The transmission networks of Plasmodium vivax characterize how the parasite transmits from one location to another, which are informative and insightful for public health policy makers to accurately predict the patterns of its geographical spread. However, such networks are not apparent from surveillance data because P. vivax transmission can be affected by many factors, such as the biological characteristics of mosquitoes and the mobility of human beings. Here, we pay special attention to the problem of how to infer the underlying transmission networks of P. vivax based on available tempo-spatial patterns of reported cases.
We first define a spatial transmission model, which involves representing both the heterogeneous transmission potential of P. vivax at individual locations and the mobility of infected populations among different locations. Based on the proposed transmission model, we further introduce a recurrent neural network model to infer the transmission networks from surveillance data. Specifically, in this model, we take into account multiple real-world factors, including the length of P. vivax incubation period, the impact of malaria control at different locations, and the total number of imported cases.
We implement our proposed models by focusing on the P. vivax transmission among 62 towns in Yunnan province, People's Republic China, which have been experiencing high malaria transmission in the past years. By conducting scenario analysis with respect to different numbers of imported cases, we can (i) infer the underlying P. vivax transmission networks, (ii) estimate the number of imported cases for each individual town, and (iii) quantify the roles of individual towns in the geographical spread of P. vivax.
The demonstrated models have presented a general means for inferring the underlying transmission networks from surveillance data. The inferred networks will offer new insights into how to improve the predictability of P. vivax transmission.
The transmission of Plasmodium vivax has induced enormous public health problems at the global level. Natural transmission of P. vivax depends on interactions between anopheles mosquitoes and human beings. There are two important factors that influence its geographical spread. First, different locations may have different risks of infection due to their heterogeneous environmental and demographical profiles. Second, human mobility may bring pathogens from high-transmission locations to low-transmission locations. In view of this, to effectively and efficiently control the geographical spread of P. vivax, it would be desirable for us to characterize how it transmits from one location to another. To achieve this, we first build a spatial transmission model to characterize both the heterogeneous infection risks at individual locations and the underlying mobility of infected populations. By doing so, we can further infer the underlying P. vivax transmission networks from tempo-spatial surveillance data by using a machine learning method (i.e., based on a recurrent neural network model). Our study offers new insights into malaria surveillance and control from the viewpoint of both system modeling and machine learning.
As one of the malaria parasites that can infect and be transmitted by human beings, Plasmodium vivax has induced enormous challenges to the public health of human population. It has been estimated that 2.5 billion people all over the world are at risk of infection with this organism, among which China accounts for 19% of the global populations at risk . To control, eliminate or even eradicate malaria, WHO has suggested that the most important measure is a timely response with the implementation of strategic intervention . This requires the establishment of effective and efficient monitoring or surveillance systems . Moreover, in practice, human mobility can introduce malaria into previously low-transmission or malaria-free areas, which has been cited amongst the significant causes of the failure of the Global Malaria Eradication Programme . Therefore, it would be desirable to investigate the underlying geographical spread of malaria, which is not apparent from surveillance data. In this paper, the transmission networks of P. vivax characterize how the parasite transmits from one geographical location to another due to human mobility. By focusing on the malaria transmission in Yunnan province, People's Republic of China, we pay special attention to the problem of how to infer the underlying transmission networks of P. vivax based on tempo-spatial patterns of observed/reported cases.
Mathematically speaking, the problem can be defined as follows: Let be a directed network with self-links, where and represent the sets of nodes and links, respectively. Each node stands for a geographical location in a malaria transmission area, and each link stands for the possible P. vivax transmission from to . For each node , let be the set of nodes that have links from , i.e., , and be the set of nodes that have links to , i.e., . Note that does not belong to either or . Moreover, we denote the weight of link as to represent the proportion of infected populations transmitting from to . Specifically, refers to the proportion of infected populations in that do not transmit. In this case, the objective is to estimate the link weights of based on surveillance data, which are formulated as tempo-spatial series (corresponding to nodes or geographical locations, such as villages or towns). For each node , the tempo-spatial series take the form of 3-tuple , which indicates that cases are observed/reported at time step at with attribute set . In this paper, the attribute set consists of the dynamically-changing temperature and rainfall over time at node , which reflects the heterogeneity of the nodes concerning the transmission potential of P. vivax.
In this paper, we focus on the problem of how to infer the underlying transmission networks of P. vivax among 62 towns located in four adjacent counties (i.e., Teng Chong, Long Ling, Ying Jiang, and Long Chuan) in Yunnan, China (see Figure 1), where the IDs and names of these towns are listed in Table 1. All these towns have been experiencing high P. vivax transmission in the past three years, with at least one year having the annual incidence rate larger than 1/10,000. Figure 2 presents the reported P. vivax cases of the 62 towns in 2005 grouped by every two weeks. It can be observed that different towns has different patterns of infections. There are three major reasons: First, due to the environmental and demographical heterogeneity of these towns, the transmission potential of P. vivax at each individual town is different. Figure 3 shows the heterogeneous transmission potential (i.e., vectorial capacity) estimated by the average temperatures and accumulated rainfall at each town based on the method proposed by Ceccato et al. . Second, human mobility from one location to another may result in geographical spread of P. vivax. Third, a large number of malaria cases in Yunnan are imported from Myanmar , which is a high-transmission country for malaria and contiguous with Yunnan.
Imported cases in this work are defined as malaria infections whose origin can be traced to an area outside the country. Based on the annual case reporting system in P.R. China, the fraction of imported cases of P. falciparum in Yunnan was about 69.0% in 2005 . While in 2011, among totally 301 reported P. falciparum cases in Yunnan, 269 of them were imported cases (i.e., the fraction of imported cases was about 89.4%) . It was also reported that the fraction of imported cases of P. vivax in China in 2011 is about 62.9% . Along this line, in this paper, we study several transmission scenarios with respect to different percentages of imported cases (i.e., 60%, 70%, 80%, and 90%) among all the reported P. vivax cases in the 62 towns. Specifically, we present a spatial transmission model and a recurrent neural network model to (i) infer the transmission networks of P. vivax from tempo-spatial surveillance data, (ii) estimate the fraction of imported cases in all reported cases for each individual town, and (iii) examine the roles of individual towns on P. vivax transmission.
Due to the complex nature of P. vivax transmission, to infer the underlying transmission networks, appropriate spatial transmission model should first be formulated. In this paper, we aggregate the tempo-spatial series of surveillance data for each individual town based on a time step with duration . In reality, may be related to the incubation period of malaria (i.e., the period from the point of infection to the appearance of symptoms of the disease). In doing so, we assume that the observed/reported infections at time step are more likely to be infected at previous time step . Generally speaking, the causes of geographical spread of P. vivax are twofold. First, within a town/node , the number of malaria infections at a time step is determined by multiple factors, such as temperature, rainfall, population size, as well as the number of infections at previous time step . Second, human mobility may introduce P. vivax from one town to another. Specifically, we focus mainly on the mobility of infected populations among different towns because patients with typical malaria symptoms will be rapidly diagnosed and treated in Yunnan, P.R. China. It is seldom for a diagnosed patient to cause further malaria infection.
To further estimate the number of infections at a node , we introduce another notion of entomological incubation rate (EIR), which is defined as the number of infectious bites received per day by a human being . Let denote the proportion of infected populations among all human populations at at time step , i.e., . Here, is the number of observed/reported infections at at time step , and is the population size of . Figure 4 shows a schemati