A Mathematical Study for the Existence and Survival of Human Population in a Polluted Environment

Rapidly rising population and increasing urbanization have the potential for producing a high level of pollution. Pollutants have the ability to change the distributions of patterns of plants and animals. Some of the main pollutant categories are water pollutants, air pollution, pesticides, and radioactive waste. Most abundantly toxicants are produced by the chemical and medical industries. We used food crops that are produced by using pesticide and herbicides, etc. Due to the enormous variety of toxic substances are present in the atmosphere, it is challenging task to determine the potential ecological and human health risk. Keeping all these things in mind, in this paper, a non-linear mathematical model is developed to examine the existence and survival of the human population in a polluted environment. For this, we have assumed four variables the human population, population pressure, urbanization, and toxicants and considered that the human population propagates logistically, urbanization and toxicants propagate at the constant rate. The qualitative analysis of the system shows that the rapid increase in urbanization increases the toxicants in the environment which causes the growth of the human population decrease. Some numerical simulations are also made to examine the validity of the model

A stage-structured two species competition mathematical model under the effect of disease

In this paper we study the dynamics of two competing species model; one of this competing species is stage structured and the disease spreads only in the other competing specie. In order to keep the model simple, we present it under the strong assumption that the disease can not cross the species barrier. Dynamical behaviors such as positivity, boundedness, stability, bifurcation and persistence of the model are studied analytically using the theory of differential equations. Computer simulations are carried out to substantiate the analytical findings. It is noted that c the loss rate of the population, T the maturation time and f the intraspecific coefficient are the key parameters which we need to control or protect th to keep away the mature healthy population from extinction and also keep the infected individuals of the latter species from extinction respectively

Study of fetomaternal outcome in eclampsia

Background: Eclampsia is a life-threatening emergency that continues to be a major cause of maternal and perinatal mortality. The purpose of our study was to analyse the trend of eclampsia in a tertiary care teaching institute and to find out the fetomaternal outcomes of eclampsia.Methods: A retrospective epidemiological study was undertaken in the department of Obstetrics and Gynaecology, Jhalawar medical college, Jhalawar during the period ‘September 2018 to August 2019’. Women who presented as eclampsia or developed eclampsia during hospital stay were included in the study. Data analysed included various maternal parameters, fetal parameters, and the outcome of the pregnancy.Results: The incidence of antepartum eclampsia was (0.92%). High risk associated factors were primigravida (65.90%), low maternal age (21-30 years), illiteracy, and inadequate antenatal care. Caesarean section was the mode of delivery in 48 cases (54.54%) most common indication was unfavourable cervix, 80.6% women had antepartum eclampsia and 68.18% women had severe preeclampsia. There was 6.8% maternal mortality, attributed to pulmonary edema and acute renal failure. Perinatal mortality was 14.77% with 8 still births and 5 neonatal deaths. Prematurity complicated 46.66% pregnancies. Thirty neonates were admitted to NICU.Conclusions: Eclampsia is one of the important causes of maternal and perinatal morbidity and mortality due to lack of proper antenatal care, low socio-economic status, and lack of education. It can be concluded that better antenatal care, early recognition of disease, timely referral, early initiation of treatment and termination of eclamptic patients improves outcome. Management of eclamptic patients should be performed at tertiary care centres, where ICU facilities, NICU facilities, and multidisciplinary units are available

Modeling and Analysis of the Spread of an Infectious Disease Cholera with Environmental Fluctuations

A nonlinear delayed mathematical model with immigration for the spread of an infectious disease cholera with carriers in the environment is proposed and analyzed. It is assumed that all susceptible are affected by carrier population density. The carrier population density is assumed to follow the logistic model and grows due to conducive human population density related factors. The model is analyzed by stability theory of differential equations and computer simulation. Both the disease-free (DFE), (CFE) and endemic equilibria are found and their stability investigated. Bifurcation analyses about endemic equilibrium are also carried out analytically using the theory of differential equations. The model study shows that the spread of the infectious disease cholera increases due to growth of carriers in the environment and disease becomes more endemic due to immigration. Numerical simulations are also carried out to investigate the influence of certain parameters on the spread of disease, to support the analytical results of the model

