Visceral leishmaniasis (VL), one of the deadliest parasitic diseases in the world, causes more than 50,000 human deaths each year and afflicts millions of people throughout South America, East Africa, South Asia, and Mediterranean Region. In 2015 the World Health Organization classified VL as a neglected tropical disease (NTD), prompting concentrated study of the VL epidemic using mathematical and simulation models. This paper reviews literature related to prevalence and prevention control strategies. More than thirty current research works were reviewed and classified based on VL epidemic study methods, including modeling approaches, control strategies, and simulation techniques since 2013. A summarization of these technical methods, major findings, and contributions from existing works revealed that VL epidemic research efforts must improve in the areas of validating and verifying VL mathematical models with real-world epidemic data. In addition, more dynamic disease control strategies must be explored and advanced simulation techniques must be used to predict VL pandemics.

Visceral leishmaniasis (VL), a vector-borne disease caused by protozoan flagellates of the genus Leishmania, is transmitted by sand flies. After malaria, VL is the second-largest parasitic killer, responsible for an estimated 500,000 infections and 51,000 deaths annually worldwide. Mathematical models proposed for VL have included the impact of dogs versus wild canids in disease dissemination and models developed to assist in control approaches. However, quantitative conditions that are required to control or eradicate VL transmission are not provided and there are no mathematical methods proposed to quantitatively calculate optimal control strategies for VL transmission. The research objective of this work was to model VL disease transmission system (specifically Zoonotic VL), perform bifurcation analysis to discuss control conditions, and calculate optimal control strategies. Three time-dependent control strategies involving dog populations, sand fly population, and humans are mainly discussed. Another strategy sometimes used in attempts to control zoonotic VL transmission, dog culling, is also evaluated in this paper.

High LNM risk is expected in tumors of IIa stage or higher and in moderately differentiated tumors. Skip metastasis and common iliac LNM are relatively common and therefore should not be neglected. Our results suggest that standardized and complete pelvic lymph node dissection under surgery is an important measure to ensure a therapeutic effect.

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This paper presents and compares four mathematical models with unique spatial effects for a prey-predator system, with Tetranychus urticae as prey and Phytoseiulus persimilis as predator. Tetranychus urticae, also known as two-spotted spider mite, is a harmful plant-feeding pest that causes damage to over 300 species of plants. Its predator, Phytoseiulus persimilis, a mite in the Family Phytoseiidae, effectively controls spider mite populations. In this study, we compared four mathematical models using a numerical simulation. These models include two known models: self-diffusion, and cross-diffusion, and two new models: chemotaxis effect model, and integro diffusion model, all with a Beddington-De Angelis functional response. The modeling results were validated by fitting experimental data. Results demonstrate that interaction scheme plays an important role in the prey-predator system and that the crossdiffusion model fits the real system best. The main contribution of this paper is in the two new models developed, as well as the validation of all the models using experimental data.