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In the present paper, the initial value problem for the third order partial delay differential equation with involution and nonlocal boundary condition is studied. The first order of accuracy difference schemes for the numerical solution of the third order partial delay differential equation with involution and nonlocal boundary condition is presented. The illustrative numerical results is provided. [ABSTRACT FROM AUTHOR]

In this study, we developed a mathematical model to study the transmission dynamics of HIV infection and analyzed the effect of horizontal and vertical transmission in Turkey. We fit the model by using confirmed HIV cases of both vertical and horizontal transmission between 2011 and 2018. By using the next generation operator, we obtained the basic reproduction number of the model which shows whether the disease persists or dies out in time. Further, the most sensitive parameters, that are efficient for the control of the infection, obtained by using forward normalized sensitivity index. The results obtained with the aid of mesh and contour plots. [ABSTRACT FROM AUTHOR]

Coronavirus disease 2019, also known as Covid-19, is an infectious disease that has infected more than nineteen million people all around the world. This virus is a member of coronavirus family but it is the most mortal one. It has named as 2019-nCoV by World Health Organization(WHO) after Chinese Center for Disease Control and Prevention(CDC) discovered a new coronavirus from a swab sample of a patient. As we know this pandemic started December 2019 in China, and it is still spreading and causing deaths all around the world. In this paper, we aimed to estimate the right size of epidemic. For that purpose, we chose 10 countries, which are affected by, and still fighting with this disease, to forecast the upcoming death rates by using the previous week deaths. These 10 countries are Argentina, Austria, Brazil, France, Iran, Italy, Sweden, Turkey, United Kingdom, and United States of America. We used the death data of WHO with assumption that data is accurate. For this estimation, firstly, we used the assumption that the reported death delay distributed according to a gamma distribution. Then, we used a binomial distribution for assumption of deaths. This binomial formula led us to find a posterior distribution which is an extension of Bayes' theorem for death ratio. Lastly, we compared our estimations with real data. [ABSTRACT FROM AUTHOR]

In many engineering and science fields sensitivity analysis has become highly interesting. For the mathematical modeling of biological phenomena, researchers use sensitivity and uncertainty analysis because of its usefulness for defining important parameters for performance of the model. It can also help in the process of experimental analysis, reducing model order, estimating parameters, taking decisions or developing recommendations for decision-makers. Here, we illustrated the use of the local sensitivity analysis to explain the effect of various parameters on a threshold parameter, R0, resulting from the study of a dynamics model inside the human-host. And it is confirmed from computed elasticity indices that the most sensitive parameter to basic reproduction number is (vector contact rate) followed by rates of transmission. Moreover, a detailed parameter estimation of the model parameters and model fitting presented with the use of field data cases from Northern Nigeria using least-square fitting method. Finally, the sensitivity analysis results shows that improving the rate of environmental hygiene and facial cleanliness will attract a consequential decrease in the size of basic reproduction number, which results in the declination of the disease transmission. [ABSTRACT FROM AUTHOR]

In this research paper, we extended an existing SIR epidemic integer model containing two strains and two vaccinations by using a system of fractional ordinary differential equations in the sense of Caputo derivative of order σ ∈ (0, 1]. Four equilibrium points were established which are disease free equilibrium, strain1 disease free equilibrium, strain2 disease free equilibrium and endemic equilibrium. Explicit analysis of the equilibrium points of the model was given by applying fractional calculus and Routh-Hurwitz criterion. Stability analysis of the equilibrium points was carried out by employing the Jacobian matrix. Numerical simulations were iterated to support the analytic results. It was shown that when both of the reproduction numbers R1 and R2 are less than one, the disease die out over time and while it persist in relation to the thriving strain when either of them is greater than one. We also studied the effect of vaccine. With the fractional order technique, the memory effect of the system is made visible and hence easier to predict. [ABSTRACT FROM AUTHOR]

In this paper, a fractional order mathematical model is constructed to study the dynamics of coronavirus. The model consists of a system of eight non-linear fractional order differential equations in Caputo sense. Existence and uniqueness of the solution of the model are studied. [ABSTRACT FROM AUTHOR]