A STUDY OF ZIGBEE TECHNOLOGY

The zigbee communication is a communication technology to connect local wireless nodes and provides high stability and transfer rate due to data communication with low power. In the nodes away from coordinator in one PAN, the signal strength is weak causing the network a shortage of low performance and inefficient use of resources due to transferring delay and increasing delay time and thus cannot conduct seamless communication. This study suggests the grouping method, that makes it possible to perform wide range data transferring depending on the node signal strength in zigbee node and analyzes the suggested algorithm through simulation. Based on IEEE 802.15.4 Low Rate-Wireless Personal Area Network (LR-WPAN) standard, the Zigbee standard has been proposed to interconnect simple, low rate and battery powered wireless devices. The de-ployment of Zigbee networks is expected to facilitate numerous applications such as Home-appliance net-works, home healthcare, medical monitoring and environmental sensors. An effective routing scheme is more important for Zigbee mesh networks. In order to achieve effective routing in Zigbee Mesh networks, a Zigbee protocol module is realized using NS-2. The suitable routing for different data services in the Zigbee application layer and a best routing strategy for Zigbee mesh network are proposed. The ZigBee standard provides network, security, and application support services operating on top of the IEEE 802.15.4 Medium AccessControl (MAC) and Physical Layer wireless standard. It employs a group of technologies to enable scalable, self-organizing, self-healing networks that can manage various data traffic patterns. ZigBee is a low-cost, low-power, wireless mesh networking standard. The low costal lows the technologyto be widely deployed in wireless control and monitoring applications, the low power-usage allows longerlife with smaller batteries, and the mesh networking which promises high reliability and larger range. ZigBee has-been developed to meet the growing demand for capable wireless networking between numerous low power devices. The aims of this network are to reduce the energy consumption and latency by enhancing routing algorithm. In a traditional tree routing when a node wants to transmit a packet to the destination, the packet has to follow child/parent relationship and go along tree topology, even if the destination is lying at nearby source. In order to solve this problem, an Enhanced Tree Routing Algorithm is introduced using ZigBee network. This algorithm can find the shortest path by computing the routing cost for all of router that stored in neighbor table, and transmit the packet to the neighbor router that can reduce the hop count of transmission. The enhanced tree routing algorithm can achieve more stable and better efficiency then the previous traditional tree routing algorithm

Modeling Spread of Polio with the Role of Vaccination

In this paper, we have proposed and analyzed a nonlinear mathematical model for the spread of Polio in a population with variable size structure including the role of vaccination. A threshold parameter, R , is found that completely determines the stability dynamics and outcome of the disease. It is found that if R 1, the disease free equilibrium is stable and the disease dies out. However, if R \u3e1, there exists a unique endemic equilibrium that is locally asymptotically stable. Conditions for the persistence of the disease are determined by means of Fonda’s theorem. Moreover, numerical simulation of the proposed model is also performed by using fourth order Runge - Kutta method. Numerically, it has been found that the system exhibits steady state bifurcation for some parameter values. It is concluded from our analysis that endemic level of infective population increases with the increase in rate of transmission of infection due to infective among susceptible class that further enhances because of transmission of infection due to latent hosts. A particular value of disease transmission coefficient r is found for which exposed and infective population dies out. It is found that periodic outbreak of the disease occurs when infection due to exposed and infective class occurs at the same rate. It is also observed from our analysis that although vaccination helps in eradicating polio by decreasing endemic equilibrium level yet careful administration of vaccination is desired because if vaccine is administered during incubation period, endemic equilibrium level increases and disease persists in the population

Mathematical Modeling and Analysis of Leukemia: Effect of External Engineered T Cells Infusion

