Narrow Results

This study examines the SPIMR rumor propagation model using the homotopy perturbation transform method (HPTM) with Atangana–Baleanu Caputo (ABC) fractional derivative. The existence and uniqueness of the solution are studied by using Picard–Lindelöf method. The basic reproduction number is calculated via the next-generation matrix method. Both rumor-free and rumor-endemic equilibrium points are determined. The findings, supported by graphical representations, demonstrate the effectiveness of HPTM in solving the SPIMR rumor propagation model, exhibiting its practical relevance in addressing rumor propagation.

In the entire world, pneumonia is one of the leading causes of death, which is particularly dangerous for young children (those under five years old) and the elderly (those over 65). A deterministic susceptible, vaccinated, exposed, infected, and recovered (SVEIR) model is used in this work to mathematically study the dynamics of pneumonia disease and examine stability analysis, basic reproduction numbers, and equilibrium points of dynamical systems theory models. Spatial equilibria are studied to model disease-free equilibria that are locally asymptotic stable. Numerical simulations of the model have been carried out using MATLAB21. The SVEIR flow and its variables for different parameter sets have been studied through numerical simulations. The solution to the issue is provided through the use of illustrated and explicated results. According to research findings, if vaccination rates rise over the necessary vaccination ratio, the sickness will finally vanish from the community.

The Susceptible, Infected and Recover (SIR) model is a very simple model to estimate the dynamics of an epidemic. In the current pandemic due to Covid-19, the SIR model has been used to estimate the dynamics of infection for various infected countries. Numerical solutions are used to obtain the value of parameters for the SIR model. The maximum and minimum basic reproduction number (14.5 and 2.3) are predicted to be in Turkey and China, respectively.

The Susceptible, Infected and Recover (SIR) model is a very simple model to estimate the dynamics of an epidemic. In the current pandemic due to Covid-19, the SIR model has been used to estimate the dynamics of infection for Bangladesh, India, Pakistan and compared with that of China. Numerical solutions are used to obtain the value of parameters for the SIR model. It is predicted that the active case in Pakistan due to the SARS-CoV-2 will be comparable with that in China whereas it will be low for Bangladesh and India. The basic reproduction number, with fluctuations, for South Asian countries are predicted to be less than that of China. The susceptible population is also estimated to be under a million for Bangladesh and India but it becomes very large for Pakistan.

COVID-19 pandemic has been raging all around the world for almost a year now, as of November 1, 2020. In this paper, we try to analyze the variation of the COVID-19 pandemic in different countries in the light of some modifications to the susceptible-infected-recovered (SIR) model. The SIR model was modified by taking time-dependent rate parameters. From this modified SIR model, the basic reproduction number, effective reproduction number, herd immunity, and herd immunity threshold are redefined. The re-outbreak of the COVID-19 is a real threat to various countries. We have used the above-mentioned quantities to find the reasons behind the re-outbreak of this disease. Also, the effectiveness of herd immunity to prevent an epidemic has been analyzed with respect to this model. We have also tried to show that there are certain universal aspects in the spread and containment of the disease in various countries for a short period of time. Finally, we have also analyzed the current pandemic situation in India and have attempted to discuss the possibilities in order to predict its future behavior using our model.

Amid growing debate between scientists and policymakers on the trade-off between public safety and reviving economy during the COVID-19 pandemic, the government of Bangladesh decided to relax the countrywide lockdown restrictions from the beginning of June 2020. Instead, the Ministry of Public Affairs officials have declared some parts of the capital city and a few other districts as red zones or high-risk areas based on the number of people infected in the late June 2020. Nonetheless, the COVID-19 infection rate had been increasing in almost every other part of the country. Ironically, rather than ensuring rapid tests and isolation of COVID-19 patients, from the beginning of July 2020, the Directorate General of Health Services restrained the maximum number of tests per laboratory. Thus, the health experts have raised the question of whether the government is heading toward achieving herd immunity instead of containing the COVID-19 pandemic. In this paper, the dynamics of the pandemic due to SARS-CoV-2 in Bangladesh is analyzed with integrated the Unscented Kalman Filter (UKF) in the SIRD model. We demonstrate that the herd immunity threshold can be reduced to 31% than that of 60% by considering age group cluster analysis resulting in a total of 53.0 million susceptible populations. With the data of COVID-19 cases till January, 2021, the time-varying reproduction numbers are used to explain the nature of the pandemic. Based on the estimations of active, severe and critical cases, we discuss a set of policy recommendations to improve the current pandemic control methods in Bangladesh.

