Mathematical Model of Dengue Disease with the Incubation Period of Virus

Dengue virus is transmitted from person to person through the biting of infected Aedes Aegypti mosquitoes. DEN-1, DEN-2, DEN-3 and DEN-4 are four serotypes of this virus. Infection with one of these four serotypes apparently produces permanent immunity to it, but only temporary cross immunity to the others. The length of time during incubation of dengue virus in human and mosquito are considered in this study. The dengue patients are classified into infected and infectious classes. The infectious human can transmit dengue virus to susceptible mosquitoes but infected human can not. The transmission model of this disease is formulated. The human population is divided into susceptible, infected, infectious and recovered classes. The mosquito population is separated into susceptible, infected and infectious classes. Only infectious mosquitoes can transmit dengue virus to the susceptible human. We analyze this model by using dynamical analysis method. The threshold condition is discussed to reduce the outbreak of this disease.

Review of a Real-Time Infectious Waste Management System Using QR Code

In the management of industrial waste, conversion from the use of paper invoices to electronic forms is currently under way in developed countries. Difficulties in such computerization include the lack of synchronization between the actual goods and the corresponding data managed by the server. Consequently, a system which utilizes the incorporation of a QR code in connection with the waste material has been developed. The code is read at each stage, from discharge until disposal, and progress at each stage can be easily reported. This system can be linked with Japanese public digital authentication service of waste, taking advantage of its good points, and can be used to submit reports to the regulatory authorities. Its usefulness was confirmed by a verification test, and put into actual practice.

The Integrated Studies of Infectious Disease Using Mathematical Modeling and Computer Simulation

In this paper we develop and analyze the model for the spread of Leptospirosis by age group in Thailand, between 1997 and 2010 by using mathematical modeling and computer simulation. Leptospirosis is caused by pathogenic spirochetes of the genus Leptospira. It is a zoonotic disease of global importance and an emerging health problem in Thailand. In Thailand, leptospirosis is a reportable disease, the top three age groups are 23.31% in 35-44 years olds group, 22.76% in 25-34 year olds group, 17.60% in 45-54 year olds group from reported leptospirosis between 1997 and 2010, with a peak in 35-44 year olds group. Our paper, the Leptosipirosis transmission by age group in Thailand is studied on the mathematical model. Some analytical and simulation results are presented.

Dynamical Network Transmission of H1N1 Virus at the Local Level Transmission Model

A new strain of Type A influenza virus can cause the transmission of H1N1 virus. This virus can spread between the people by coughing and sneezing. Because the people are always movement, so this virus can be easily spread. In this study, we construct the dynamical network model of H1N1 virus by separating the human into five groups; susceptible, exposed, infectious, quarantine and recovered groups. The movement of people between houses (local level) is considered. The behaviors of solutions to our dynamical model are shown for the different parameters.

Dengue Disease Mapping with Standardized Morbidity Ratio and Poisson-gamma Model: An Analysis of Dengue Disease in Perak, Malaysia

Dengue disease is an infectious vector-borne viral disease that is commonly found in tropical and sub-tropical regions, especially in urban and semi-urban areas, around the world and including Malaysia. There is no currently available vaccine or chemotherapy for the prevention or treatment of dengue disease. Therefore prevention and treatment of the disease depend on vector surveillance and control measures. Disease risk mapping has been recognized as an important tool in the prevention and control strategies for diseases. The choice of statistical model used for relative risk estimation is important as a good model will subsequently produce a good disease risk map. Therefore, the aim of this study is to estimate the relative risk for dengue disease based initially on the most common statistic used in disease mapping called Standardized Morbidity Ratio (SMR) and one of the earliest applications of Bayesian methodology called Poisson-gamma model. This paper begins by providing a review of the SMR method, which we then apply to dengue data of Perak, Malaysia. We then fit an extension of the SMR method, which is the Poisson-gamma model. Both results are displayed and compared using graph, tables and maps. Results of the analysis shows that the latter method gives a better relative risk estimates compared with using the SMR. The Poisson-gamma model has been demonstrated can overcome the problem of SMR when there is no observed dengue cases in certain regions. However, covariate adjustment in this model is difficult and there is no possibility for allowing spatial correlation between risks in adjacent areas. The drawbacks of this model have motivated many researchers to propose other alternative methods for estimating the risk.

