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Mathematical Modeling of the Transmission Dynamics of Syphilis Disease Using Differential Transformation Method
Issue:
Volume 5, Issue 2, June 2020
Pages:
47-54
Received:
21 February 2020
Accepted:
9 March 2020
Published:
24 March 2020
Abstract: In this work, we developed a mathematical model for the transmission dynamics of the Syphilis disease under some assumptions made. The method of differential transformation is employed to compute an approximation to the solution of the non-linear systems of differential equations for the transmission dynamic of the disease model. The differential transformation method is a semi-analytic numerical method or technique, which depends on Taylor series and has application in many areas including Biomathematics. The disease-free equilibrium of the syphilis model is analyzed for local asymptotic stability and the associated epidemic basic reproduction number R0 is less than unity. It is also known that the global dynamics of the disease are completely determined by the basic reproduction number. Sensitivity analysis is performed on the model’s parameters to investigate the most sensitive parameters in the dynamics of the disease, for control and eradication.
Abstract: In this work, we developed a mathematical model for the transmission dynamics of the Syphilis disease under some assumptions made. The method of differential transformation is employed to compute an approximation to the solution of the non-linear systems of differential equations for the transmission dynamic of the disease model. The differential t...
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Population Dynamics of Two Mutuality Preys and One Predator with Harvesting of One Prey and Allowing Alternative Food Source to Predator
Solomon Tolcha,
Boka Kumsa Bole,
Purnachandra Rao Koya
Issue:
Volume 5, Issue 2, June 2020
Pages:
55-64
Received:
1 January 2020
Accepted:
13 March 2020
Published:
31 March 2020
Abstract: In this paper, the interactions among three species populations are considered. The system includes two mutuality preys and one predator. The second prey is harvested. While dependent on preys, the predator has an alternative food source also. The three species interaction can be described as a food chain in which two preys help each other but the predator attacks both the preys according to type I and II functional responses respectively. These population interactions are modeled mathematically using ordinary differential equations. It is shown that the solution of the model is both positive and bounded. The equilibrium points of the model are found and they are analyzed to identify a threshold that will guarantee the coexistence of the populations. Positive equilibrium points of the system are identified and their local and global stability analysis is carried out. Numerical simulation study of the model is conducted to support the results of the mathematical analysis. It is pointed out that as long as harvesting rate on the prey population is smaller than its intrinsic growth rate the coexistence of the system can be achieve. The results of the analysis and the discussion of the population dynamics is lucidly presented in the text of the paper.
Abstract: In this paper, the interactions among three species populations are considered. The system includes two mutuality preys and one predator. The second prey is harvested. While dependent on preys, the predator has an alternative food source also. The three species interaction can be described as a food chain in which two preys help each other but the ...
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Mathematical Model of the Transmission Dynamics of Lassa Fever Infection with Controls
Sambo Dachollom,
Chinwendu Emilian Madubueze
Issue:
Volume 5, Issue 2, June 2020
Pages:
65-86
Received:
23 February 2020
Accepted:
16 March 2020
Published:
31 March 2020
Abstract: After fifty years of documented history of Lassa fever in Nigeria, the country is still recording the highest record of outbreaks worldwide with Ebonyi state been the most affected state in the whole of Eastern Nigeria. This has activated interventional measures coming from both the government and scholars. The government through the Nigeria Centre for Disease Control (NCDC) and other sister agencies has activated an emergency response by establishing management centres which operates in association with specialist teaching hospitals in the endemic states, the scholars on the other hand are approaching the menace from two broad but complimentary aspects of sciences namely; the medical sciences and the natural sciences. The medical researchers focus more on developing reliable laboratory diagnosis, quicker methods of identifying the LASV and drug/vaccine formulation, the natural scientist (Bio-mathematicians) on the other hand focuses on modeling the dynamic transmission and controls among the various hosts of the LASV. This paper presents a mathematical model that tracks the transmission dynamics of Lassa fever in two different but complimentary host; human host and rat host. The model incorporates a death infectious human compartment capable of infecting susceptible population. The model analysis, basic reproduction number, existence of endemic equilibrium and bifurcation analysis was analyzed. It was established that the disease-free equilibrium point is stable when the reproduction number, R0<1 and the disease dies out. Numerical simulation was carried out with parametized data for Ebonyi State, Eastern Nigeria. The numerical simulation reveals that sensitization of susceptible population, quarantined of exposed humans and isolation of infectious humans, the practice of best international safety measures among health care workers, establishment of more Lassa fever diagnostic centres and precautionary burial practices remains the best control measures in the dynamic transmission of Lassa fever.
Abstract: After fifty years of documented history of Lassa fever in Nigeria, the country is still recording the highest record of outbreaks worldwide with Ebonyi state been the most affected state in the whole of Eastern Nigeria. This has activated interventional measures coming from both the government and scholars. The government through the Nigeria Centre...
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Comparative Study of Various Methods of Handling Missing Data
Fredrick Ochieng’ Odhiambo
Issue:
Volume 5, Issue 2, June 2020
Pages:
87-93
Received:
2 October 2019
Accepted:
13 April 2020
Published:
30 April 2020
Abstract: Scientific literature lack straight forward answer as to the most suitable method for missing data imputation in terms of simplicity, accuracy and ease of use among the existing methods. Exploration various methods of data imputation is done, and then a robust method of data imputation is proposed. The paper uses simulated data sets generated for various distributions. A regression function on the simulated data sets is used and obtained the residual standard errors for the function obtained. Data are randomly from the set of independent variables to create artificial data-non response and use suitable methods to impute the missing data. The method of Mean, regression, hot and cold decking, multiple, median imputation, list wise deletion, EM algorithm and the nearest neighbour method are considered. This paper investigates the three most common traditional methods of handling missing data to establish the most optimal method. The suitability is hence determined by the method whose imputed data sample characteristic does not vary considerably from the original data set before imputation. The variation is here determined using the regression intercept and the residual standard error. R statistical package has been used widely in most of the regression cases. Microsoft excel is used to determine the correlation of columns in hot decking method; this is because it is readily available as a component of Microsoft package. The results from data analysis section indicated an intercept and R-squared values that closely mirror those of original data sets, suggesting that median imputation is a better data imputation method among the conventional methods. This finding is important from the research point of view, given the many cases of data missingness in scientific research. Finding and using the median is simple and as such most researchers have a ready tool at hand for handling missing data.