Politics is a crucial aspect of society. It has a very high impact on the development of a community and its population. Thinking and acts of a few political persons/parties affect the whole population. In our work, a dynamical mathematical model is being considered to investigate the ideological pressure and change in a region where a group is being violent to achieve the desired political results. The estimation of model parameters is made, and the results of general elections of a specific region (Basque country) are used to paint the future political scenario of the region by the derived model. Analytical investigation for the system of nonlinear differential equations governing the social phenomenon is also done. The worth of the considered model is shown by stability analysis.

It is generally, but not always, accepted that alternative food plays a stabilizing role in predator–prey interaction. Parasites, on the other hand, have the ability to change both the qualitative and quantitative dynamics of its host population. In recent times, researchers are showing growing interest in formulating models that integrate both the ecological and epidemiological aspects. The present paper deals with the effect of alternative food on a predator–prey system with disease in the predator population. We show that the system, in the absence of alternative food, exhibits different dynamics viz. stable coexistence, limit cycle oscillations, period-doubling bifurcation and chaos when infection rate is gradually increased. However, when predator consumes alternative food coupled with its focal prey, the system returns to regular oscillatory state from chaotic state through period-halving bifurcations. Our study shows that alternative food may have larger impact on the community structure and may increase population persistence.

This study investigates the effects of vaccination and treatment on the spread of HIV/AIDS. The objectives are (i) to derive conditions for the success of vaccination and treatment programs and (ii) to derive threshold conditions for the existence and stability of equilibria in terms of the effective reproduction number R. It is found, firstly, that the success of a vaccination and treatment program is achieved when R_0t<R₀, R_0t<R_0v and γ_eR_VT(σ)<R_UT(α), where R_0t and R_0v are respectively the reproduction numbers for populations consisting entirely of treated and vaccinated individuals, R₀ is the basic reproduction number in the absence of any intervention, R_UT(α) and R_VT(σ) are respectively the reproduction numbers in the presence of a treatment (α) and a combination of vaccination and treatment (σ) strategies. Secondly, that if R<1, there exists a unique disease free equilibrium point which is locally asymptotically stable, while if R>1 there exists a unique locally asymptotically stable endemic equilibrium point, and that the two equilibrium points coalesce at R=1. Lastly, it is concluded heuristically that the stable disease free equilibrium point exists when the conditions R_0t<R₀, R_0t<R_0v and γ_eR_VT(σ)<R_UT(α) are satisfied.

In this paper, the asymptotical behavior of a chemostat model for E. coli and the virulent phage T4 is analyzed. The basic reproduction number R₀ is proved to be a threshold which determines the outcome of the virulent phage T4. If R₀ < 1, the virus dies out; if R₀ > 1, the virus persists. Sufficient conditions for the Hopf bifurcation are also established. The theoretical results show that increasing the input of nutrient will result in an increase in the equilibrium population density of the virulent bacteriophage T4, but will have no effect on the equilibrium population density of E. coli. The results also show that increasing the input of nutrient or increasing the average lytic time for the infected E. coli can destabilize the interaction between E. coli and T4.

A schistosomiasis and HIV/AIDS co-infection model is presented as a system of nonlinear ordinary differential equations. Qualitative analysis (properties) of the model are presented. The disease-free equilibrium is shown to be locally asymptotically stable when the associated epidemic threshold known as the basic reproduction number for the model is less than unity. The Centre Manifold theory is used to show that the schistosomiasis only and HIV/AIDS only endemic equilibria are locally asymptotically stable when the associated reproduction numbers are greater than unity. The model is numerically analyzed to assess the effects of schistosomiasis on the dynamics of HIV/AIDS. Analysis of the reproduction numbers and numerical simulations show that an increase of schistosomiasis cases result in an increase of HIV/AIDS cases, suggesting that schistosomiasis control have a positive impact in controlling the transmission dynamics of HIV/AIDS.

