Effective Contact Rate Research Articles

The impact of vaccination on the modeling of COVID-19 dynamics: a fractional order model.

The coronavirus disease 2019 (COVID-19) is a recent outbreak of respiratory infections that have affected millions of humans all around the world. Initially, the major intervention strategies used to combat the infection were the basic public health measure, nevertheless, vaccination is an effective strategy and has been used to control the incidence of many infectious diseases. Currently, few safe and effective vaccines have been approved to control the inadvertent transmission of COVID-19. In this paper, the modeling approach is adopted to investigate the impact of currently available anti-COVID vaccines on the dynamics of COVID-19. A new fractional-order epidemic model by incorporating the vaccination class is presented. The fractional derivative is considered in the well-known Caputo sense. Initially, the proposed vaccine model for the dynamics of COVID-19 is developed via integer-order differential equations and then the Caputo-type derivative is applied to extend the model to a fractional case. By applying the least square method, the model is fitted to the reported cases in Pakistan and some of the parameters involved in the models are estimated from the actual data. The threshold quantity ({mathcal {R}}_0) is computed by the Next-generation method. A detailed analysis of the fractional model, such as positivity of model solution, equilibrium points, and stabilities on both disease-free and endemic states are discussed comprehensively. An efficient iterative method is utilized for the numerical solution of the proposed model and the model is then simulated in the light of vaccination. The impact of important influential parameters on the pandemic dynamics is shown graphically. Moreover, the impact of different intervention scenarios on the disease incidence is depicted and it is found that the reduction in the effective contact rate (up to 30%) and enhancement in vaccination rate (up to 50%) to the current baseline values significantly reduced the disease new infected cases.

Modelling and qualitative analysis of an illicit drugs model with saturated incidence rate and relapse

Drug abuse is now regarded as a global issue that brings severe consequences on the health, social well-being, and economy. In this study, an illicit drugs model with saturated incidence rate and relapse of individuals who quit using drugs is proposed and analyzed qualitatively. This study aims to determine the behavior of a drug epidemic when the psychological or inhibitory effect and relapse are being considered as well as assist the policymakers in devising effective control measures. The basic reproduction number \(R_0\) is derived and used as a threshold parameter in the global stability analysis. It is found that the drug-free equilibrium is globally asymptotically stable when \(R_0\le 1\). This implies that we can eradicate a drug epidemic when the threshold \(R_0\) is less than or equal to one, irrespective of the initial population size of drug users. On the other hand, the drug persistent equilibrium is globally asymptotically stable when \(R_0>1\). This indicates that the phenomenon of drug use will remain in a community when the threshold \(R_0\) is greater than one, irrespective of the initial population size of drug users. Next, the sensitivity analysis is performed and the results show that the effective contact rate should be targeted to reduce its value. The numerical simulations are also carried out to illustrate the analytical results and investigate the relationship between the measure of psychological or inhibitory effect and the number of drug users.

Sensitivity Analysis of a Mathematical Modeling of Ebola Virus Population Dynamics in the Presence of Vaccine

The virus (Ebola virus) (EBV) belongs to the Filoviri-dae family which is a filovirus and is a serious disease which leads to hemorrhagic disease in human and non human such as chimpanzee, gorilla, porcupine, fruit bats etc. In this paper, a mathematical modeling for the population dynamics of EBV diseases in the presence of vaccination was developed. The research shows that, using the human control reproduction number ( Rc )as response and infectious individual as response function, that the sensitive parameters in the formulated system (1) are the personal hygiene (ε ), humans to human contact rate ( β1 ), modification parameter (η ), human vaccination rate ( ρ ), proper burial (φ ) and humans natural mortality rate (μh ). The study shows that personal hygiene rate, effective contact rate of humans, natural mortality of humans’ rate, vaccination rate and proper burial rate are very sensitive to both reproduction number and infectious humans.