The aim of this paper is to show how North Cyprus fights Covid-19 by using the basic reproduction number R0 and effective reproduction number Rt. According to the Wikipedia page with title Covid-19 pandemic in Northern Cyprus, North Cyprus is the first country in Europe to free from Covid-19. One of the important reasons of this is that the government decided for tackling Covid-19 pandemic by using R0 and Rt daily. For R0, we constructed a new SEIR model by using the real data for North Cyprus. From March 11, 2020 to May 15, 2020 R0, varies from 0.65 to 2.38. [ABSTRACT FROM AUTHOR]

Covid-19 is the most recently discovered infectious disease affecting the countries all around the world. SARS-CoV-2, which is a member of coronavirus family, is the virus that makes the infection. Until the 28th of September 2020, almost 34 million people infected by the virus and more than 1 million people died all around the world. One of the most discussed ideas about the disease to die out is vaccination. In our study, we tried to analyze this idea and show the effect of vaccine for Covid-19. Our work starts with constructing an SVI mathematical model. Afterwards, we made the analyze of our model. Then, by taking into consideration of incoming passengers and precautions that should be taken, we used the vaccination idea with changing the percentage of vaccinated people in a population. In last section, we used numerical simulations to support our idea. In our work, we conclude that vaccination is substantially effective if we consider the other things that affect the disease which is incoming passengers and precautions like wearing mask, maintaining social distance, etc. [ABSTRACT FROM AUTHOR]

Erlang distribution is continuous probability distribution that has application in several field such as stochastic process and mathematical biology, due to its relation with exponential and gamma distribution. In the sense that, the duration of the successive calls follows the Erlang distribution, if individual telephone calls is exponentially distributed to the time period. In this study, Bayesian estimation was employed in the estimation of scale parameter of weighted Erlang distribution. The posterior distribution was derived under two informative priors, which are inverse exponential and inverse chi -square prior. The Bayes estimate and their relative posterior risks were derived under the assumption of Squared Error Loss Function (SELF), and Precautionary Loss Function (PLF). A Monte Carlo simulation was carried out in order to obtain the numerical value of the estimates. It was observed that SELF performs best when inverse exponential prior is used. [ABSTRACT FROM AUTHOR]

In the present paper, the initial value problem for the third order partial differential equation with time delay is studied. The first and second order of accuracy difference schemes for the numerical solution of the third order partial differential equation with time delay are presented. The illustrative numerical results are provided. [ABSTRACT FROM AUTHOR]

In the present paper, the initial value problem for the third order partial differential equations with time delay in a Hilbert space with self-adjoint positive definite operator is investigated. The main theorem on stability of this problem is established. The application of this theorem is presented. [ABSTRACT FROM AUTHOR]

In the present paper, stability of initial-boundary value problem for the system of partial differential equations for observing HIV mother to child transmission epidemic models is studied. Applying operator approach, theorems on stability of this problem and of difference schemes for approximate solutions of this problem are established. The generality of the approach considered in this paper, however, allows for treating a wider class of multidimensional problems. Numerical results are provided. [ABSTRACT FROM AUTHOR]

In this work, two models with and without vaccine are constructed. Delay effect is considered for these model. When we are talking about delay on this paper we mean that incubation period. If we have enough vaccine the effect of delay is very tiny. However if there is no vaccine you can see the effect of delay. Two equilibria which are disease free and endemic equilibriums are found and using Lyapunov function, the global stabilities of each equilibria are shown for both models. For the first model it is found that DFE E0 is globally asymtotically stable when R¹0 < 1 and endemic equilibrium E1 is always asymtotically stable. With using similar method E0 is asymptotically stable when R²0 < 1 and E1 is always globally asymptotically stable for model 2. In the last section numerical simulations are given for both models. [ABSTRACT FROM AUTHOR]

We present a mathematical model of cancer growth in the bladder that includes the immune cells, BCG, immune checkpoints and drug therapy (checkpoint inhibitor) in the form of a control function. The control function blocks the action of immune checkpoints on the immune system. Our aim here is to apply optimal control theory to find a control strategy that will minimize the number of cancer cells in the bladder and cost of control. Existence of the optimal control is stated and Pontryagin's maximum principle is used to characterize the nature of the control function. The optimality system obtained gives a two-point boundary value problem; hence, we use the forward-backward sweep method to present the numerical solutions of the system. The optimality conditions and characterization of the control are discussed. [ABSTRACT FROM AUTHOR]