The basic models of within-host viral infection, proposed by Nowak and May² and Perelson and Nelson,⁵ have been widely used in the studies of HBV and HIV infections. The basic reproduction numbers of the two models are proportional to the number of total cells of the host's organ prior to the infection. In this paper, we formulate an amended Perelson and Nelson's model with standard incidence. The basic reproduction number of the amended model is independent of total cells of the host's organ. If the basic reproduction number R₀ < 1, then the infection-free equilibrium is globally asymptotically stable and the virus is cleared; if R₀ > 1, then the virus persists in the host, and solutions approach either an endemic equilibrium or a periodic orbit. Numerical simulations of this model agree well with the clinical HBV infection data. This can provide a possible interpretation for the viral oscillation behaviors, which were observed in chronic HBV infection patients.

Primary prevention measures designed to alter susceptibility and/or reduce exposure of susceptible individuals to diseases, remain the mainstay in the fight against HIV/AIDS. A model for HIV/AIDS, that investigates the reduction in infection by advocating for sexual behavior change through public-health information campaigns and withdrawal of individuals with AIDS from sexual activity is proposed and analyzed. The contact rate is modeled using an incidence function with saturation that depends on the number of infectives. The dynamics of the model is determined using the model reproduction number . Numerical simulations are presented to illustrate the role of some key epidemiological parameters. The results from the study demonstrate that an increase in the rate of dissemination of effective public-health information campaigns results in a decrease in the prevalence of the disease. Similarly, an increase in the fraction of individuals with AIDS who withdraw from sexual activities reduces the burden of the disease.

In this paper, we propose a mathematical model to describe the transmission dynamics of infectious diseases with targeted antiviral prophylaxis strategy. Our model incorporates seasonal driving force since seasonal force has a great effect on the spread of infectious diseases. Based on the local stability of disease free equilibrium we derive the control reproduction number . Sufficient conditions for the global stability of the disease free equilibrium are obtained. Using the persistence theory for discrete dynamical system, we prove that the infectious disease will remain endemic if . Simulation results are also provided to study the effect of targeted antiviral prophylaxis on transmission dynamics of infectious disease and investigate the influence of seasonality on the efficiency of targeted antiviral prophylaxis strategy.

Approximately one-third of the world's population that is at risk to malaria lives in India. Plasmodium falciparum, a deadly form of malaria, accounts for about 50% of the cases there. Since 1940s, India has used a number of programs to combat the disease with variable success. Since 1998, the total numbers of malaria cases, and in particular P. falciparum cases, have been steadily declining, making India one of the success stories among the countries supported by the Roll Back Malaria (RBM) Partnership. This article considers India's P. falciparum control methods from the perspective of a Ross-MacDonald type model. The model is fitted to the P. falciparum cases in India over the period 1983–2009. We focus on the disease reproduction number as being a measure of success of programs. Before the start of RBM measures, the disease reproduction number was , meaning that the incidence of disease was increasing among the population. With the new control measures , suggesting that P.falciparum cases may be declining to zero but extremely slowly. The model here projects 0.734 million cases of P. falciparum malaria for 2010, down from 1.14 million cases in 2000. This impressive 36% decrease falls somewhat short of the RBM's goal of 50% reduction. However, a sensitivity analysis of the disease reproduction number done here suggests that India's control programs do apply controls at the most critical points in the disease cycle; namely, mosquito biting rates, mosquito mortality, and treatment of infected humans. This suggests that as more resources become available, they should be applied to strengthen these controls. The novelty here is in fitting recent data on malaria from India to derive current values of the disease reproduction number.

In this paper we present a susceptible–infectious–susceptible (SIS) model that describes the transmission dynamics of cutaneous Leishmaniasis. The model treats a vector population and several populations of different mammals. Members of the human population serve as the incidental hosts, and members of the various animals populations serve as reservoir hosts. We establish the basic reproduction number and the equilibrium conditions of the system. We use a generalization of the Lyapunov function approach to show that when the basic reproduction number is less than or equal to one, the diseases-free equilibrium is a global attractor, and that when it is greater than one the endemic equilibrium is a global attractor. We present numerical simulations that demonstrate the dynamics of the model for a system containing a human population and a single animal population.