Modeling the Effect of Vaccination and Treatment on the Transmission Dynamics of Hepatitis B Virus and HIV/AIDS Coinfection

Hepatitis B and HIV/AIDS coinfections are common globally due to their similar mode of transmission. Since HIV infection modifies the course of HBV infection by increasing the rate of chronicity, prolonging HBV viremia, and increasing liver disease-associated deaths, individuals with coinfection of both diseases have a higher tendency of developing cirrhosis of the liver, higher levels of HBV DNA, reduced rate of clearance of the hepatitis B e antigen (HBeAg), and more likely to die than an individual with a single infection. This nature of HBV-HIV/AIDS coinfection motivated us to conduct this study. In this paper, we proposed and rigorously analyzed a deterministic mathematical model with the aim of investigating the effect of vaccination against hepatitis B virus and treatment for all infections on the transmission dynamics of HBV-HIV/AIDS coinfection in a population. We proved that the solutions of the submodels and the coinfection model are positive and bounded. The models are studied qualitatively using the stability theory of differential equations, and the effective reproduction numbers of the models are derived using the next generation matrix method. Stability of the equilibria of the submodels and the coinfection model is analyzed using Routh-Hurwitz criteria. The disease-free and endemic equilibria of the submodels and the coinfection model are computed, and both local and global asymptotic stability conditions for those equilibria are discussed. We performed a sensitivity analysis to illustrate the influence of different parameters on the effective reproduction number of HBV-HIV/AIDS coinfection model, and we identified the most sensitive parameters are ω B and ω H , which are the effective contact rates for HBV and HIV transmission, respectively. The numerical simulation of the model is done using MATLAB, and the findings from the simulations are discussed. It is observed that if the vaccination and treatment rates are increased, then the number of individuals susceptible to both infections and HBV-HIV/AIDS coinfection decreases and even falls to zero over time. Hence, it is concluded that vaccination against hepatitis B virus infection, treatment of hepatitis B and HIV/AIDS infections, and HBV-HIV/AIDS infection at the highest possible rate is very essential to control the spread of HBV-HIV/AIDS coinfection as an important public health problem.

Bifurcation Analysis of a Mathematical Model for the Covid-19 Infection among Pregnant and Non-Pregnant Women

A mathematical study and analysis of the covid-19 disease is essential in the control and eradication of the dreadful covid-19 infection. This research work is focused on the covid-19 infection among the women population. The women population was divided into seven compartments. These compartments were built into a deterministic model presented as a system of ordinary differential equations. Basic mathematical analyses such as positivity of solution, the disease-free equilibrium and the basic reproduction number, were performed on the model. The model assumes only positive solutions and the total population size is bounded. The next generation matrix approach was employed in generating the basic reproduction number R0. The sensitivity analysis revealed that among the most sensitive parameters of R0 are the effective contact rate for Covid-19 transmission, the modification parameter accounting for increased susceptibility to covid-19 infection by pregnant women, and the transmission coefficient of the infectious pregnant women. The bifurcation analysis revealed a forward bifurcation which guarantees the stability of the disease-freeequilibrium when R0 is lowered below unity. Numerical simulations, using Mathematica Version 12.0 package, are given to show the effects of the most sensitive parameters of the basic reproduction number on the number of infectious cases of covid-19.

Optimal control design incorporating vaccination and treatment on six compartment pandemic dynamical system

In this paper, a mathematical model of the COVID-19 pandemic with lockdown that provides a more accurate representation of the infection rate has been analyzed. In this model, the total population is divided into six compartments: the susceptible class, lockdown class, exposed class, asymptomatic infected class, symptomatic infected class, and recovered class. The basic reproduction number (R0) is calculated using the next-generation matrix method and presented graphically based on different progression rates and effective contact rates of infective individuals. The COVID-19 epidemic model exhibits the disease-free equilibrium and endemic equilibrium. The local and global stability analysis has been done at the disease-free and endemic equilibrium based on R0. The stability analysis of the model shows that the disease-free equilibrium is both locally and globally stable when R0<1, and the endemic equilibrium is locally and globally stable when R0>1 under some conditions. A control strategy including vaccination and treatment has been studied on this pandemic model with an objective functional to minimize. Finally, numerical simulation of the COVID-19 outbreak in India is carried out using MATLAB, highlighting the usefulness of the COVID-19 pandemic model and its mathematical analysis.