In this paper, a nonlinear model is proposed and analyzed to study the spread of Leukemia by considering the effect of genetically engineered patients T cells to attack cancer cells. The model is governed by four dependent variables namely; naive or susceptible blood cells, infected or dysfunctional blood cells, cancer cells and immune cells. The model is analyzed by using the stability theory of differential equations and numerical simulation. We have observed that the system is stable in the local and global sense if antigenicity rate or rate of stimulation of immune cells is greater than a threshold value dependent on the density of immune cells. Further, external infusion of T cells (immune cells) reduces the concentration of cancer cells and infected cells in the blood. It is observed that the infected cells decrease with the increase in antigenicity rate or stimulation rate of immune response due to abnormal cancer cells present in the blood. This indicates that immune cells kill cancer cells on being stimulated and as antigenicity rate increases rate of destruction of cancer cells also increase leading to decrease in the concentration of cancer cells in the body. This decrease in cancer cells further causes decrease in the concentration of infected or dysfunctional cells in the body

Clinical presentation, diagnosis and management of bacterial vaginosis: a hospital based cross-sectional study

Background: Bacterial vaginosis is most common cause of vaginal discharge. Clinical presentation varies from person to person. The management of bacterial vaginosis is largely syndromic and empirical, it is usually based on naked eye examination of vaginal discharge and that is unsatisfactory because the diagnostic accuracy is lost without microscopic examination. The modern management of bacterial vaginosis demands a specific diagnosis which is a combination of naked eye examination plus laboratory workup.Methods: The study was carried out on 183 females with complaint of vaginal discharge in the outpatient department of obstetrics and gynecology. Specimens were collected in outpatient department of Jhalawar Medical College in associated Zanana Hospital. The laboratory work was conducted in the department of microbiology in Jhalawar Medical College, Jhalawar, Rajasthan, India.Results: The prevalence of microbial positivity in our study was 79.9%. Bacterial vaginosis was the most common diagnosis seen in 86 (47.0%) cases. Maximum patients presented with complaint of copious amount of foul-smelling yellow discharge.Conclusions: The study concludes that it is important to know the various presentations, confirm the diagnosis by proper microbiological tests, and provide appropriate treatment to patients to prevent resistance and recurrence of bacterial vaginosis

Unicornuate uterus with functional non communicating rudimentary horn: a refractory cause of dysmenorrhea

Mullerian duct anomalies are rare. Unicornuate uterus with a non-communicating rudimentary horn is a rare type of mullerian duct anomaly which occurs due to defective fusion of malformed duct with contralateral duct. The incidence is approximately 1:100000. Patient usually remain asymptomatic due to the absence of functional endometrium in most of the cases. If the rudimentary uterine horn has an endometrium lined uterine cavity and doesn’t communicate externally then the signs and symptoms of obstructed menstruation appears, as soon as menarche begins. It will be associated with severe dysmennorhoea and hematometra. Other complications may be abdominal lump, chronic pelvic pain, infertility, endometriosis, adenomyosis and ectopic pregnancy in rudimentary horn. Authors are presenting a case of refractory dysmenorrhea with lump abdomen in a patient with unicornuate uterus with functional non communicating horn. In a patient with refractory dysmenorrhea mullerian duct anomaly should be kept as differential diagnosis

Changing trends in cesarean delivery: rate and indications

Background: Caesarean section is a time honoured approach which was introduced in clinical practice as a lifesaving procedure both for the mother and the baby. The study was to compare the cesarean delivery rates over last 7 years and to examine the indications contributing to changed trends, if any.Methods: To compare the rate and indications of cesarean delivery over last 7 years. Data were collected in a retrospective manner from all the deliveries that occurred between January 1 and December 31 in 2009, 2012, 2015, in the Department of Obstetrics and Gynaecology at Jhalawar Medical College, Jhalawar, Rajasthan, India. The rate and indications of primary and repeat cesarean sections were analyzed among the live births to estimate the relative contribution of each indication to the overall increase in rate. Repeat caesarean delivery rate increased from 24.66/1000 live births in 2009 to 46.56/1000 live births in 2015. FD, scar tenderness, NPOL mainly contributed to it.Results: The cesarean delivery rate increased from 149.33/1000 live births in 2009 to 234.03/1000 live births in 2015, with an increase in primary cesarean delivery rate from 124.66/1000 live births in 2009 to 187.46/1000 live births in 2015. Fetal distress, non-progression of labor, obstetric indications contributed to this increase.Conclusions: There is significant increase in the total cesarean rate with primary cesarean due to fetal distress accounting for most of the increase