Asep K. Supriatna

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.

A Critical Protection Level Derived from Dengue Infection Mathematical Model Considering Asymptomatic and Symptomatic Classes

In this paper we formulate a model of dengue fever transmission by considering the presence of asymptomatic and symptomatic compartments. The model takes the form as a system of differential equations representing a host-vector SIR (Susceptible – Infective -Recovered) disease transmission. It is assumed that both host and vector populations are constant. It is also assumed that reinfection of recovered hosts by the disease is possible due to a wanning immunity in human body. We analyze the model to determine the qualitative behavior of the model solution and use the concept of effective basic reproduction number (p) as a control criteria of the disease transmission. The effect of mosquito biting protection (e.g. by using insect repellent) is also considered. We compute the long-term ratio of the asymptomatic and symptomatic classes and show a condition for which the iceberg phenomenon could appear.

Marine biological metapopulation with coupled logistic growth functions: The MSY and quasi MSY

In this paper we develop a mathematical model for a harvested marine biological stock. The stock consists of two discretely separated sub-stocks which are connected by the dispersal of individuals, and hence forms a metapopulation structure. The model assumes that the production function of each stock follows a logistic equation, hence the full system of the stocks governed by a couple of logistic equations. We find the formula of the maximum sustainable yield (MSY) for each sub-stock, which is extendable to a metapopulation with several discretely separated sub-populations. We also give a numerical simulation to illustrate the application of the formula for two-patch case, based on the quasi maximum sustainable yield. The simulation shows that ignoring the existence of the coupling of the system resulting in a lower total harvest from the population. This indicates a financial lost potential arising from an inappropriate recognition of a metapopulation structure in a fishery industry.

Mathematical model of temephos resistance in Aedes aegypti mosquito population

Aedes aegypti is the main vector of dengue disease in many tropical and sub-tropical countries. Dengue became major public concern in these countries due to the unavailability of vaccine or drugs for dengue disease in the market. Hence, the only way to control the spread of DF and DHF is by controlling the vectors carrying the disease, for instance with fumigation, temephos or genetic manipulation. Many previous studies conclude that Aedes aegypti may develop resistance to many kind of insecticide, including temephos. Mathematical model for transmission of temephos resistance in Aedes aegypti population is discussed in this paper. Nontrivial equilibrium point of the system and the corresponding existence are shown analytically. The model analysis have shown epidemiological trends condition that permits the coexistence of nontrivial equilibrium is given analytically. Numerical results are given to show parameter sensitivity and some cases of worsening effect values for illustrating possible conditions in t...

Mathematical Model Of Tuberculosis Transmission With Reccurent Infection And Vaccination

This paper presents a model of tuberculosis transmission with vaccination by explicitely considering the total number of recovered individuals, either from natural recovery or due to vaccination. In this paper the endemic and nonendemic fixed points, basic reproduction number, and vaccination reproduction number are given. Some results regarding the stability of the fixed points and the relation to the basic reproduction numbers are analysed. At the end of this study, the numerical computation presented and it shows that vaccination is capable to reduce the number of laten and infectious populations.

A Dengue Vaccination Model for Immigrants in a Two-Age-Class Population

We develop a model of dengue transmission with some vaccination programs for immigrants. We classify the host population into child and adult classes, in regards to age structure, and into susceptible, infected and recovered compartments, in regards to disease status. Since migration plays important role in disease transmission, we include immigration and emigration factors into the model which are distributed in each compartment. Meanwhile, the vector population is divided into susceptible, exposed, and infectious compartments. In the case when there is no incoming infected immigrant, we obtain the basic reproduction ratio as a threshold parameter for existence and stability of disease-free and endemic equilibria. Meanwhile, in the case when there are some incoming infected immigrants, we obtain only endemic equilibrium. This indicates that screening for the immigrants is important to ensure the effectiveness of the disease control.

Estimation of the Basic Reproductive Ratio for Dengue Fever at the Take-Off Period of Dengue Infection

