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The susceptible-infectious-susceptible (SIS) infectious disease models without spatial heterogeneity have limited applications, and the numerical simulation without considering models’ global existence and uniqueness of classical solutions might converge to an impractical solution. This paper aims to develop a robust and reliable numerical approach to the SIS epidemic model with spatial heterogeneity, which characterizes the horizontal and vertical transmission of the disease.

This study used stability analysis methods from nonlinear dynamics to evaluate the stability of SIS epidemic models. Additionally, the authors applied numerical solution methods from diffusion equations and heat conduction equations in fluid mechanics to infectious disease transmission models with spatial heterogeneity, which can guarantee a robustly stable and highly reliable numerical process. The findings revealed that this interdisciplinary approach not only provides a more comprehensive understanding of the propagation patterns of infectious diseases across various spatial environments but also offers new application directions in the fields of fluid mechanics and heat flow. The results of this study are highly significant for developing effective control strategies against infectious diseases while offering new ideas and methods for related fields of research.

Through theoretical analysis and numerical simulation, the distribution of infected persons in heterogeneous environments is closely related to the location parameters. The finding is suitable for clinical use.

The theoretical analysis of the stability theorem and the threshold dynamics guarantee robust stability and fast convergence of the numerical solution. It opens up a new window for a robust and reliable numerical study.

Agriculture is the backbone of a country, contributing more than half of the sector of economy throughout the world. The need for precision agriculture is essential in evaluating the conditions of the crops with the aim of determining the proper selection of pesticides. The conventional method of pest detection fails to be stable and provides limited accuracy in the prediction. This paper aims to propose an automatic pest detection module for the accurate detection of pests using the hybrid optimization controlled deep learning model.

The paper proposes an advanced pest detection strategy based on deep learning strategy through wireless sensor network (WSN) in the agricultural fields. Initially, the WSN consisting of number of nodes and a sink are clustered as number of clusters. Each cluster comprises a cluster head (CH) and a number of nodes, where the CH involves in the transfer of data to the sink node of the WSN and the CH is selected using the fractional ant bee colony optimization (FABC) algorithm. The routing process is executed using the protruder optimization algorithm that helps in the transfer of image data to the sink node through the optimal CH. The sink node acts as the data aggregator and the collection of image data thus obtained acts as the input database to be processed to find the type of pest in the agricultural field. The image data is pre-processed to remove the artifacts present in the image and the pre-processed image is then subjected to feature extraction process, through which the significant local directional pattern, local binary pattern, local optimal-oriented pattern (LOOP) and local ternary pattern (LTP) features are extracted. The extracted features are then fed to the deep-convolutional neural network (CNN) in such a way to detect the type of pests in the agricultural field. The weights of the deep-CNN are tuned optimally using the proposed MFGHO optimization algorithm that is developed with the combined characteristics of navigating search agents and the swarming search agents.

The analysis using insect identification from habitus image Database based on the performance metrics, such as accuracy, specificity and sensitivity, reveals the effectiveness of the proposed MFGHO-based deep-CNN in detecting the pests in crops. The analysis proves that the proposed classifier using the FABC+protruder optimization-based data aggregation strategy obtains an accuracy of 94.3482%, sensitivity of 93.3247% and the specificity of 94.5263%, which is high as compared to the existing methods.

The proposed MFGHO optimization-based deep-CNN is used for the detection of pest in the crop fields to ensure the better selection of proper cost-effective pesticides for the crop fields in such a way to increase the production. The proposed MFGHO algorithm is developed with the integrated characteristic features of navigating search agents and the swarming search agents in such a way to facilitate the optimal tuning of the hyperparameters in the deep-CNN classifier for the detection of pests in the crop fields.