Prostitution has been linked with drug/alcohol misuse for ages. A mathematical model to explore the relationship between prostitution and drug/alcohol misuse is proposed and analyzed. The epidemic thresholds known as the reproduction numbers and equilibria for the model are determined and stabilities analyzed. Analysis of the reproduction numbers suggest that prostitution enhances drug/alcohol misuse and vice-versa. Numerical simulations further show high levels of prostitution (drug/alcohol misuse) control in the absence of drug/alcohol misuse (prostitution). Results from this study suggests to effectively control prostitution (drug/alcohol misuse) require strategies that address both prostitution and drug/alcohol misuse. Addressing only one social issue like prostitution through poverty eradication may not be enough to stem prostitution as some would be turning to prostitution to support drug/alcohol addiction. The same scenario happens to drug/alcohol misuse.

The number of cases of H5N1 avian influenza in birds and humans exhibit seasonality which peaks during the winter months. What causes the seasonality in H5N1 cases is still being investigated. This article addresses the question of modeling the periodicity in cumulative number of human cases of H5N1. Three potential drivers of influenza seasonality are investigated: (1) seasonality in bird-to-bird transmission; (2) seasonality caused by wild bird migration or seasonal fluctuation of avian influenza in wild birds; (3) seasonality caused by environmental transmission. A framework of seven models is composed. The seven models involve these three mechanisms and combinations of the mechanisms. Each of the models in the framework is fitted to the cumulative number of humans cases of H5N1. The corrected akaike information criterion (AICc) is used to compare the models and it is found that the model with periodic bird-to-bird transmission rate best explains the data. The best fitted model with the best fitted parameters gives a reproduction number of highly pathogenic avian influenza . The best fitted model is a simple SI epidemic model with periodic transmission rate and disease-induced mortality, however, this model is capable of very complex dynamical behavior such as period doubling and chaos.

Substance abuse remains a global menace in spite of recurrent warnings, seizures, social and pharmacological effects associated with addiction to drugs. In this paper, we use a mathematical model which is a combination of the classical SIS and SIR models to investigate the dynamics of substance abuse. Initiation into drug use is based on contact of those at risk (the susceptible population) with drug users at different levels of drug use. We evaluate the threshold number and use it to analyze the model. We show that when this threshold number is less than unity, the drug-free steady state is globally asymptotically stable and when this threshold number is greater than unity the drug-persistent steady state is also globally stable. The impact of amelioration, rehabilitation and re-initiation on drug epidemics is investigated. Amelioration in presence of quitting for light users is observed to reduce the prevalence of substance abuse and this is supported by numerical simulations. The results show that both prevention and treatment/rehabilitation are necessary strategies for reduction of drug epidemics. Our recommendation is that preventive strategies should be directed toward reducing the contact rate and treatment should be combined with psychotherapy to accelerate quitting and reduce re-initiation.

At present, H5N1 avian influenza (AI) is a zoonotic disease where the transmission to humans occurs from infected domestic birds. Since 2003, more than 500 people have been infected and nearly 60% of them have died. If the H5N1 virus becomes efficiently human-to-human transmittable, a pandemic will occur with potentially high mortality. A mathematical model of AI, which involves human influenza, is introduced to better understand the complex epidemiology of AI and the emergence of a pandemic strain. Demographic and epidemiological data on birds and humans are used for the parameterization of the model. The differential equation system faithfully projects the cumulative number of H5N1 human cases and captures the dynamics of the yearly cases. The model is used to rank the efficacy of the current control measures used to prevent the emergence of a pandemic strain. We find that culling without re-population and vaccination are the two most efficient control measures each giving 22% decrease in the number of H5N1 infected humans for each 1% change in the affected parameters (μ_b, ν_b for culling and β_b, ν_b for vaccination). Control measures applied to humans, such as wearing protective gear, are not very efficient, giving less than 1% decrease in the number of H5N1 infected humans for each 1% decrease in β_Y, the bird-to-human transmission coefficient of H5N1. Furthermore, we find that should a pandemic strain emerge, it will invade, possibly displacing the human influenza virus in circulation at that time. Moreover, higher prevalence levels of human influenza will obstruct the invasion capabilities of the pandemic H5N1 strain. This effect is not very pronounced, as we find that 1% increase in human influenza prevalence will decrease the invasion capabilities of the pandemic strain with 0.006%.