Dynamics and optimal control of a spatial diffusion HIV/AIDS model with ART and PrEP treatments

In this paper, to investigate the synthetic effect of PrEP (pre-exposure prophylaxis) and ART (antiretrovial therapy) on HIV transmission among MSM (men who have sex with men) in heterogenous environment, an realistic HIV epidemic model with spatial diffusion is established. Here, HIV infectious people are divided into three immunity based compartments, i.e., CD4+ T cell count less than 350, between 350 and 500, and more than 500, respectively. The basic reproduction number $R_0$ is established and proved as a threshold parameter: The global asymptotic stability of the disease-free steady state holds for $R_0<1$, and the disease will be present if $R_0>1$. Considering the substantial advantages of PrEP and ART in controlling HIV transmissions among MSM, the optimal control problem is presented for the case of positive constant diffusion coefficients, which minimize the total population of susceptible individual and HIV infected individual, the cost of PrEP and ART thearpy. As an illustration of our theoretical results, we conduct numerical simulations. We also conduct an optimal control case study where model parameters are estimated from the demographic and epidemiological data from China. This work suggests: (1) Spatial factors cannot be ignored during the HIV intervention; (2)Taking the PrEP intervention measure for HIV transmissions among MSM as early as possible will help to improve the control efficiency and reduces its cost; (3) Reducing the PrEP drug costs will promote the efficiency of PrEP treatment in preventing the spread of HIV among MSM.

Dynamics of Mosquito Population Models with Spatial Diffusion

In this paper, we study some reaction-diffusion models of interactive dynamics of the wild and sterile mosquitoes. The well-posedness of the concerned model is proved. The stability of the steady states is discussed. Numerical simulations are presented to illustrate our theoretical results.

Impact of Governmental interventions on epidemic progression and workplace activity during the COVID-19 outbreak

In the first quarter of 2020, the COVID-19 pandemic brought the world to a state of paralysis. During this period, humanity saw by far the largest organized travel restrictions and unprecedented efforts and global coordination to contain the spread of the SARS-CoV-2 virus. Using large scale human mobility and fine grained epidemic incidence data, we develop a framework to understand and quantify the effectiveness of the interventions implemented by various countries to control epidemic growth. Our analysis reveals the importance of timing and implementation of strategic policy in controlling the epidemic. We also unearth significant spatial diffusion of the epidemic before and during the lockdown measures in several countries, casting doubt on the effectiveness or on the implementation quality of the proposed Governmental policies.

Spatial Diffusion of E-Commerce in China’s Counties: Based on the Perspective of Regional Inequality

In recent decades, China has been on a new journey toward a digital economy of which e-commerce accounts for a substantial proportion. Despite some controversy, the innovation diffusion hypothesis and efficiency hypothesis of online shopping have been tested in research on the urban–rural dual structure. However, research on the spatial diffusion model of online business is sparse. Based on the online business and online shopping index released by the Ali Research Institute, this article compares the spatial diffusion model of online shopping and online business in the core–periphery structure based on the inequality between the eastern and western regions of China. Our study suggests that online business trends are in line only with the innovation diffusion hypothesis, with marginal counties having lower levels of online business. Online shopping, on the other hand, is in line with the innovation diffusion hypothesis and partially with the efficiency hypothesis, with a higher index of online shopping in the core regions and some peripheral counties. The discrepancy in the spatial diffusion mode is due to the differences in aims and supporting elements between online business and online shopping. Apart from infrastructure, the diffusion of online business is largely constrained by the regional industrial base, while online shopping is influenced by income and savings levels, which is the main reason for the differences in the spatial diffusion of online business and online shopping. We argue that the diffusion of online business has not led to the ability to balance regional inequalities at the national scale, while online shopping has the potential to bridge core and peripheral disparities better than online businesses, not in terms of the ability to bridge economic disparities, but in terms of the potential to reduce spatial consumption inequalities and welfare gains.

Review of Experience in Recent Studies on the Dynamics of Land Urbanisation

Urbanisation rapidly accelerated in the 20th century. Along with the increasing dynamics of this phenomenon, the desire to know its origins and its course as well as to anticipate its effects is also growing. Investigations into the mechanisms governing urbanisation have become the subject of numerous studies and research projects. In addition, there has been a rapid increase in the number of tools and methods used to track and measure this phenomenon. However, new methods are still being sought to identify changes in space caused by urbanisation. Some of the indicators of urbanisation processes taking place include quantitative, qualitative and structural changes in land use, occurring at a certain time and place. These processes, related to human activity at a given time and in a given area, are determined by spatial diffusion, usually spreading from the city center towards the peripheral zones. Changes in land use involve the transition from less intensive to more intensive forms of land use. The constant effort to acquire new land for development, the search for alternative solutions for the location of investments and the need to determine the correct direction of development generates the need to constantly apply newer methods in the study of the dynamics of urbanisation processes. This paper presents an overview of recent studies and the most interesting—in the authors’ opinion—methods used in research into the dynamics of urbanisation processes. The main objective of the authors was to produce a compendium to guide the reader through the wide range of topics and to provide inspiration for their own research.

