Natural Death Rate Research Articles

Mathematical Formulation of a Co-infection Model and its Analyses for Monkeypox and HIV/AIDS Infections

The dynamics of the co-infection of monkeypox and HIV/AIDS is examined from a mathematical perspective via a deterministic 13-compartment model. This consists of the investigation of the equilibrium points, the basic reproduction numbers and the equilibrium points’ stability. The mathematical analysis reveals that the model is epidemiologically well-posed, and that the basic reproduction number for the monkeypox sub-model is a function of the likelihood of getting infected, the rate of effective contact, the infection coefficient of the monkeypox-infectious class, the monkeypox prevention measure, the progression rate from monkeypox-exposed class to monkeypox-infectious class, the natural death rate, the vaccination rate and the waning rate of the vaccine. It also depends on the recovery rate for the monkeypox-exposed class and the monkeypox-induced death rate. The analysis also reveals that the basic reproduction number for the HIV/AIDS sub-model is a function of the likelihood of getting infected, the rate of effective contact, the HIV/AIDS prevention measure, the infection coefficient of the monkeypox-infectious class, the HIV/AIDS-induced death rate, the natural death rate, the infection coefficient of AIDS-only class, and the progression rate of HIV-only class to AIDS-only. The stability analysis reveals that the disease-free equilibrium of the sub-models are globally asymptomatically stable, when the basic reproduction number is less than unity. Numerical simulations of the model reveal the effect of changes in certain parameter values on the population sizes. Increasing or lowering the values of certain parameters can significantly affect the sizes of some classes. The Maple 18 programming software was used to carry out all calculations and numerical simulations.

Optimal control of susceptible mature pest concerning disease-induced pest-natural enemy system with cost-effectiveness

Abstract This article addresses the pressing issue of pest outbreaks in India, which poses significant challenges for farmers and ecologists. A novel system is proposed for effective control that leverages natural enemies. Here, the pests are classified into juveniles and mature individuals, further categorized as susceptible or infected. The study introduces harvesting, incorporating external efforts and natural phenomena, in a pest-epidemic prey–predator system featuring a prey-stage structure. The model reveals three equilibria: trivial, boundary (indicating the absence of natural enemies), and interior equilibria. Notably, the trivial equilibrium is consistently unstable. As demonstrated by stability analysis, the survival or extinction of natural enemies hinges on control variables, including the harvesting rate, disease transmission rate, and natural death rate. Local stability is assessed using the Routh–Hurwitz criterion, while global stability is explored through the Lyapunov method. Furthermore, optimal control theory and Pontryagin’s maximum principle are applied for model optimization, unveiling crucial optimality conditions and determining the optimal harvesting rate for susceptible mature prey. Numerical computations validate theoretical insights, offering valuable guidance for formulating policies that optimize the control of susceptible adult pests within a disease-induced pest-natural enemy system, ensuring sustained cost-effectiveness.

DETERMINISTIC AND STOCHASTIC MODEL FOR THE TRANSMISSION OF LASSA FEVER

Many models on the transmission dynamics of Lasser fever were based on purely deterministic approach. This approach does not put into cognizance randomness which is inherent in disease transmission resulting from differences in immunity levels, contact patterns, hygienic practices and mutation rates among so many other possibilities.  In this work, we attempt to demonstrate the impact of uncertainties in the mode of transmission of Lassa fever by subjecting the dynamics to some white noise modeled by the Brownian motion as a Wiener process. An existing deterministic model involving the Susceptible, Exposed, Infected and Recovered (SEIR) individuals was transformed into a stochastic differential equation model by applying the procedure proposed by Allen et al (2008). The resulting system of Stochastic Differential Equations (SDE) was solved numerically using the Milstein scheme for SDEs. An algorithm for the method was developed and implemented in Python programming language. Numerical simulations of the model was done using four sets of parameters;  , representing the natural birth rate, the natural death rate , the recovering rate from infected to recovered, transmission rate from exposed to infected ,transmission rate from susceptible to exposed  are carried out to investigate the transmission dynamic of Lassa fever. The results of the simulations indicate that randomness does affect transmission of Lassa fever. We therefore recommend that factors such as social behavior, hygienic practices, contact patters, mutation rate should be considered while formulating mathematics models of disease transmission.

