- Threshold dynamics
- Time periodicity
- Two strains

### ASJC Scopus subject areas

- Analysis
- Engineering(all)
- Economics, Econometrics and Finance(all)
- Computational Mathematics
- Applied Mathematics

### Cite this

*Nonlinear Analysis: Real World Applications*,

*51*, [102966]. https://doi.org/10.1016/j.nonrwa.2019.102966

**Dynamics of a time-periodic two-strain SIS epidemic model with diffusion and latent period.** / Zhao, Lin; Wang, Zhi Cheng; Ruan, Shigui.

Research output: Contribution to journal › Article

*Nonlinear Analysis: Real World Applications*, vol. 51, 102966. https://doi.org/10.1016/j.nonrwa.2019.102966

}

TY - JOUR

T1 - Dynamics of a time-periodic two-strain SIS epidemic model with diffusion and latent period

AU - Zhao, Lin

AU - Wang, Zhi Cheng

AU - Ruan, Shigui

PY - 2020/2/1

Y1 - 2020/2/1

N2 - Coinfection of hosts with multiple strains or serotypes of the same agent, such as different influenza virus strains, different human papilloma virus strains, and different dengue virus serotypes, is not only a very serious public health issue but also a very challenging mathematical modeling problem. In this paper, we study a time-periodic two-strain SIS epidemic model with diffusion and latent period. We first define the basic reproduction number R0 i and introduce the invasion number Rˆ0 i for each strain i(i=1,2), which can determine the ability of each strain to invade the other single-strain. The main question that we investigate is the threshold dynamics of the model. It is shown that if R0 i⩽1(i=1,2), then the disease-free periodic solution is globally attractive; if R0 i>1⩾R0 j(i≠j,i,j=1,2), then competitive exclusion, where the jth strain dies out and the ith strain persists, is a possible outcome; and if Rˆ0 i>1(i=1,2), then the disease persists uniformly. Finally we present the basic framework of threshold dynamics of the system by using numerical simulations, some of which are different from that of the corresponding multi-strain SIS ODE models.

AB - Coinfection of hosts with multiple strains or serotypes of the same agent, such as different influenza virus strains, different human papilloma virus strains, and different dengue virus serotypes, is not only a very serious public health issue but also a very challenging mathematical modeling problem. In this paper, we study a time-periodic two-strain SIS epidemic model with diffusion and latent period. We first define the basic reproduction number R0 i and introduce the invasion number Rˆ0 i for each strain i(i=1,2), which can determine the ability of each strain to invade the other single-strain. The main question that we investigate is the threshold dynamics of the model. It is shown that if R0 i⩽1(i=1,2), then the disease-free periodic solution is globally attractive; if R0 i>1⩾R0 j(i≠j,i,j=1,2), then competitive exclusion, where the jth strain dies out and the ith strain persists, is a possible outcome; and if Rˆ0 i>1(i=1,2), then the disease persists uniformly. Finally we present the basic framework of threshold dynamics of the system by using numerical simulations, some of which are different from that of the corresponding multi-strain SIS ODE models.

KW - Basic reproduction number

KW - Competitive exclusion

KW - SIS epidemic model

KW - Threshold dynamics

KW - Time periodicity

KW - Two strains

UR - http://www.scopus.com/inward/record.url?scp=85068869203&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85068869203&partnerID=8YFLogxK

U2 - 10.1016/j.nonrwa.2019.102966

DO - 10.1016/j.nonrwa.2019.102966

M3 - Article

VL - 51

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

SN - 1468-1218

M1 - 102966

ER -