Abstract-Diseases which are transmitted by vector mosquitoes are major health problems in many countries. Although many mathematical models for diseases had been formulated, they are customized. As these diseases are spread by a common vector, similarities in the disease transmission are notable hence it will be beneficial to construct a general model which encompasses the epidemiology aspects and transmission of mosquito-borne diseases. In this paper, a SI (SusceptibleInfectious) generic model for mosquito borne diseases is formulated. The model is made up of partial differential reactiondiffusion equations which incorporate both the human and mosquito populations. Numerical simulation of this model is presented.
Abstract-Mosquito-borne diseases are of tremendous public health concern. To study and enhance the understanding of these infectious diseases, we present a reaction-diffusion generic model for mosquito-borne diseases. It is significant that a model can be generalized for mosquito-borne diseases. One of the objectives of mathematical models is to identify factors which contribute to the spread of diseases. The traveling wave front is examined and the minimum spread speed is acquired numerically. We analyze the impact of human random movement and spatial heterogeneity on the dissemination of disease through numerical simulations. It is shown that the increment of human diffusion decreases the basic reproduction number. However, spatial heterogeneity in transmission of disease contributes to the upsurge of infection.
To keep an eye on the status of high-quality processes for fraction nonconforming, the synthetic double sampling (SDS) np chart is a helpful tool. The SDS np chart is a hybrid between the double sampling (DS) np chart and the conforming run length (CRL) chart. The performance of a control chart is typically judged solely using the average run length (ARL). However, as the shape of the run length (RL) distribution varies with the magnitude of the shift in the process fraction nonconforming, the ARL no longer provides clear interpretation of a chart’s performance. Subsequently, enhanced DS np charts that use median run length (MRL) and expected median run length (EMRL) measures, including SDS np with MRL have recently been proposed for addressing this setback. To broaden the functionality of SDS np, in this work, the unexplored use of EMRL as alternative performance measure is developed by means of Markov chain model. Additionally, in both the zero-state (ZS) and steady-state (SS) modes, the novel optimal designs algorithms are described for computing the optimal charting parameters of the SDS np chart, for both MRL1 and EMRL1 minimizations, without any unfavourable feature of bilateral sensitivity. Both the MRL and EMRL performances of SDS np, synthetic np, and DS np charts are compared. Optimal designs charting parameters and sensitivity analyses are provided to aid the practical application of SDS np chart.
Double sampling (DS) control charts are widely regarded as an effective process monitoring tool owing to their remarkable properties, such as the ability to detect small and moderate process shifts efficiently with the reduced sample size. Since the shape of the run length distribution is highly right-skewed for the process small shift size and becomes almost symmetric when the process shift size is large, the use of median run length (MRL) as a performance measure is therefore more representative. Existing works on the DS np chart construction were performed by taking an approach that the shift size of the process fraction nonconforming is assumed to be known. However, the shift size of the fraction nonconforming is usually unknown by the quality practitioners in practice. Herein, to address this issue, the expected median run length (EMRL) has been suggested as a performance measure for the unknown shift size. This paper suggests an optimal design procedure for the DS np chart based on the EMRL criterion. An example is provided to illustrate the construction of the EMRL-based DS np chart. The DS np chart is compared with a competing chart based on the EMRL criterion. Findings obtained reveal that when the shift size is unknown, the EMRL is an alternative performance measure for the DS np chart, with greater sensitivity observed for the DS np chart in contrast to the standard np chart for detecting a wide range of shifts.
Mosquitoes can cause a lot of suffering to humans by transferring diseases. Malaria is a mosquito-borne disease caused by the parasite Plasmodium. It is an acute public health issue in many countries and can be fatal. Considering the similarity in the transmission of mosquito-borne diseases, a generic spatial-temporal model for transmission of multiple mosquito-borne diseases was formulated. The main concern here is whether the numerical results produced by this reactiondiffusion generic model are comparable with actual cases. Here, the actual notified weekly cases for 36 weeks, which is from week 39 in 2012 to week 22 in 2013, for four districts in Sarawak, Malaysia, namely Kapit, Song, Belaga and Marudi are compared with simulations of the generic model. The random movement of human and mosquito populations are taken into account. It is discovered that the numerical results are in good agreement to the actual malaria cases in the four districts.
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