SEIQR Model Sensitivity and Bifurcation Analysis of SARS-CoV-2 Dynamics with International in-out Mobility Control in Indonesia

This study aims to analyze the SEIQR model for the SARS-CoV-2 dynamic by considering in-out mobility. The model construction is based on the COVID-19 response strategy implemented by the Indonesian government, then analyzing the model by determining the equilibrium point and basic reproduction number, analyzing model stability, parameter sensitivity, and bifurcation. The results show that the model has stable disease-free and disease-endemic critical points when the parameter inequality conditions based on the Routh-Hurwitz criteria are satisfied. Numerical simulations show that the system takes a long time to reach equilibrium. Furthermore, the sensitivity analysis of the basic reproduction number shows that the most sensitive parameters are natural birth and death rate susceptible, contact rate of susceptible individuals with infected individuals from local and international subjects, and rate of exposed individuals who have infected. Thus, efforts to handle COVID-19 in Indonesia can be improved by focusing on controlling international in-out mobility, so that the number of exposed individuals who have been infected can be reduced. Moreover, the bifurcation analysis shows that the system undergoes forward or backward bifurcation under disease-free conditions if certain coefficient values are satisfied based on the Castillo-Chavez and Song conditions.

Stationary distribution and extinction of a stochastic HIV/AIDS model with nonlinear incidence rate.

This paper studies a stochastic HIV/AIDS model with nonlinear incidence rate. In the model, the infection rate coefficient and the natural death rates are affected by white noise, and infected people are affected by an intervention strategy. We derive the conditions of extinction and permanence for the stochastic HIV/AIDS model, that is, if $ R_0^s < 1, $ HIV/AIDS will die out with probability one and the distribution of the susceptible converges weakly to a boundary distribution; if $ R_0^s > 1 $, HIV/AIDS will be persistent almost surely and there exists a unique stationary distribution. The conclusions are verified by numerical simulation.

Some essential oils as potential control agents for varroa mite (Varroa destructor) in infected honey bees (Apis mellifera).

Ecto-parasite, varroa mite, (Varroa destructor), is the primary pest affecting the apiculture sector globally in various regions. This study examined the toxicity of nine essential oils to Apis mellifera L. and the acaricidal impact of those oils against V. destructor. The acaricidal effects of nine essential oils, extracted from plant materials were used. In the screening experiment, 10 mg of the active ingredients of the plant material extracts were prepared in an alcohol solution with concentrations of 5%, 10%, and 15%. For each type of plant extract, five female V. destructor were transferred to a Petri dish with five worker bees incubated at 70% humidity and 33°-34° for 2 days, for each treatment four replicates were used compared to the control. Forty-eight hours following treatment, the number of dead and live mites was counted to determine the mortality rate. In the second assay experiment, the best five essential oils of the previous experiment were selected to re-assess their effectiveness on varroa mites and honeybee workers by using a concentration of 15%. Five females of V. destructor were transferred to a Petri dish with 10 adult bees and treated with the solution of the selected oils. Five replicates and control treatments were taken for each sample simultaneously. Dead and live bees were counted for each replicate at 48 hours after treatment. There were no significant differences between the concentrations used of each oil on the rate of death of mites, and its effectiveness ranged between 70.0% and 53.3% compared to the control groups. In addition, the best oil used was bitter melon, with a death rate of 80% at a concentration of 15%, while peppermint oil showed the lowest death rate of 45% at a concentration of (5%). However, all these treatments were statistically highly significant compared with the natural death rate in control (2%). In the second test, the results of the statistical analysis indicated that there were highly significant differences (P0.05 <0.0001) in the average numbers of dead varroa mites compared to the control when using a 15% concentration of five selected oils. On the other hand, there was no statistically significant difference in the honey bee workers' mortality rate between the treatment and control groups (P0.05 <0.3390), and it was relatively low for all treatments except the basil oil, where the bee mortality rate was 16% compared to the control (10%). It is clear from this experiment that bitter melon oil can be used to control varroa mites and it can be considered safe for honey bees as well as for the environment.

