Deciphering role of inter and intracity human dispersal on epidemic spread via coupled reaction-diffusion models

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Deciphering role of inter and intracity human dispersal on epidemic spread via coupled reaction-diffusion models M. A. Aziz-Alaoui1 · Parimita Roy1,2 Received: 29 June 2020 / Revised: 14 October 2020 / Accepted: 21 October 2020 © Korean Society for Informatics and Computational Applied Mathematics 2020

Abstract Human mobility has been significantly influencing public health since time immemorial. A susceptible-infected-deceased epidemic reaction diffusion network model using asymptotic transmission rate is proposed to portray the spatial spread of the epidemic among two cities due to population dispersion. Qualitative behaviour including global attractor and persistence property are obtained. We also study asymptotic behaviour of the whole network with the help of asymptotic behaviour at individual cities. The epidemic model shows up two equilibria, (i) the disease-free, and (ii) unique endemic equilibria. An expression that can be used to calculate the basic reproduction number for heterogeneous environment, for the entire network is obtained. We use graph theory to analyze the global stability of our diffusive two-city model. We also performed bifurcation analysis and discovered that endemic equilibrium changes stability via Hopf bifurcations. A significant reduction in the number of infectives were observed when proper migration rate is maintained between the cities. Numerical results are provided to illuminate and clarify theoretical findings. Simulation experiments for two-dimensional spatial models show that infectious populations will increase if contact heterogeneity is increased, but it will decline if infective populations perform more local random movement. We observe that infection risk may be understated if the parameters used to estimate the basic reproduction number remains unchanged through space or time. Keywords Reaction-diffusion · Heterogeneity · Global stability · Reproduction number · Pattern formation Mathematics Subject Classification 92B05 · 35B36 · 35B40

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Parimita Roy [email protected] M. A. Aziz-Alaoui [email protected]

1

Normandy Univ, UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, 76600 Le Havre, France

2

School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, Punjab, India

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M. A. Aziz-Alaoui, P. Roy

1 Introduction A record of past events in human mankind shows that infectious disease has a profound effect on human populations, including their development and evolution. Individual’s health status is affected by many factors, such as the quantity of time spent in a specific place, availability and access to affordable health care, complex economic and social factors, educational attainments, and lifestyles. Despite significant advances in medical sciences, infectious disease affects both the human and animal population in many parts of the world. As we know, performing experiments on the population is forbidden one can use mathematical model to investigate the transmission, predict the outbreak and even control of epidemics [2]. At present, mat