### Journals Information

Mathematics and Statistics Vol. 7(1), pp. 14 - 24
DOI: 10.13189/ms.2019.070103
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## Integro-Differential Age-Structured System for Influenza Transmission Dynamics

Ana Vivas-Barber 1, Sunmi Lee 2,*
1 Mathematics Department, Norfolk State University, Norfolk, VA, USA
2 Department of Applied Mathematics, Kyung Hee University, Yongin-si, 446-701, Republic of Korea

ABSTRACT

Influenza infection shows a wide range of severity and it is well known that a significant proportion of individuals is asymptomatic or experience mild infections. Also, It is widely accepted that influenza transmission dynamics depends on age distributions. An integro-partial differential system is considered for influenza transmission dynamics, which includes the standard Susceptible-Infected-Recovered (SIR) classes with a quarantine (Q) class and an asymptomatic class (A). In this work, we extend the previous model to an integro-partial differential model by including age-structure. We establish the existence of an endemic steady state distribution and its explicit expression. Then, an analytic expression for the basic reproduction number is obtained. Furthermore, we prove the local and global stability of the disease-free equilibrium. Some numerical simulations of the basic reproduction number have been carried out using age-dependent influenza parameter values. This study can provide effective interventions and implementing age-dependent countermeasures.

KEYWORDS
Influenza Dynamics with Age-structure, Basic Reproductive Number, Steady-state Solution, Stability Analyses

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Ana Vivas-Barber , Sunmi Lee , "Integro-Differential Age-Structured System for Influenza Transmission Dynamics," Mathematics and Statistics, Vol. 7, No. 1, pp. 14 - 24, 2019. DOI: 10.13189/ms.2019.070103.

(b). APA Format:
Ana Vivas-Barber , Sunmi Lee (2019). Integro-Differential Age-Structured System for Influenza Transmission Dynamics. Mathematics and Statistics, 7(1), 14 - 24. DOI: 10.13189/ms.2019.070103.