ANÁLISE DA COVID-19 NA MACRORREGIÃO DE SAÚDE NORTE DE MINAS, BRASIL: dinâmica espacial e redes urbanas

ANALYSIS OF COVID-19 IN THE NORTHERN MINAS HEALTH MACROREGION, BRAZIL: spatial dynamics and urban networksANÁLISIS DE COVID-19 EN LA MACROREGIÓN DE SALUD DEL NORTE DE MINAS, BRASIL: dinámica espacial y redes urbanasRESUMOEste texto analisa o processo de difusão espacial da COVID-19 na Macrorregião de Saúde Norte de Minas. Para isso, contextualiza-se a Rede Urbana de Minas Gerais, focalizando o setor de saúde e os deslocamentos referentes a esse serviço na Macro Norte. Apresenta um diagnóstico e mapeamento dos casos e óbitos de COVID-19 no período de Abril de 2020 a Março de 2021, ápice da crise epidemiológica no Brasil e também nessa região. Utilizou-se uma abordagem qualitativa, levantamento, organização e sistematização de dados de COVID-19 em Minas Gerais, além de produtos cartográficos analíticos e gráficos. No que tange às análises sobre a disseminação do vírus, o conceito de redes urbanas com a ampliação das interações espaciais é importante para a compreensão da dinâmica da pandemia. A análise aponta que com a pandemia os deslocamentos para Montes Claros e demais sedes microrregionais ratificam o desigual acesso da população às estruturas de saúde de alta complexidade e, ainda, reflete o processo rápido de difusão do vírus no território norte mineiro a partir da rede urbana.Palavras-chave: Rede Urbana; COVID-19; Macro Norte.ABSTRACTThis text analyzes the spatial diffusion process of COVID-19 in the Northern Minas Health Macroregion. To this end, the Urban Network of Minas Gerais is contextualized, focusing on the health sector and the displacements related to this service in Macro Norte. It presents a diagnosis and mapping of COVID-19 cases and deaths from April 2020 to March 2021, apex of the epidemiological crisis in Brazil and also in this region. A qualitative approach, survey, organization and systematization of data from COVID-19 in Minas Gerais was used, in addition to analytical and graphical cartographic products. Regarding the analysis of the spread of the virus, the concept of urban networks with the expansion of spatial interactions is important for understanding the dynamics of the pandemic. The analysis points out that with the pandemic, displacements to Montes Claros and other micro-regional headquarters ratify the population's unequal access to highly complex health structures, and also reflects the rapid process of spreading the virus in northern Minas Gerais from the urban network.Keywords: Urban Network; COVID-19; North Macroregion.RESUMENEste texto analiza el proceso de difusión espacial de COVID-19 en la Macrorregión de Salud Norte de Minas. Para ello, se contextualiza la Red Urbana de Minas Gerais, enfocando se en el sector salud y los desplazamientos relacionados con este servicio en Macro Norte. Presenta un diagnóstico y mapeo de casos y muertes de COVID-19 desde abril de 2020 hasta marzo de 2021, ápice de la crisis epidemiológica en Brasil y también en esta región. Se utilizó un enfoque cualitativo, relevamiento, organización y sistematización de los datos del COVID-19 en Minas Gerais, además de productos cartográficos analíticos y gráficos. En cuanto al análisis de la propagación del virus, el concepto de redes urbanas con expansión de interacciones espaciales es importante para comprender la dinámica de la pandemia. El análisis señala que con la pandemia, los desplazamientos a Montes Claros y otras sedes microrregionales ratifican el acceso desigual de la población a estructuras de salud de alta complejidad, y también refleja el rápido proceso de propagación del virus en el territorio norte de Minas Gerais desde el ámbito de la red urbana.Palabras clave: Red Urbana; COVID-19; Macro Norte.

The spatial diffusion of fertility decline in Egypt (1950–2006)

While the Egyptian fertility transition has been widely addressed in the literature, few researches have studied the spatial dimension of fertility. Using population census data, the aim of this study is to describe and measure the evolution of the geography of fertility on a subnational scale (qism/markaz), focusing on the period between 1960 and 2006. We assumed that the decline in fertility had spread spatially through Egypt, the spatial diffusion occurring through two traditional mechanisms: contagion and hierarchical diffusion. Our results confirm our hypotheses and highlight the importance of studying the spatial diffusion of the fertility transition. This study is unique for the Egyptian context given the long period and fine territorial scale considered. Our study constitutes an important addition to the existing group of studies on the spatial diffusion of fertility. Finally, it contributes to gaining further insight into a demographic dynamic which is fundamental for the future of Egypt.