Impact of climate on COVID-19 transmission: A study over Indian states

Coronavirus Disease-2019 (COVID-19) started in Wuhan province of China in November 2019 and within a short time, it was declared as a worldwide pandemic by World Health Organisation due to the very fast worldwide spread of the virus. There are a few studies that look for the correlation with infected individuals and different environmental parameters using early data of COVID-19 but there is no study so far that deals with the variation of effective reproduction number and environmental factors. Effective reproduction number is the driving parameter of the spread of a pandemic and it is important to study the effect of various environmental factors on effective reproduction number to understand the effect of those factors on the spread of the virus. We have used time-dependent models to investigate the variation of different time-dependent driving parameters of COVID-19 like effective reproduction number and contact rate using data from India as a test case. India is a large population country that is highly affected due to the COVID-19 pandemic and has a wide span of different temperature and humidity regions and is ideal for such study. We have studied the impact of temperature and humidity on the spread of the virus of different Indian states using time-dependent epidemiological models SIRD, and SEIRD for a long time scale. We have used a linear regression method to look for any dependency between the effective reproduction number with the relative humidity, absolute humidity, and temperature. The effective reproduction number shows a negative correlation with both relative and absolute humidity for most of the Indian states, which are statistically significant. This implies that relative and absolute humidity may have an important role in the variation of effective reproduction number. Most of the states (six out of ten) show a positive correlation while two (out of ten) show a negative correlation between effective reproduction number and average air temperature for both SIRD and SEIRD models.

A switching dynamic model based on phased COVID-19 data in Chongqing and its evaluation.

ObjectivesAlthough COVID-19 has been controlled in China, the risk of invasion of imported cases remains. We aimed to characterize the impact of the number of imported cases and the implementation of first-level emergency response (FLER) policy.MethodsA SCQIHR switching model was constructed and verified by the complete phased data of COVID-19 in Chongqing in 2020. Then it was used to investigate the impact of the number of imported cases and the timing of FLER. Lastly, it was evaluated by three actual scenarios in Chongqing in 2021.ResultsThe proposed model can fit the multidimensional time series well. After the implementation of FLER, the mean effective reproduction number, contact rate and misdetection rate were decreased significantly, but the quarantine rate for close contacts and isolation rate for non-hospitalized infectious cases were increased significantly. The peaks of quarantined close contacts and hospitalized infectious cases increased linearly with the increase of the number of imported cases and the lag of FLER time, which was verified by three actual scenarios in Chongqing in 2021.ConclusionsThese findings can provide guidance for local public health policy-making and allocation of medical resources, reduce the impact of COVID-19 on the local population.

A numerical technique for solving infectious disease model

In the medical aspect of life, there are multiple ways of formulating a model that can be used to determine if a disease will become a pandemic or an epidemic. In this research, we discussed how we could use the numerical approach by applying the revised SEQIuIdRF (Susceptible, Exposed, Quarantined, Infected undetected, Infected detected, Recovered, and Failed) model to control or contain an infectious disease (COVID-19) by applying the effective contact rate. MATLAB software was used to solve the SEQIuIdRF model by considering population growth, mortality rate, infection rate, disease-induced death, failed treatment rate, and recovery rate, which gave pictographic diagrams of the increase and decrease of the infectious disease in the community.

A Mathematical Model of the Transmission Dynamics of Bovine Schistosomiasis with Contaminated Environment.