POPULATION PARAMETERS OF BLUE SWIMMING CRAB PORTUNUS PELAGICUS IN THE TIWORO STRAIT, SOUTHEAST SULAWESI

The blue swimming crab (Portunus pelagicus) has a wide distribution in the fishing ground waters for fishermen's activity in the Tiworo Strait. The coastal area of Tiworo Strait has quite a lot of crab potential. Therefore, it is used as one of the pilot locations for sustainable crab management projects of the Indonesian Blue Swimming Crab Association (APRI). Growth, total mortality, natural death, fishing mortality, and the exploitation rate were the population parameters of crabs that need to be known so that management can be carried out in a sustainable manner of fisheries. A study on the population parameters of crabs has been conducted in the Tiworo Strait, based on carapace width frequencies data collected from Juli to December 2021 and analyzed using FISAT (FAO-Iclarm Stock Assessment Tool) II. The total sample is 7,809 samples, where the number of male blue swimming crabs is 3,295 samples and 4,514 females. The average size of the blue swimming crab carapace width caught was 107.57 mm for males and 110.65 mm for females. The results of the study showed that the growth rate (K) was 1.01/year, the total mortality rate (Z) was 0.67/year, the natural death rate (M) was 1.25/year, and the fishing mortality rate was 0.58/year. The exploitation rate (E) of blue swimming crab was 0.86, which showed symptoms of over–exploitation, so the management of crabs in these waters must be carried out more carefully to sustain the availability of crab resource stocks. &#x0D; Keywords: blue swimming crab, width, weight, Tiworo Strait

A cell-level dynamical model for malaria parasite infection with antimalarial drug treatment

Malaria is an infectious disease caused by intracellular parasites of the genus Plasmodium. It is a major health problem around the world. In this study, a cell-level mathematical model of malaria parasites with antimalarial drug treatments is formulated and analyzed. The model consists of seven compartments for cell populations. We analyzed the qualitative behavior of the model using various techniques. The stability analysis of the parasite-free equilibrium is obtained, whereas it is locally and globally stable if the basic reproduction number R0&lt;1. The parasite persistence equilibrium point exists, and it is locally asymptotically stable if R0&gt;1. The sensitivity analysis of the basic reproduction number is computed, and the results show that the infection rate of the erythrocyte by merozoites, the average number of merozoites per ruptured infected erythrocyte cells, the natural death rate of merozoites, and the requirement rate of the uninfected erythrocyte are the most influential parameters within-host dynamics of malaria infection. Different numerical simulations are performed to supplement our analytical findings. The effect of primary tissue schizontocides, blood schizontocides, and gametocytocides on infected hepatocytes, infected erythrocytes, and gametocytes have been investigated, respectively. Finally, some counterplots are presented in order to investigate the impact of parameters on the basic reproduction number. The in-host basic reproduction number decreases as the antimalarial treatment administration increases. Therefore, increasing antimalarial treatment administration is the best way to mitigate the in-host malaria infection.

MATHEMATICAL MODELLING OF PRIMARY INFECTION TUBERCULOSIS WITH ASTHMA AS A SECOND INFECTION

Tuberculosis is an infectious disease caused by Mycobacterium Tuberculosis. Tuberculosis patients undergoing long-term tuberculosis treatment have a high risk to get asthma as a second infection. A person suffering from asthma cannot recover. Asthma therapy is only to control the development of asthma so that asthma does not get worse. In this study we discusses the spread of tuberculosis with asthma as a secondary infection. We perform the model into system of non- linear differential equation that consist of  six equation because the population divided into six sub-population which are susceptible, infected by tuberculosis, undergoing tuberculosis treatment, infected by asthma, undergoing asthma treatment and recovered from tuberculosis. From the model that has been formed, we perform the analysis to obtain the equilibrium point and the basic reproduction number. Then we show the local stability of the equilibrium point and perform simulations to provide an illustration. From the analytical result, we got that the spread influence by recruitment rate, infection rate, natural death rate, tuberculosis treatment rate and death rate because of tuberculosis.