Estimating the basic reproductive ratio ℛ 0 of dengue fever has continued to be an ever-increasing challenge among epidemiologists. In this paper we propose two different constructions to estimate ℛ 0 which is derived from a dynamical system of host-vector dengue transmission model. The construction is based on the original assumption that in the early states of an epidemic the infected human compartment increases exponentially at the same rate as the infected mosquito compartment (previous work). In the first proposed construction, we modify previous works by assuming that the rates of infection for mosquito and human compartments might be different. In the second construction, we add an improvement by including more realistic conditions in which the dynamics of an infected human compartments are intervened by the dynamics of an infected mosquito compartment, and vice versa. We apply our construction to the real dengue epidemic data from SB Hospital, Bandung, Indonesia, during the period of outbreak Nov. 25, 2008–Dec. 2012. We also propose two scenarios to determine the take-off rate of infection at the beginning of a dengue epidemic for construction of the estimates of ℛ 0: scenario I from equation of new cases of dengue with respect to time (daily) and scenario II from equation of new cases of dengue with respect to cumulative number of new cases of dengue. The results show that our first construction of ℛ 0 accommodates the take-off rate differences between mosquitoes and humans. Our second construction of the ℛ 0 estimation takes into account the presence of infective mosquitoes in the early growth rate of infective humans and vice versa. We conclude that the second approach is more realistic, compared with our first approach and the previous work.

Optimal number of fishing fleet for a sustainable fishery industry

This paper develops a mathematical model of optimal fleet number of fishing vessels. We considering two aspects related to the vessels. The first aspect is the availability and reliability of the vessels. The fishing vessel is vital equipment in the fishery industry that used to extract commercial marine species from the ocean. For this reason, to maintain a high level of profitability, a vessel should readily available when needed. Here we will consider a situation when there is a maintenance contract available from the agent. The owner of the fleet (a firm or a country) will decide the number of vessels for the fleet that should be bought from the agent together with the available maintenance service contract offer by the agent. The second aspect is the sustainability of the commercial marine stock in the ocean. In this paper we combine the two aspect simultaneously. Specifically, we will look for the number of fishing vessels that should be bought by the firm which maximizing the net profit earn by the firm from the use of the vessels to exploit the commercial fish stock while warranting that the fish stock is in the sustainable condition. We will assume that the fish species follow the logistic growth equation with and all the vesells maximize the fish catch at the maximum sustainable yield (MSY).

Modeling mass drug treatment and resistant filaria disease transmission

It has been indicated that a long term application of combined mass drug treatment may contribute to the development of drug resistance in lymphatic filariasis. This phenomenon is not well understood due to the complexity of filaria life cycle. In this paper we formulate a mathematical model for the spread of mass drug resistant in a filaria endemic region. The model is represented in a 13-dimensional Host-Vector system. The basic reproductive ratio of the system which is obtained from the next generation matrix, and analysis of stability of both the disease free equilibrium and the coexistence equilibria are shown. Numerical simulation for long term dynamics for possible field conditions is also shown.

Lymphatic Filariasis Transmission and Control: A Mathematical Modelling Approach

Lymphatic filariasis has an effect on almost 120 million individuals all over the world. The disease may cause a chronic morbidity if the persons who are infected are left untreated. It is endemic in many parts of tropical countries. To prevent worldwide parasite transmission, the World Health Organization initiated the Global Programme to Eliminate Lymphatic Filariasis (GPELF) by eliminating filarial parasites from their human hosts (Molyneux & Zagaria, 2002). Various GPELF implementations are done in many participating countries. In 2004 alone there were more than thirty countries have started elimination program and this number is still rising. Various degrees of success have emerged as a result of the implementation of this program. Although it was reported that in some places the program has interrupted the transmission, in many other places the program could not stop the transmission of the disease (WHO, 2005). It has been argued that strategic choices and operational or biological factors contribute to the success or failure of the program. In general, it is difficult to evaluate the success or the failure of a health program, especially in the beginning of the program. A mathematical model provides useful tools for planning and evaluation of control program in disease elimination (Goodman, 1994). In our earlier work (Supriatna et al., 2009) we develop a mathematical model for the transmission of Lymphatic Filariasis disease in Jati Sampurna, Indonesia. In Indonesia, the disease is already alarming. For example, the incidence of filariasis in Jati Sampurna (a district in the West Java province) is more than 1%. Within less than five years since the date of the publication confirming that Jati Sampurna is an endemic area, almost all regions nearby Jati Sampurna, and other relatively far distance areas are affected by the disease, and some of them are also categorized as endemic areas. Other cases of filarial prevalence are reported outside Java island, such as in Alor islands (the province of Nusa Tenggara Timur). On Alor islands, both B. timori and W. bancrofti are circulated, with a prevalence of up to 20% (Supali et al., 2002). Indonesia joined the GPELF since 2001 and implemented administration of a single dose regimen of diethylcarbamazine (DEC) and albendazole in endemic areas (Krentel et al., 2006). Our previous model tries to capture the effectiveness of this scenario in the attempt of controlling the spread of the disease, inspired by the transmission of the disease in Jati Sampurna. The model assumes that acute infected humans are infectious and treatment is given to a certain number of acute infected humans found from screening process. The screening is