Determination of in Vitro Susceptibility of the Typhoid Pathogens to Synergistic Action of Euphorbia Hirta, Euphorbia Heterophylla and Phyllanthus Niruri for Possible Development of Effective Anti-Typhoid Drugs

Studies were carried out to determine the in vitro susceptibility of the typhoid pathogens to combined action of Euphorbia hirta, Euphorbia heterophylla and Phyllanthus niruri. Clinical isolates of the typhoid bacilli were subjected to susceptibility testing using agar diffusion technique and the minimum inhibitory concentration (MIC) determined with tube dilution technique. These isolates, when challenged with doses of the extracts from the three medicinal plants showed zones of inhibition as wide as 26±0.2mm, 22±0.1mm and 18±0.0mm respectively. The minimum inhibitory concentration (MIC) revealed organisms inhibited at varying concentrations of extracts: E. hirta (S. typhi 0.250mg/ml, S. paratyphi A 0.125mg/ml, S. paratyphi B 0.185mg/ml and S. paratyphi C 0.225mg/ml), E. heterophylla (S. typhi 0.280mg/ml, S. paratyphi A 0.150mg/ml, S. paratyphi B 0.200mg/ml and S. paratyphi C 0.250mg/ml) and P. niruri (S. typhi 0.150mg/ml, S. paratyphi A 0.100mg/ml, S. paratyphi B 0.115mg/ml and S. paratyphi C 0.125mg/ml). The results of the synergy between the three plants in the ration of 1:1:1 showed very low MICs for the test pathogens as follows S. typhi 0.025mg/ml, S. paratyphi A 0.080mg/ml, S. paratyphi B 0.015mg/ml and S. paratyphi C 0.10mg/ml with the diameter zone of inhibition (DZI) ranging from 35±0.2mm, 28±0.4mm, 20±0.1mm and 32±0.3mm respectively. The secondary metabolites were identified using simple methods and HPLC. Organic components such as anthroquinones, different alkaloids, tannins, 6-ethoxy-1,2,3,4-tetrahydro-2,2,4-trimethyl and steroids were identified. The prevalence of Salmonellae, a deadly infectious disease, is still very high in parts of Nigeria. The synergistic action of these three plants is very high. It is concluded that pharmaceutical companies should take advantage of these findings to develop new anti-typhoid drugs from these plants.

Analysis of a Mathematical Model for Dengue Disease in Pregnant Cases

Dengue fever is an important human arboviral disease. Outbreaks are now reported quite often from many parts of the world. The number of cases involving pregnant women and infant cases are increasing every year. The illness is often severe and complications may occur. Deaths often occur because of the difficulties in early diagnosis and in the improper management of the diseases. Dengue antibodies from pregnant women are passed on to infants and this protects the infants from dengue infections. Antibodies from the mother are transferred to the fetus when it is still in the womb. In this study, we formulate a mathematical model to describe the transmission of this disease in pregnant women. The model is formulated by dividing the human population into pregnant women and non-pregnant human (men and non-pregnant women). Each class is subdivided into susceptible (S), infectious (I) and recovered (R) subclasses. We apply standard dynamical analysis to our model. Conditions for the local stability of the equilibrium points are given. The numerical simulations are shown. The bifurcation diagrams of our model are discussed. The control of this disease in pregnant women is discussed in terms of the threshold conditions.

Transmission Model for Plasmodium Vivax Malaria: Conditions for Bifurcation

Plasmodium vivax malaria differs from P. falciparum malaria in that a person suffering from P. vivax infection can suffer relapses of the disease. This is due the parasite being able to remain dormant in the liver of the patients where it is able to re-infect the patient after a passage of time. During this stage, the patient is classified as being in the dormant class. The model to describe the transmission of P. vivax malaria consists of a human population divided into four classes, the susceptible, the infected, the dormant and the recovered. The effect of a time delay on the transmission of this disease is studied. The time delay is the period in which the P. vivax parasite develops inside the mosquito (vector) before the vector becomes infectious (i.e., pass on the infection). We analyze our model by using standard dynamic modeling method. Two stable equilibrium states, a disease free state E0 and an endemic state E1, are found to be possible. It is found that the E0 state is stable when a newly defined basic reproduction number G is less than one. If G is greater than one the endemic state E1 is stable. The conditions for the endemic equilibrium state E1 to be a stable spiral node are established. For realistic values of the parameters in the model, it is found that solutions in phase space are trajectories spiraling into the endemic state. It is shown that the limit cycle and chaotic behaviors can only be achieved with unrealistic parameter values.