Schistosomiasis, a vector-borne chronically debilitating infectious disease, is a serious public health concern for humans and animals in the affected tropical and sub-tropical regions. We formulate and theoretically analyze a deterministic mathematical model with snail and bovine hosts. The basic reproduction number [Formula: see text] is computed and used to investigate the local stability of the model's steady states. Global stability of the endemic equilibrium is carried out by constructing a suitable Lyapunov function. Sensitivity analysis shows that the basic reproduction number is most sensitive to the model parameters related to the contaminated environment, namely: shedding rate of cercariae by snails, cercariae to miracidia survival probability, snails-miracidia effective contact rate and natural death rate of miracidia and cercariae. Numerical results show that when no intervention measures are implemented, there is an increase of the infected classes, and a rapid decline of the number of susceptible and exposed bovines and snails. Effects of the variation of some of the key sensitive model parameters on the schistosomiasis dynamics as well as on the initial disease transmission threshold parameter [Formula: see text] are graphically depicted.

Mathematical modeling and simulating of Helicobacter pylori treatment and transmission implications on stomach cancer dynamics

Deterministic mathematical model of the nonlinear first-order differential equation is proposed considering both direct and indirect contact transmission to capture some of the control measures such as treatment in limiting the infection. Six compartments are considered in the model that is; susceptible humans, exposed humans, infected humans with H. pylori , treated humans, infected humans with stomach cancer and the bacteria concentration from the environment. The qualitative behavior of the model was performed including, the existence of nonnegative invariant solution, boundness region, equilibria (both disease-free as well as endemic) and stabilities of two-equilibrium point. Moreover, control reproduction number and bifurcation analysis were also studied. Based on the analysis of sensitivity, the method of partial rank correlation coefficient (PRCC) and Latin hypercube sampling (LHS) was studied to find out which parameters are useful for the model. Furthermore, sensitivity analysis of some parameters was also studied based on the control reproduction number. The simulation results show that increasing the Helicobacter pylori infections treatment rate, has a vital role in the reduction of infections and stomach cancer in the community. Therefore, we concluded that effective treatment rate and low contact rate are most significant to eradicate stomach cancer from the community.

Calibrating COVID-19 susceptible-exposed-infected-removed models with time-varying effectivecontact rates.

We describe the population-based susceptible-exposed-infected-removed (SEIR) model developed by the Irish Epidemiological Modelling Advisory Group (IEMAG), which advises the Irish government on COVID-19 responses. The model assumes a time-varying effective contact rate (equivalently, a time-varying reproduction number) to model the effect of non-pharmaceutical interventions. A crucial technical challenge in applying such models is their accurate calibration to observed data, e.g. to the daily number of confirmed new cases, as the history of the disease strongly affects predictions of future scenarios. We demonstrate an approach based on inversion of the SEIR equations in conjunction with statistical modelling and spline-fitting of the data to produce a robust methodology for calibration of a wide class of models of this type.This article is part of the theme issue ‘Data science approaches to infectious disease surveillance’.

A fractional-order multi-vaccination model for COVID-19 with non-singular kernel

This work examines the impact of multiple vaccination strategies on the dynamics of COVID-19 in a population using the Atangana-Baleanu derivative. The existence and uniqueness of solution of the model is proven using Banach’s fixed point theorem. Local and global asymptotic stability of the equilibria of the model is also proven (under some conditions). Conditions for the existence of a unique or multiple equilibria are also derived and the model is shown to undergo backward bifurcation under certain scenarios. Using available data for the Pfizer, Moderna and Janssen vaccination programme for the city of Texas, United States of America from March 13, 2021 to June 29, 2021, the model is fitted using the three data sets. The three vaccination rates ν1,ν2 and ν3 corresponding to each vaccine as well as the effective contact rate for COVID-19 transmission, β, are estimated. Simulations of the model under different vaccination strategies are carried out. The results show that the three vaccination strategies not only cause significant reduction in the new asymptomatic and vaccinated symptomatic cases but also cause great decrease in the total number of vaccinated symptomatic individuals with severe COVID-19 illness.

