## Vivax Firmware 19 UPDATED

Vivax Firmware 19

in this paper, we present a novel approach to reconstruct the underlying transmission networks of *p. vivax* based on tempo-spatial surveillance data and use the reconstructed transmission networks to study the roles of individual towns on *p. vivax* transmission. the overall procedure is summarized in fig 1. based on the tempo-spatial data set, we first build a spatial transmission model by using a recurrent neural network model to infer the underlying *p. vivax* transmission networks from the surveillance data at individual nodes (i.e., geographical locations).

in the following, we introduce how to model the spatial diffusion of *p. vivax* in terms of *nested transmission*. in fact, from a dynamical perspective, the time-evolution of malaria transmission in a town (i.e., the system dynamics) mainly depends on three components: the dynamics of the infection sources (i., ), the dynamics of the transmission network (i., ), and the dynamics of host immunity (i., ). the immunity of hosts in a town mainly depends on the immunity they have accumulated from one or more previous infections (i., ), and the probability of new infections from the outside (i. in this paper, the dynamics of the infection sources is estimated by using the *backward difference approximation* (bda) algorithm, which is a simple and powerful technique to approximate the solution of a nonlinear system of difference equations [20]. this is because it can take advantage of the implicitness of the *self-inflicted effect* (i., ), which is equal to the proportion of infected people at a time step being infected at the current time step as shown in (1). hence, the infection sources can be modeled as follows: (7)which stands for the proportion of infected people at time step being infected at the current time step. to model the dynamics of the transmission network (i., ), we first have to model the evolution of the infection spreading process. for this purpose, we adopt the *heterogeneous diffusion model* (hda) [21], which is described as follows: (8)where refers to the number of infected people at time step at node and has the same meaning as (7). based on the model (8), the proportion of infected people at time step at node is given by: (9)where is the proportion of infected people at time step at node. besides, to model the dynamics of host immunity (i., ), we have the following model: (10)where is the proportion of people with immunity at time step at node and represents the proportion of people with immunity at time step at node having acquired immunity from at time step, which can be calculated by: (11)note that the immunity of hosts in a town mainly depends on the immunity they have accumulated from one or more previous infections (i. as shown in figure 10, the dynamics of the immunity of the human population can be described as follows: (12)by taking into consideration the immunity of the hosts (i., ), the proportion of people with immunity at time step at node is given by: (13)where is the proportion of people with immunity at time step at node.

it has been proposed by rueda et al. [15] that the recurrent neural network (i.e., rnn) model can be effectively used to infer the underlying transmission networks of p. vivax. this paper extends their work by applying the rnn model to infer the transmission networks of p. vivax in the 62 towns. specifically, the rnn model can be expressed as:

where y(t) is the vector (i.e., number of cases at week t) of p. vivax; h(t) is the observed vector (i., number of reported cases in each town) of p. vivax; f(t) is the posteriori vector (i., the network predicted vector at week t) of p. vivax; h(t) is a matrix of row vectors where each row vector represents the vector of a town; and f(t) is a row vector. obviously, the time index t is weekly and the prediction is made at the next week, that is, t+1.

in the following, we present the results of the proposed model to infer the spatial transmission dynamics of p. vivax in yunnan province. to this end, we first have to solve the optimization problem in (6) to learn the transmission weights of p. vivax for all the 62 towns in yunnan. after that, we can estimate the number of new infections of each town at each time step. finally, we can use the estimated numbers of new infections to plot the evolution of p. vivax in yunnan. the results are shown in figure 11, where the number of estimated new infections at each time step is shown as a blue dot.

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