On the stochastic engine of contagious diseases in exponentially growing populations

The purpose of this paper is to analyze the mechanism for the interplay of deterministic and stochastic models for contagious diseases. Deterministic models for contagious diseases are prone to predict global stability. Small natural birth and death rates in comparison to disease parameters like the contact rate and the removal rate ensures that the globally stable endemic equilibrium corresponds to a tiny average proportion of infected individuals. Asymptotic equilibrium levels corresponding to low numbers of individuals invalidate the deterministic results.Diffusion effects force probability mass functions of the stochastic model to possess similar stability properties as the deterministic model. Particular simulations of the stochastic model predict, however, oscillatory patterns. Small and isolated populations show longer periods, more violent oscillations, and larger probabilities of extinction.We prove that evolution maximizes the infectiousness of the disease as measured by the ability to increase the proportion of infected individuals. This holds provided the stochastic oscillations are moderate enough to keep the proportion of susceptible individuals near a deterministic equilibrium.We close our paper with a discussion of the herd-immunity concept and stress its close relation to vaccination-programs.

A simple model to control the wild mosquito with sterile release

This article studies a simple population dynamics model for interaction between wild and sterile mosquitoes. The model has at most two positive equilibria. Local stability of the positive equilibria is analyzed with respect to the total number of offspring production and the natural death rate. Numerical studies show the bi-stability of the positive equilibrium and the extinction equilibrium, as there always exist solutions that converge to the extinction equilibrium. We also discuss the threshold release rate of the sterile population to achieve the extinction of wild mosquitoes and perform sensitivity analysis with respect to the release rate.

Numerical treatment for mathematical model of farming awareness in crop pest management

The most important factor for increasing crop production is pest and pathogen resistance, which has a major impact on global food security. Pest management also emphasizes the need for farming awareness. A high crop yield is ultimately achieved by protecting crops from pests and raising public awareness of the devastation caused by pests. In this research, we aim to investigate the intricate impacts of nonlinear delayed systems for managing crop pest management (CPM) supervised by Ordinary Differential Equations (ODEs). Our focus will be on highlighting the intricate and often unpredictable relationships that occur over time among crops, pests, strategies for rehabilitation, and environmental factors. The nonlinear delayed CPM model incorporated the four compartments: crop biomass density [B(t)], susceptible pest density [S(t)], infected pest density [I(t)], and population awareness level [A(t)]. The approximate solutions for the four compartments B(t), S(t), I(t), and A(t) are determined by the implementation of sundry scenarios generated with the variation in crop biomass growth rate, rate of pest attacks, pest natural death rate, disease associated death rate and memory loss of aware people, by means of exploiting the strength of the Adams (ADS) and explicit Runge-Kutta (ERK) numerical solvers. Comparative analysis of the designed approach is carried out for the dynamic impacts of the nonlinear delayed CPM model in terms of numerical outcomes and simulations based on sundry scenarios.