Effect of 2021 assembly election in India on COVID-19 transmission.

India is one of the countries in the world which is badly affected by the COVID-19 second wave. Assembly election in four states and a union territory of India was taken place during March–May 2021 when the COVID-19 second wave was close to its peak and affected a huge number of people. We studied the impact of assembly election on the effective contact rate and the effective reproduction number of COVID-19 using different epidemiological models like SIR, SIRD, and SEIR. We also modeled the effective reproduction number for all election-bound states using different mathematical functions. We separately studied the case of all election-bound states and found all the states showed a distinct increase in the effective contact rate and the effective reproduction number during the election-bound time and just after that compared to pre-election time. States, where elections were conducted in single-phase, showed less increase in the effective contact rate and the reproduction number. The election commission imposed extra measures from the first week of April 2021 to restrict big campaign rallies, meetings, and different political activities. The effective contact rate and the reproduction number showed a trend to decrease for few states due to the imposition of the restrictions. We also compared the effective contact rate, and the effective reproduction number of all election-bound states and the rest of India and found all the parameters related to the spread of virus for election-bound states are distinctly high compared to the rest of India.

Qualitative analysis and dynamical behavior of a Lassa haemorrhagic fever model with exposed rodents and saturated incidence rate

We have proposed an unprecedented deterministic model of Lassa Hemorrhagic fever (LHF) model with nonlinear force of LHF infection to capture the transmission dynamics and long-term effects of the disease. The Qualitative analyses we have conveyed on this model using well-established methods viz: Cauchy's differential theorem, Birkhoff & Rota's theorems verify and reveal the well-posedness of the model respectively. We established that an LHF-free equilibrium termed the disease-free equilibrium (DFE) exists for this model and this equilibrium, however, from our stability analyses, tends to be stable when the basic reproduction number computed via the next generation matrix method is less than unity (one); and unstable otherwise. Furthermore, we have carried out a sensitivity analysis to check for the variation effects of the model parameters when increased or decreased using the normalized forward-sensitivity index; unraveling the most sensitive parameters which requires the attention of the healthcare workers as; the effective contact rates β1,β2andβ3, and the rodents’ recruitment rate ΩR. After which numerical simulations of the model were carried out to verify our qualitative analyses (Stability and sensitivity analysis) and to study the dynamical behavior of the model; showing that the presence of saturation instantaneously causes the system to approach a DFE/LHF-Free equilibrium. From these qualitative analyses and numerical simulation results, we recommend early intervention and early treatment of Lassa hemorrhagic virus infection (LAHV) with Ribavirin on the infected, maximum hygiene practices and periodic evacuation of rodents in households in order to curb the recruitment of wild/rodents.

A mathematical analysis of the dynamics of chikungunya virus transmission

In this paper, a deterministic model for the dynamics of chikungunya virus transmission is formulated and analyzed. It is shown that the model has a disease free equilibrium (DFE) and by using the basic reprodution number (R0) local stability of DFE is proved when R0 &lt; 1. Also, the global stability of DFE is investigated by Lyapunov function and LaSalle Invariance Principle. We show that there exists a unique endemic equilibrium (EE) of the model which is locally asymptotically stable whenever R0 &gt; 1 and establish the global stability of the EE when R0 &gt; 1, by using Lyapunov function and LaSalle Invariance Principle for a special case. Numerical simulations and sensitivity analysis show that the destruction of breeding sites and reduction of average life spans of vector would be effective prevention to control the outbreak. Controlling of effective contact rates and reducing transmissions probabilities may reduce the disease prevalence. GANITJ. Bangladesh Math. Soc.41.1 (2021) 41-61

Propagation Analysis of COVID-19: An SIR Model-Based Investigation of the Pandemic.

