Communication in Biomathematical Sciences

Qualitative Behavioral Analysis in Mosquito Dynamics Model with Wolbachia

Dani Suandi — 2023-01-25

The Aedes Aegypti mosquito is the primary vector that can transmit diseases to humans such as zika, dengue fever, chikungunya, and yellow fever. This mosquito species is controlled to reduce the frequency of its bites on humans. Several methods have been developed to control mosquito populations, ranging from natural insecticides to artificial ones. However, the impact of these insecticides leads to resistance. Wolbachia
bacteria as a promising alternative in reducing the spread of viruses on humans due to free resistance. This work constructs a genetic population model in the form of differential equation system that describes mosquito
population dynamics by involving random mating between mosquito populations with and without Wolbachia bacteria. The stability of the equilibrium was analyzed locally here. Numerical simulations and sensitivity analyzes are presented to confirm the analytical results and investigate the effect of the parameters involved on the model. The results show that the success of the expansion of Wolbachia-infected mosquitoes depends on the fitness level of the mosquito species. The more Wolbachia mosquitoes are released into nature, the more possibility this mosquito expansion will be successful.

A Nonstandard Numerical Scheme for a Predator-Prey Model Involving Predator Cannibalism and Refuge

Maya Rayungsari — 2023-07-01

In this study, we implement a Nonstandard Finite Difference (NSFD) scheme for a predator-prey model involving cannibalism and refuge in predator. The scheme which is considered as a discrete dynamical system is analyzed. The performed analysis includes the determination of equilibrium point and its local stability. The system has four equilibrium points, namely the origin, the prey extinction point, the predator extinction point, and the coexistence point, which have exactly the same form and existence conditions as those in continuous system. The local stability of each first three equilibrium points is consistent with the one in continuous system. The stability of the coexistence point depends on the integration time step size. Nevertheless, the NSFD scheme allows us to choose the integration time step size for the solution to converge to a feasible point more flexible than the Euler and 4th order Runge-Kutta schemes. These are shown via numerical simulations.

Pongo Abelii Population Model with Changes in Carrying Capacity

Karsten Maynard Jabriel — 2023-07-01

Pongo abelii is an endangered orangutan species. The reduction of Pongo abelii can be caused by the removal or loss of orangutans from the population and habitat loss. In general, research on population dynamics with changing carrying capacity is rarely done and it is simulated in this study. We adopted the Verhulst logistic model to model the population dynamics of Pongo abelii. This study aimed to see the effect of increasing the carrying capacity on the population of the endangered Pongo abelii species. From the results of this study, it is concluded that for areas other than Tripa Swamp, Siranggas/Batu Ardan, and East Batang Toru (Sarulla), the addition of carrying capacity is one of the effective options that is urgently needed to maintain a large population of orangutans. For the Tripa Swamp, Siranggas/Batu Ardan, and East Batang Toru (Sarulla) areas, suppressing the number of orangutans loss population is needed to maintain the population, which consists of poaching as trade, conflict killing, hunting/food, wounding, and fire. The results of this study can provide suggestions for tackling the declining population of Pongo abelii species by prohibiting the expansion of the species’ habitat

A Mathematical Model and Study of Viral Hepatitis among Population in Afghanistan

A. H. Hasmani — 2023-07-04

Despite availability of strategies against viral hepatitis, it is still a serious disease, which millions of people are already infected with, hence it yet needs to be focused on. As an attempt, we formulated a single mathematical model describing behaviour of all strains of viral hepatitis, presented in the literature. The basic reproduction number(R_0) at disease free equilibrium point is computed, feasible region has been determined. For local stability of the model, R_0 has been taken into account and for global stability of the model Lyapunov method is followed. The model is then applied to the data available for Afghanistan for the year 2020. Based on the data, values of the parameters are estimated, using Minimum Mean Absolute Error (MAE) method. Numerical simulation is performed to support the model and then the results are plotted and represented graphically. One-at-a-time sensitivity analysis (OAT) method is used for sensitivity analysis and involved parameters have been examined for the propose of sensitivity analysis, it indicated that infection rates of acute and chronic states of viral hepatitis are the most sensitive and critical parameters. It has been observed that large number of populations can become infected followed by small increment of infection rates. It has also been noticed that, entire population of Afghanistan could become infected, if no prevention measures were taken. The model presented in this paper is useful for forecasting outbreak by viral hepatitis and it can further be modified by including prevention measures.

Assessing The Impact of Medical Treatment and Fumigation on The Superinfection of Malaria: A Study of Sensitivity Analysis

Bevina D. Handari — 2023-07-04

Malaria is a disease caused by the parasite Plasmodium, transmitted by the bite of an infected female Anopheles. In general, five species of Plasmodium that can cause malaria. Of the five species, Plasmodium falciparum and Plasmodium vivax are two species of Plasmodium that can allow malaria superinfection in the human body. Typically, the popular intervention for malaria eradication is the use of fumigation to control the vector population and provide good medical services for malaria patients. Here in this article, we formulate a mathematical model based on a host-vector interaction. Our model considering two types of plasmodium in the infection process and the use of medical treatment and fumigation for the eradication program. Our analytical result succeeds in proving the existence of all equilibrium points and how their existence and local stability criteria depend not only on the control reproduction number but also in the invasive reproduction number. This invasive reproduction number represent how one plasmodium can dominate other plasmodium. Our sensitivity analysis shows that fumigation is the most influential parameter in determining all control reproduction numbers. Furthermore, we find that the order in which numerous intervention measures are taken will be very crucial to determine the level of success of our malaria eradication program.

Data-Driven Generating Operator in SEIRV Model for COVID-19 Transmission

Nadia — 2023-07-04

The COVID-19 (SARS-CoV-2) vaccine has been extensively implemented through large-scale programs in numerous countries as a preventive measure against the resurgence of COVID-19 cases. In line with this vaccination effort, the Indonesian government has successfully inoculated over 74% of its population. Nevertheless, a significant decline in the duration of vaccine-induced immunity has raised concerns regarding the necessity of additional inoculations, such as booster shots. Prior to proceeding with further inoculation measures, it is imperative for the government to assess the existing level of herd immunity, specifically determining whether it has reached the desired threshold of 70%. To shed light on this matter, our objective is to ascertain the herd immunity level following the initial and subsequent vaccination programs, while also proposing an optimal timeframe for conducting additional inoculations. This study utilizes COVID-19 data from Jakarta and employs the SEIRV model, which integrates time-dependent parameters and incorporates an additional compartment to represent the vaccinated population. By formulating a dynamic generator based on the cumulative cases function, we are able to comprehensively evaluate the analytical and numerical aspects of all state dynamics. Simulation results reveal that the number of individuals protected by the vaccine increases following the vaccination program; however, this number subsequently declines due to the waning effect of the vaccine. Our estimates indicate that the vaccination program in Jakarta has achieved herd immunity levels exceeding 70% from October 2021 to February 2022, thus underscoring the necessity of rolling out further inoculations no later than February 2022.