Stability Analysis for the Spread of Mumps Based on SIQR Model

Mumps is an infectious disease caused by a virus that is quite dangerous because vaccine strategies often fail. In severe cases, mumps can lead to infection of the covering of the brain (15%), pancreatitis (4%), permanent deafness, and painful swelling of the testes which rarely causes infertility. In addition, genetic mutations that are continuously carried out by the virus and the movement of individuals from one area to another can result in the spread of causing an epidemic in an area. This study discusses the spread of mumps by assuming there is a population of individuals who are quarantined. In addition, it is possible to die from mumps in the presence of complications from other diseases. The purpose of this research is to look at the behavior of the system solution analytically depending on the basic reproduction number ( ) accompanied by numerical simulations on initial values with certain parameters. The SIQR model is used by assumes that individuals who have recovered will get permanent immunity against Mumps. The analysis was carried out around the disease-free equilibrium point and the endemic equilibrium point. It was found that the disease-free equilibrium point is locally asymptotically stable with conditions . This means that if the birth rate is less than the natural death rate and the contact rate between individuals infected with mumps and susceptible individuals is less than the sum of the recovery rate, death rate and quarantine rate, then the mumps outbreak will eventually disappear from the population. On the other hand, the local asymptotically stable endemic equilibrium point if . This means that if the mumps disease is about to become epidemic and infected individuals are still in the population. This can be interpreted as if the birth rate is greater than the natural death rate and the contact rate between individuals infected with mumps and susceptible individuals is greater than the sum of the recovery rate, death rate and quarantine rate then the mumps outbreak will still exist in the population. However, if the value of the quarantine rate is increased, the value will decrease and the quarantined individual population approaches the infected individual population. This means that the proposed quarantine scenario with the addition of class Q makes the system solution better. Furthermore, a simulation was carried out with the Maple 18 program.

Stability Analysis of the SIR-SI Model for Dengue Fever Transmission with Saturated Birth Rate

The SIR-SI mathematical model for the problem of dengue virus spread which has been discussed in previous studies has not involved the saturated birth rate of mosquito. This discussion aims to construct and analyze the SIR-SI model which involves competition factors in mosquito population growth so that the model used to predict the number of dengue virus infections becomes more realistic. In addition, sensitivity analysis and numerical simulations of the models that have been constructed are also discussed. The method used is a literature study using theories derived from reputable articles. The results of this discussion show that the existence of an equilibrium point and its stability depends on the basic reproduction number. If the basic reproduction number is less than one, the number of cases of dengue fever infection will decrease. However, if the basic reproduction number is more than one, the number of cases of dengue infection will not decrease and even tend to be constant at a certain number. The average parameter of bites carried out by one mosquito in all humans () is the most dominant in increasing the spread of dengue disease in humans. On the other hand, mosquitoes' natural death rate parameter () is the most dominant in reducing the spread of dengue fever in humans. This information provides input and evaluation to decision-makers in solving the problem of the spread of dengue fever.

On epidemic spreading in metapopulation networks with time-varying contact patterns.

Considering that people may change their face-to-face communication patterns with others depending on the season, we propose an epidemic model that incorporates a time-varying contact rate on a metapopulation network and its second-neighbor network. To describe the time-varying contact mode, we utilize a switched system and define two forms of the basic reproduction number corresponding to two different restrictions. We provide the theoretical proof for the stability of the disease-free equilibrium and confirm periodic stability conditions using simulations. The simulation results reveal that as the period of the switched system lengthens, the amplitude of the final infected density increases; however, the peak infected density within a specific period remains relatively unchanged. Interestingly, as the basic reproduction number grows, the amplitude of the final infected density within a period gradually rises to its maximum and then declines. Moreover, the contact rate that occupies a longer duration within a single period has a more significant influence on epidemic spreading. As the values of different contact rates progressively increase, the recovery rate, natural birth rate, and natural death rate all decrease, leading to a larger final infection density.

An introduction to modelling through a microbial interaction application

This paper describes a teaching experiment in a Numerical Methods course for Master of Science students. The experiment uses scientific papers to develop modelling studies in the context of wine fermentation microbial interactions. The course involves theoretical and laboratory classes that focus on implementing numerical methods using Matlab for Initial Value Problems and Boundary Value Problems. The students are asked to formalise the mathematical model and build their own experiments using the information provided in the papers. Additionally, a parameter estimation experiment is organised, which involves generating synthetic data and computing noisy data to estimate the natural death rate of sensitive yeast. The results show that data noise significantly affects the parameter estimate and that scaling the data can help reduce the impact of measurement errors. The presented results can be used to investigate other possible assignments, such as how the evaluation of the Jacobian affects the estimation performance and compare different optimisation algorithms.

Contagious photons: Laser dynamics and the susceptible-infected-recovered model.

