Impact of human mobility on the transmission dynamics of infectious diseases

Energ. Ecol. Environ. https://doi.org/10.1007/s40974-020-00164-4 ORIGINAL ARTICLE Impact of human mobility on the transmission dynamics of infectious diseases Anupam Khatua1 • Tapan Kumar Kar1 • Swapan Kumar Nandi2 • Soovoojeet Jana3 • Yun Kang4 1 Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal 711103, India Department of Mathematics, Nayabasat P. M. Sikshaniketan, Paschim Medinipur, West Bengal 721253, India 3 Department of Mathematics, Ramsaday College, Amta, Howrah, West Bengal 711401, India 4 Science and Mathematics Faculty, College of Integrative Sciences and Arts, Arizona State University, Mesa, AZ 85212, USA 2 Received: 25 December 2019 / Revised: 27 March 2020 / Accepted: 17 April 2020 Ó The Joint Center on Global Change and Earth System Science of the University of Maryland and Beijing Normal University 2020 Abstract Spatial heterogeneity is an important aspect to be studied in infectious disease models. It takes two forms: one is local, namely diffusion in space, and other is related to travel. With the advancement of transportation system, it is possible for diseases to move from one place to an entirely separate place very quickly. In a developing country like India, the mass movement of large numbers of individuals creates the possibility of spread of common infectious diseases. This has led to the study of infectious disease model to describe the infection during transport. An SIRS-type epidemic model is formulated to illustrate the dynamics of such infectious disease propagation between two cities due to population dispersal. The most important threshold parameter, namely the basic reproduction number, is derived, and the possibility of existence of backward bifurcation is examined, as the existence of backward bifurcation is very unsettling for disease control and it is vital to know from modeling analysis when it can occur. It is shown that dispersal of populations would make the disease control difficult in comparison with nondispersal case. Optimal vaccination and treatment controls are determined. Further to find the best cost-effective strategy, cost-effectiveness analysis is also performed. Though it is & Tapan Kumar Kar Anupam Khatua Swapan Kumar Nandi Soovoojeet Jana Yun Kang not a case study, simulation work suggests that the proposed model can also be used in studying the SARS epidemic in Hong Kong, 2003. Keywords SIRS epidemic model  Basic reproduction number  Nonlinear treatment function  Backward bifurcation  Cost-effectiveness analysis Mathematics Subject Classification 92D30  34K20  49J15 1 Introduction Mathematical modeling is considered as one of the most major and effective tools to predict the transmission mechanism of various infectious diseases. The use of mathematical models to describe the dynamics of such diseases was started a long time ago. Kermack and McKendrick (1933) were the first to introduce the mathematical model to analyze the characteristics of epidemic problems. However, this dynamical system approach for epidemiological problems was not so popular until the early 1990s. Some major and recent developments can be found in Diekmann and Heesterbeek (1999), Keeling and Rohani (2008), Makinde (2007), Smith (2008), Thomasey and Martcheva (2008), Okosun et al. (2011), Kar and Mondal (2011), Kar and Jana (2013a, b), Jana et al. (2016a, b). In the last couple of decades, there is a rapid advancement of transportation system throughout the globe. People now move from one place to another very quickly, and this quick movement of human is an important driver to spread the emerging and re-emerging infectious diseases. For 123 A. Khatua et al. instance, in 2003, SARS epidemic occurred in a wide region of Asia including China due to population dispersal. The H1N1 (swine flu) pandemic in 2009 is now considered to have been the fastest moving pandemic in world history (Lipsitch et al. 2009). Recently, Ebola virus also threatened to become epidemic in vast region of Africa mainly due to the incautious movement of human population. Also, in recent past time, we have witnessed the severe outbreak of many emerging infectious diseases including MERS-CoV, SARS-CoV, Zika, and the very latest addition is novel coronavirus (COVID-19). For these types of diseases, human mobility can influence the disease dynamics mainly in two ways: Movements may cast new pathogens into the susceptible group, or it may enhance the contact rate between the susceptible and infected people. The severe acute respiratory syndrome (SARS) originated in China in 2002 and spread to 29 countries; MERS-CoV originated in Saudi Arabia in 2012 and later, has been identified in 27 countries; and Ebola virus disease began in Sierra Leone in 2014 and spread to several countries via international travel. Presently, novel COVID-19 originated in China and has spread very quickly throughout the globe. Therefore, spatial heterogeneity related to travel is a very important aspect to be considered in infectious disease modeling approach. Some mathematical models on transmission dynamics of infectious diseases due to population dispersal are available in Wang and Mulone (2003), Arino and Van den Driessche (2003), Wang and Zhao (2004), while Wang and Zhao (2005) proposed an age-structured epidemic model and established the conditions of uniform persistence and global extinction of the disease. In the context of developing countries, Cui et al. (2006) proposed a transport-related SIS-type disease model. Later, Wan and Cui (2007) extended this model as an SEIS-type disease model to describe the infection during transportation. However, Meloni et al. (2011) proposed and analyzed a metapopulation model incorporating the mobility of humans. Findlater and Bogoch (2018) studied the effects of human movement, specially via air on the spread of infectious disease. Some other perspective of human movement on the disease dynamics can be found in Wesolowski et al. (2016), Sallah et al. (2017), Kraemer et al. (2019) and the references cited therein. Thus, in recent times, some advancement has been made in developing models with global transportation flows. However, still only a few theoretical and computational approaches have studied the effect of human mobility in the large-scale spreading of the epidemics. But the social and spatial widespread of several infectious diseases demands the re-evaluation and improvement of mathematical models that we use to understand the public health problems throughout the world. 123 The most important aspect of mathematical epidemiology is to find out the best possible way to control such diseases. From the past epidemic outbreaks for the diseases including pox, cholera, malaria, etc., it can be observed that quarantine and isolation of infected individuals is a very useful control to reduce the level of infection from community (Kar et al. 2013; Jana et al. 2017). In contempo (...truncated)