Abstract: Scientific literature lack straight forward answer as to the most suitable method for missing data imputation in terms of simplicity, accuracy and ease of use among the existing methods. Exploration various methods of data imputation is done, and then a robust method of data imputation is proposed. The paper uses simulated data sets generated for v...
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Mathematical Modelling of Deforestation of Forested Area Due to Lack of Awareness of Human Population and Its Conservation
Ararso Hussen Teru,
Purnachandra Rao Koya
Issue:
Volume 5, Issue 2, June 2020
Pages:
94-104
Received:
3 January 2020
Accepted:
10 March 2020
Published:
12 May 2020
Abstract: As the density of human population increases the forest density will be highly affected by population from time to time for agricultural, industrial, economic purpose, and etc. Because of lack of awareness about the importance of forestry resources, the human populations clear forests for different purposes. Keeping this in mind, a nonlinear mathematical model is proposed and analyzed to study the deforestation of forest resources due to lack of clear information about utility of the forest as well as to increase forestry resources by plantation on the conservation of forestry resources. The model is in the form of ordinary differential equations. The result of this study shows that as the density of population as well as population pressure increases, the cumulative density of forest resources decreases. Reversely, the test of supporting human awareness on the importance of forest resources for global purposes show that as awareness of human population increases the declaration of forest resources decreases. In addition to this, increasing the density of forest resources through plantation may replace the clear-cut of forest area. This help the conservation carried out to in force the pressure of human population to save the forest density and forest habit. For these findings analytical and numerical analyses are performed.
Abstract: As the density of human population increases the forest density will be highly affected by population from time to time for agricultural, industrial, economic purpose, and etc. Because of lack of awareness about the importance of forestry resources, the human populations clear forests for different purposes. Keeping this in mind, a nonlinear mathem...
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SEIRS Mathematical Model for Malaria with Treatment
Alemu Geleta Wedajo,
Purnachandra Rao Koya,
Dereje Legesse Abaire
Issue:
Volume 5, Issue 2, June 2020
Pages:
105-117
Received:
1 January 2020
Accepted:
5 May 2020
Published:
28 May 2020
Abstract: In this paper a deterministic mathematical model for the spread of malaria in human and mosquito populations are presented. The model has a set of eight non – linear differential equations with five state variables for human and three for mosquito populations respectively. Susceptible humans can be infected when they are bitten by an infectious mosquito. They then progress through the exposed, infectious, treatment and recovered or immune classes before coming back to the susceptible class. Susceptible mosquitoes can become infected when they bite infectious humans, and once infected they move through exposed and infectious class. However, mosquitoes once infected will never recover from the disease during their lifetime. That is, infected mosquitoes will remain infectious until they die. Formula for the basic reproduction number R0 is established and used to determine whether the disease dies out or persists in the populations. It is shown that the disease – free equilibrium point is locally asymptotically stable using the magnitude of Eigen value and Routh – Hurwitz stability Criterion. Result and detailed discussion of the analysis as well as the simulation study is incorporated in the text of the paper lucidly.
Abstract: In this paper a deterministic mathematical model for the spread of malaria in human and mosquito populations are presented. The model has a set of eight non – linear differential equations with five state variables for human and three for mosquito populations respectively. Susceptible humans can be infected when they are bitten by an infectious mos...
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Modeling and Stability Analysis of Host-parasite Population Dynamics
Geremew Kenassa Edessa,
Purnachandra Rao Koya
Issue:
Volume 5, Issue 2, June 2020
Pages:
118-128
Received:
1 January 2020
Accepted:
5 May 2020
Published:
28 May 2020
Abstract: In this study, a mathematical model is developed to explore the population dynamics of two host species. Both the hosts depend on the same resources and the availability of such resources is limited in nature. If the host populations increase abnormally the limited natural resources will be used up. Hence, the concept of parasite is brought in to the picture to regulate the host populations. The parasite is a mechanism that reduces the host populations. However, on one hand if the parasite attacks more the hosts may extinct and on the other hand if the parasite do not attack then the host populations may increase and resource may be used up. Hence, the parasite is expected to maintain a balance so that neither the host populations nor the resources extinct. Here, both the hosts are classified in to susceptible and infected and hence the model comprises of four populations: Susceptible Host–1, Infected Host–1, Susceptible Host–2 and Infected Host–2. Thus, the mathematical model comprises of a system of four first order non-linear ordinary differential equations. Mathematical analysis of the model is conducted. Positivity and boundedness of the solution have been verified and thus shown that the model is physically meaningful and biologically acceptable. Equilibrium points of the model are identified and stability analysis is conducted. Simulation study is conducted in order to support the mathematical analysis using software packages Mat lab and DeDiscover.
Abstract: In this study, a mathematical model is developed to explore the population dynamics of two host species. Both the hosts depend on the same resources and the availability of such resources is limited in nature. If the host populations increase abnormally the limited natural resources will be used up. Hence, the concept of parasite is brought in to t...
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