We explore a complete analogy between the classic susceptible-infected-recovered epidemiological model with natural birth and death rates, and class-B laser equations. As a result, recently derived asymptotic formulas in the former context can be used to describe the switch-on intensity pulse of a laser suddenly brought well above the lasing threshold, as in active Q-switching. Conversely, the well-studied laser relaxation oscillations find a companion behavior in epidemiology, emphasizing nontrivial timescales. Finally, we discuss the possible correspondence between multistrain outbreaks and multimode lasing.

COMBINED IMPACT OF CANNIBALISM AND ALLEE EFFECT ON THE DYNAMICS OF A PREY–PREDATOR MODEL

In ecological environment, Allee effect is one of the important factors which cause significant changes to the system dynamics. In this paper, using the theory of dynamical systems, we analyze a variation of a standard cannibalistic two-dimensional prey–predator model with Holling type-II functional response in the presence of both weak and strong Allee effects. We have analyzed the impact of strong and weak Allee effects on the dynamics of a cannibalistic system, knowing the dynamics of the cannibalistic model without Allee effect. We have deduced that in the presence of cannibalism, both strong and weak Allee effects generate bistability between equilibrium points. For strong Allee effect, bistability occurs between trivial equilibrium point and predator-free equilibrium point as well as between trivial and coexistence equilibrium points. But for weak Allee effect, bistability occurs only between coexistence equilibrium points. We also pointed out that the cannibalistic system without Allee effect exhibits tristability among the trivial equilibrium point, coexistence equilibrium point having low prey concentration and coexistence equilibrium point having comparatively high prey concentration. But in the presence of strong Allee effect, cannibalistic system experiences tristability among trivial and two other stable coexistence equilibrium points. By a comprehensive bifurcation analysis, we have observed that Allee effect enriches both the local and global dynamics of the system. Here, we have reported all possible codimension-one and codimension-two bifurcations extensively by choosing cannibalism, Allee effect and predator natural death rate as the bifurcation parameters. In the analysis of bifurcations, we have explored the existence of transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation, Bogdanov–Takens bifurcation and Bautin bifurcation. Our analytical findings are validated through exhaustive numerical simulations. Finally, we have reported a comparative study between the impacts of strong and weak Allee effects on the dynamics of the cannibalistic system.

Modeling the Spread of COVID-19 Using Nonautonomous Dynamical System with Simplex Algorithm-Based Optimization for Time-Varying Parameters

The S I R D V (Susceptible, Infected, Recovered, Death, Vaccinated) compartmental model along with time-varying parameters is used to model the spread of COVID-19 in the United States. Time-varying parameters account for changes in transmission rates, people’s behaviors, safety precautions, government regulations, the rate of vaccinations, and also the probabilities of recovery and death. By using a parameter estimation based on the simplex algorithm, the system of differential equations is able to match real COVID-19 data for infections, deaths, and vaccinations in the United States of America with relatively high precision. Autoregression is used to forecast parameters in order to forecast solutions. Van den Driessche’s next-generation approach for basic reproduction number agrees well across the entire time period. Analyses on sensitivity and elasticity are performed on the reproduction number with respect to transmission, exit, and natural death rates in order to observe the changes from a small change in parameter values. Model validation through the Akaike Information Criterion ensures that the model is suitable and optimal for modeling the spread of COVID-19.

GENERAL THEORY FOR SIGNIFICANCE OF CULLING IN TWO-WAY DISEASE TRANSMISSION BETWEEN HUMANS AND ANIMALS

An epidemic model is proposed to comprehend the disease dynamics between humans and animals and back to humans with a culling intervention strategy. The proposed model is separated into two cases with two different culling rates: (1) at a per-capita constant rate and (2) constant population being culled. The global asymptotic stability of equilibria is determined in terms of the basic reproduction numbers. Further, we find that the culling rate (2) considered in the model could change the dynamics by having multiple positive equilibria. Sensitivity analysis recommends developing a strategy that promotes animals’ natural and disease-related death rates. By ranking the efficacies of various intervention strategies, we obtain that vaccination in the human population, isolation and public awareness are the largely effective control interventions. Our general theory raises concerns about both human and animal populations becoming reservoirs of the disease and affecting each other dynamically.