Edy Soewono

A two-age-classes dengue transmission model

In this paper, we discuss a two-age-classes dengue transmission model with vaccination. The reason to divide the human population into two age classes is for practical purpose, as vaccination is usually concentrated in one age class. We assume that a constant rate of individuals in the child-class is vaccinated. We analyze a threshold number which is equivalent to the basic reproduction number. If there is an undeliberate vaccination to infectious children, which worsens their condition as the time span of being infectious increases, then paradoxically, vaccination can be counter productive. The paradox, stating that vaccination makes the basic reproduction number even bigger, can occur if the worsening effect is greater than a certain threshold, a function of the human demographic and epidemiological parameters, which is independent of the level of vaccination. However, if the worsening effect is to increase virulence so that one will develop symptoms, then the vaccination is always productive. In both situations, screening should take place before vaccination. In general, the presence of class division has obscured the known rule of thumb for vaccination.

An optimal control problem arising from a dengue disease transmission model

An optimal control problem for a host-vector Dengue transmission model is discussed here. In the model, treatments with mosquito repellent are given to adults and children and those who undergo treatment are classified in treated compartments. With this classification, the model consists of 11 dynamic equations. The basic reproductive ratio that represents the epidemic indicator is obtained from the largest eigenvalue of the next generation matrix. The optimal control problem is designed with four control parameters, namely the treatment rates for children and adult compartments, and the drop-out rates from both compartments. The cost functional accounts for the total number of the infected persons, the cost of the treatment, and the cost related to reducing the drop-out rates. Numerical results for the optimal controls and the related dynamics are shown for the case of epidemic prevention and outbreak reduction strategies.

Fourth order non-linear systems arising in combined free and forced convection flow of a second order fluid

Solutions to the fourth-order non-linear systems arising in combined free and forced convection flow of a second-order fluid, over a stretching sheet, are obtained. Existence (or non-existence) and uniqueness (or non-uniqueness) results of the problem are obtained and discussed. Moreover, ranges of parametric values are obtained for which the system has a unique pair of solutions, a double pair of solutions, and infinitely many monotonically decaying solutions at infinity.

A with-in host Dengue infection model with immune response

A model of viral infection of monocytes population by Dengue virus is formulated here. The model can capture phenomena that dengue virus is quickly cleared in approximately 7 days after the onset of the symptoms. The model takes into account the immune response. It is shown that the quantity of free virus is decreasing when the viral invasion rate is increasing. The basic reproduction ratio of model without immune response is reduced significantly by adding the immune response. Numerical simulations indicate that the growth of immune response and the invasion rate are very crucial in identification of the intensity of infection.

Existence and nonuniqueness of solutions of a singular nonlinear boundary-layer problem

Abstract Sufficient conditions for existence and nonuniqueness of positive solutions of the singular boundary value problem g ( x ) g ″( x ) + h ( x ) = 0, − k ⩽ x k > 0, g ′(− k ) = C , g (1) = 0 are obtained. Also, it is proved that the solutions with g(−k) > −Ck ( for C and g(−k) > ( k 2 ) √ −2h(−k) ( for C > 0) are unique. Furthermore, it is shown numerically that for h ( x ) = x there are exactly two Solutions for the problem.

On solutions of some singular, non-Linear differential equations arising in boundary layer theory

Abstract Solutions for a class of singular, non-linear, second-order differential equations arising in boundary layer theory with suction/injection, when Crocco variables are employed, are obtained. Existence, uniqueness, and analyticity results are established for boundary conditions corresponding to flow of a uniform stream past a semi-infinite flat plate (classical problem of Blasius) and for the flow behind weak expansion. Since the standardization technique (in Refs. [8, 9, 11]) does not work, a new technique is developed and used in proving existence and uniqueness theorems. Furthermore, the analytical solutions are compared with the numerical ones.

An Investigation on Gas Lift Performance Curve in an Oil-Producing Well

The main objective in oil production system using gas lift technique is to obtain the optimum gas injection rate which yields the maximum oil production rate. Relationship between gas injection rate and oil production rate is described by a continuous gas lift performance curve (GLPC). Obtaining the optimum gas injection rate is important because excessive gas injection will reduce production rate, and also increase the operation cost. In this paper, we discuss a mathematical model for gas lift technique and the characteristics of the GLPC for a production well, for which one phase (liquid) is flowing in the reservoir, and two phases (liquid and gas) in the tubing. It is shown that in certain physical condition the GLPC exists and is unique. Numerical computations indicate unimodal properties of the GLPC. It is also constructed here a numerical scheme based on genetic algorithm to compute the optimum oil production.

Optimization of Gas Injection Allocation in a Dual Gas Lift Well System

1. Abstract Optimization problem for oil production in a multi gas lift wells system is discussed. The main problem is to identify allocation of gas injection for each well to obtain maximum total oil production. The gas injection rate is constrained by a maximum limit. Oil production rate is a nonlinear function of gas injection rate, which is unknown explicitly. In existing approaches, the nonlinear function is estimated from empirical or numerical simulation data, by curve fltting using regression method, or estimated by piecewise linear function. We developed here, a mathematical model for gas lift well system, where the ∞uid ∞ow in reservoir and pipes consists of liquid and gas, so the conditions represent two phase ∞ow phenomena. Relationship between gas injection and oil production is given implicitly from the model. We have also developed a computation scheme to solve the optimization problem. Considering complexity of the problem, computation scheme is developed based on genetic algorithms. Our results show quite good estimation for optimum solution. The approach also gives better quality prediction over existing approach, since all computation results come from the model, not from regression or interpolation. 2. Keywords: Gas Lift, Gas Lift Performance Curve, Constrained Optimization, Genetic Algorithm.

Advances in mosquito dynamics modeling

It is preliminarily known that Aedes mosquitoes be very close to humans and their dwellings also give rises to a broad spectrum of diseases: dengue, yellow fever, and chikungunya. In this paper, we explore a multi-age-class model for mosquito population secondarily classified into indoor–outdoor dynamics. We accentuate a novel design for the model in which periodicity of the affecting time-varying environmental condition is taken into account. Application of optimal control with collocated measure as apposed to widely used prototypic smooth time-continuous measure is also considered. Using two approaches, least square and maximum likelihood, we estimate several involving undetermined parameters. We analyze the model enforceability to biological point of view such as existence, uniqueness, positivity, and boundedness of solution trajectory, also existence and stability of (non)trivial periodic solution(s) by means of the basic mosquito offspring number. Some numerical tests are brought along at the rest of the paper as a compact realistic visualization of the model. Copyright

A model for the spatial transmission of dengue with daily movement between villages and a city

Dengue is a re-emergent vector-borne disease affecting large portions of the worlds population living in the tropics and subtropics. The virus is transmitted through the bites of female Aedes aegypti mosquitoes, and it is widely believed that these bites occur primarily in the daytime. The transmission of dengue is a complicated process, and one of the main sources of this complexity is due to the movement of people, e.g. between home and their places of work. Hence, the mechanics of disease progression may also differ between day and night. A discrete-time multi-patch dengue transmission model which takes into account the mobility of people as well as processes of infection, recovery, recruitment, mortality, and outbound and return movements is considered here. One patch (the city) is connected to all other patches (the villages) in a spoke-like network. We obtain here the basic reproductive ratio (ℛ0) of the transmission model which represents a threshold for an epidemic to occur. Dynamical analysis for vector control, human treatment and vaccination, and different kinds of mobility are performed. It is shown that changes in human movement patterns can, in some situations, affect the ability of the disease to persist in a predictable manner. We conclude with biological implications for the prevention and control of dengue virus transmission.