Lumpy skin disease (LSD) is a transboundary disease affecting cattle and has a detrimental effect on the cattle industries in numerous countries in Africa, Europe and Asia. In 2021, LSD outbreaks have been reported in almost all of Thailand's provinces. Indeed, fitting LSD occurrences using mathematical models provide important knowledge in the realm of animal disease modeling. Thus, the objective of this study is to fit the pattern of daily new LSD cases and daily cumulative LSD cases in Thailand using mathematical models. The first- and second-order models in the forms of Lorentzian, Gaussian and Pearson-type VII models are used to fit daily new LSD cases whereas Richard's growth, Boltzmann sigmoidal and Power-law growth models are utilized to fit the curve of cumulative LSD cases. Based on the root-mean-squared error (RMSE) and Akaike information criterion (AIC), results showed that both first and second orders of Pearson-type VII models and Richard's growth model (RGM) were fit to the data better than other models used in the present study. The obtained models and their parameters can be utilized to describe the LSD outbreak in Thailand. For disease preparedness purposes, we can use the first order of the Pearson-type VII model to estimate the time of maximum infected cases occurring when the growth rate of infected cases starts to slow down. Furthermore, the period when the growth rate changes at a slower rate, known as the inflection time, obtained from RGM allows us to anticipate when the pandemic has peaked and the situation has stabilized. This is the first study that utilizes mathematical methods to fit the LSD epidemics in Thailand. This study offers decision-makers and authorities with valuable information for establishing an effective disease control strategy.

A swarming model is a model that describes the behavior of the social aggregation of a large group of animals or the community of humans. In this work, the swarming model that includes the short-range repulsion and long-range attraction with the presence of time delay is investigated. Moreover, the convergence to a consensus representing dispersion and cohesion properties is proved by using the Lyapunov functional approach. Finally, numerical results are provided to demonstrate the effect of time delay on the motion of the group of agents.

The Cucker and Smale model is a well‐known flocking model that describes the emergence of flocks based on alignment. The first part focuses on investigating this model, including the effect of time delay and the presence of a leader. Furthermore, the control function is inserted into the dynamics of a leader to drive a group of agents to target. In the second part of this work, leadership‐based optimal control is investigated. Moreover, the existence of the first‐order optimality conditions for a delayed optimal control problem is discussed. Furthermore, the Runge–Kutta discretization method and the nonlinear conjugate gradient method are employed to solve the discrete optimality system. Finally, the capacity of the proposed control approach to drive a group of agents to reach the desired places or track the trajectory is demonstrated by numerical experiment results.

In this paper, we introduce a new class of proximal connected-image contractions in the framework of b-metric spaces endowed with a directed graph. By employing auxiliary functions, we establish several existence and uniqueness results for best proximity points and fixed points under appropriate contractive conditions. To demonstrate the applicability of our theoretical findings, we apply the main results to a class of fractional differential equations, showing the effectiveness of the proposed approach.

This article introduces a new concept of compatible contraction in metric spaces. By utilizing graph properties, namely being orbitally edge-preserving, we establish the existence of fixed points under these conditions. Furthermore, under specific assumptions on the mapping, the uniqueness of the fixed point is guaranteed. We provide illustrative examples to clarify the theoretical developments. To demonstrate the practical utility of this framework, we apply it to specific classes of integral and differential equations, specifically focusing on nonlinear fourth-order boundary value problems. We show that these problems satisfy the proposed contraction criteria, ensuring their solution via iterative methods. Numerical experiments on various fourth-order boundary value problems validate the effectiveness of our approach.

The development of an optimally designed rain gauge network is crucial for achieving cost-efficient operation and maintenance and maintaining the overall accuracy of rainfall estimation. Traditional rainfall monitoring network optimization relies primarily on statistical methods without consideration of the underlying network configuration. This study presents a hybrid optimization approach integrating graph theory related to centrality (betweenness and clustering coefficient), minimum spanning tree (MST) and simulated annealing (SA) for monitoring station reduction. The proposed hybrid MST-SA algorithm with adaptive graph weighting applies to 317 monitoring stations in the northern Thailand using 11 years of wet-season rainfall data (2012–2022). Six main scenarios, involving the removal of 5 to 30 stations, are analyzed through the adjustment of the trade-off parameter between correlation and centrality. The results indicate that the proposed method outperforms the approach based solely on the correlation coefficient. This hybrid MST-SA approach achieves faster convergence and effectively preserves the continuity of spatial information throughout the domain. Furthermore, as the number of reduced stations increases, the influence of centrality becomes increasingly pronounced compared to that obtained solely from correlation analysis.