TY - JOUR
T1 - Global well-posedness of infectious disease models without life-time immunity
T2 - The cases of cholera and avian influenza
AU - Yamazaki, K.
N1 - Publisher Copyright:
© The authors 2017. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
PY - 2018/12/5
Y1 - 2018/12/5
N2 - We study the systems of partial differential equations with diffusion that model the dynamics of infectious diseases without life-time immunity, in particular the cases of cholera from Wang &Wang (2015, J. Biol. Dyn., 9, 233 "261) and avian influenza from Vaidya et al. (2012, Discrete Contin. Dyn. Syst. Ser. B, 17, 2829 "2848). In both works, similarly to all others in the literature on various models of infectious diseases and more, it had to be assumed for a technical reason that the diffusivity coefficients of the susceptible, infected and recovered individuals, humans or birds, had to be identical in order to prove the existence of their unique solutions for all time. Considering that such uniform diffusivity strengths among the susceptible, infected and recovered hosts may not always be plausible in real world, we investigate the global well-posedness issue when such conditions are relaxed. In particular for the cholera model from Wang &Wang (2015, J. Biol. Dyn., 9, 233 "261), we prove the global well-posedness with no condition on the diffusivity coefficients at all. For the avian influenza model from Vaidya et al. (2012, Discrete Contin. Dyn. Syst. Ser. B, 17, 2829 "2848), we prove the global well-posedness with no condition on the diffusivity coefficients if the spatial dimension is one, and under a partial condition that the diffusivity coefficients of the susceptible and the infected hosts are same otherwise.
AB - We study the systems of partial differential equations with diffusion that model the dynamics of infectious diseases without life-time immunity, in particular the cases of cholera from Wang &Wang (2015, J. Biol. Dyn., 9, 233 "261) and avian influenza from Vaidya et al. (2012, Discrete Contin. Dyn. Syst. Ser. B, 17, 2829 "2848). In both works, similarly to all others in the literature on various models of infectious diseases and more, it had to be assumed for a technical reason that the diffusivity coefficients of the susceptible, infected and recovered individuals, humans or birds, had to be identical in order to prove the existence of their unique solutions for all time. Considering that such uniform diffusivity strengths among the susceptible, infected and recovered hosts may not always be plausible in real world, we investigate the global well-posedness issue when such conditions are relaxed. In particular for the cholera model from Wang &Wang (2015, J. Biol. Dyn., 9, 233 "261), we prove the global well-posedness with no condition on the diffusivity coefficients at all. For the avian influenza model from Vaidya et al. (2012, Discrete Contin. Dyn. Syst. Ser. B, 17, 2829 "2848), we prove the global well-posedness with no condition on the diffusivity coefficients if the spatial dimension is one, and under a partial condition that the diffusivity coefficients of the susceptible and the infected hosts are same otherwise.
KW - avian influenza
KW - cholera
KW - diffusion
KW - global existence
KW - infectious diseases
UR - http://www.scopus.com/inward/record.url?scp=85059286686&partnerID=8YFLogxK
U2 - 10.1093/imammb/dqx016
DO - 10.1093/imammb/dqx016
M3 - Article
C2 - 29088361
AN - SCOPUS:85059286686
SN - 1477-8599
VL - 35
SP - 427
EP - 445
JO - Mathematical Medicine and Biology
JF - Mathematical Medicine and Biology
IS - 4
ER -