Faculty of Mathematics and Natural Sciences

Dynamical System of Zikav Disease Spread Through The Isolation with Two Groups of Infected Population

Sun, 01 Jan 2017 00:00:00 GMT

Dynamical System of Zikav Disease Spread Through The Isolation with Two Groups of Infected Population Ainisa, Syifa N.; Jaharuddin, Jaharuddin; Nugrahani, Endar H. A viral disease ZIKAV (Zika virus) caused by a type of a Flavivirus closely related to dengue is primarily transmitted to humans by the bites of infected mosquitoes from the Aedes aegypti. Seeking to understand the dynamics of spread of the ZIKAV disease, we propose SEIIJRV1V2V3 mathematical models for vector transmission of the virus, sexual contact transmission, isolation, and conducted stability analysis. Isolation is one of the ways to disease control. This isolation is done on symptomatic-infected human population to prevent the spread of the disease. We calculate the basic reproduction number R0 and show that for R0 < 1, the disease-free equilibrium is locally asymtotically stable. In addition, it is shown that for a special case when R0 > 1, the endemic equilibrium is locally asymptotically stable. Numerical simulations are shown to support the analytical results and allow us to have a clear view of the effect of isolation.

Dynamical System for Ebola Outbreak within Vaccination Treatment

Sun, 01 Jan 2017 00:00:00 GMT

Dynamical System for Ebola Outbreak within Vaccination Treatment Irwan, Egi; Jaharuddin, Jaharuddin; Sianturi, Paian Ebola Virus Disease (EVD) is a deadly disease caused by Ebola virus. The mathematical model of Ebola virus transmission dynamics is formulated by considering both human and vector populations. This research aims to analyse dynamic systems of EVD transmission considering vaccination treatment. The equilibrium points and basic reproduction number (R0 ) are determined. There are two equilibrium points, namely, disease-free equilibrium and endemic equilibrium points. The results of model analysis show that the disease-free equilibrium is locally asymptotically stable if R0 < 1. The endemic equilibrium is found to be unique, positive and asymptotically stable if R0 > 1. Numerical simulation is performed for showing the population dynamic of both human and vector for time.

Dynamics of Cholera Transmission with hyperinfactious State of Bacteria

Fri, 01 Jan 2016 00:00:00 GMT

Dynamics of Cholera Transmission with hyperinfactious State of Bacteria Rahmi, Nur; Jaharuddin, .; Nugrahani, E.H. Cholera is an infection of the small intestine caused by the gram-negative bacterium, Vibrio cholerae. The mathematical models discussed in this study is a model of the cholera transmission with hyperinfectious state of bacteria. This study aims to modify the cholera model by involving hyperinfectious state of bacteria and taking into account the effect of vaccination, treatment and water sanitation. Then we performed the stability analysis around equilibrium point. There are two equilibria, namely disease free and endemic equilibrium. The results of model analysis shows that the number of each subpopulation of humans and bacteria is asymptotically stable around disease free equilibrium if the basic reproduction number is less than one, and asymptotically stable around the positive endemic equilibrium if the basic reproduction number is greater than one. Numerical analysis is given to justify the theorem from mathematical analysis and to see the effect of parameters variation (i.e. vaccination, treatment and water sanitation) to the number of infected humans.

Traveling wave solutions for the nonlinear boussinesq water wave equation

Fri, 01 Jan 2016 00:00:00 GMT

Traveling wave solutions for the nonlinear boussinesq water wave equation Jaharuddin, . The Boussinesq equation is one of the nonlinear evolution equations which describes the model of shallow water waves. By using the modified F-expansion method, we obatained some exact solutions. Some exact solutions expressed by hyperbolic function and exponential function are obtained. The results show that the modified F-expansion method is straightforward and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics and engineering sciences