The paper investigates the spread pattern and dynamics of Covid-19 propagation based on SIR model. Using the model dynamics, an analytical estimation has been obtained for virus span, its longevity, growing pattern, etc. Experimental simulations are carried out on the data of four regions of India over a period of two months of country-wide lockdown. The analysis illustrates the effect of lockdown on the contact rate and its implication. Simulation results illustrate that there is a cut-down in effective contact rate by a considerable factor ranging from 2 to 4 for the selected regions. Further, the estimates for the vaccines to be developed, maximum range and span of the disease can be also estimated. Results portray that the SIR model is a significant tool to cast the dynamics and predictions of Covid-19 outbreak in comparison to other epidemic models. The study demonstrates the progression of real time data in accordance with the SIR model with high accuracy.

On study of fractional order epidemic model of COVID-19 under non-singular Mittag–Leffler kernel

This paper investigates the analysis of the fraction mathematical model of the novel coronavirus (COVID-19), which is indeed a source of threat all over the globe. This paper deals with the transmission mechanism by some affected parameters in the problem. The said study is carried out by the consideration of a fractional-order epidemic model describing the dynamics of COVID-19 under a non-singular kernel type of derivative. The concerned model examine via non-singular fractional-order derivative known as Atangana-Baleanu derivative in Caputo sense (ABC). The problem analyzes for qualitative analysis and determines at least one solution by applying the approach of fixed point theory. The uniqueness of the solution is derived by the Banach contraction theorem. For iterative solution, the technique of iterative fractional-order Adams–Bashforth scheme is applied. Numerical simulation for the proposed scheme is performed at various fractional-order lying between 0, 1 and for integer-order 1. We also compare the compartmental quantities of the said model at two different effective contact rates of β. All the compartments show convergence and stability with growing time. The simulation of the iterative techniques is also compared with the Laplace Adomian decomposition method (LADM). Good comparative results for the whole density have been achieved by different fractional orders and obtain the stability faster at the low fractional orders while slowly at higher-order.

SEIR order parameters and eigenvectors of the three stages of completed COVID-19 epidemics: with an illustration for Thailand January to May 2020

By end of October 2020, the COVID-19 pandemic has taken a tragic toll of 1150 000 lives and this number is expected to increase. Despite the pandemic is raging in most parts of the world, in a few countries COVID-19 epidemics subsided due to successful implementations of intervention measures. A unifying perspective of the beginnings, middle stages, and endings of such completed COVID-19 epidemics is developed based on the order parameter and eigenvalue concepts of nonlinear physics, in general, and synergetics, in particular. To this end, a standard susceptible-exposed-infected-recovered (SEIR) epidemiological model is used. It is shown that COVID-19 epidemic outbreaks follow a suitably defined SEIR order parameter. Intervention measures switch the eigenvalue of the order parameter from a positive to a negative value, and in doing so, stabilize the COVID-19 disease-free state. The subsiding of COVID-19 epidemics eventually follows the remnant of the order parameter of the infection dynamical system. These considerations are illustrated for the COVID-19 epidemic in Thailand from January to May 2020. The decay of effective contact rates throughout the three epidemic stages is demonstrated. Evidence for the sign-switching of the dominant eigenvalue is given and the order parameter and its stage-3 remnant are identified. The presumed impacts of interventions measures implemented in Thailand are discussed in this context.

System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

The emergence of the COVID-19 outbreak has caused a pandemic situation in over 210 countries. Controlling the spread of this disease has proven difficult despite several resources employed. Millions of hospitalizations and deaths have been observed, with thousands of cases occurring daily with many measures in place. Due to the complex nature of COVID-19, we proposed a system of time-fractional equations to better understand the transmission of the disease. Non-locality in the model has made fractional differential equations appropriate for modeling. Solving these types of models is computationally demanding. Our proposed generalized compartmental COVID-19 model incorporates effective contact rate, transition rate, quarantine rate, disease-induced death rate, natural death rate, natural recovery rate, and recovery rate of quarantine infected for a holistic study of the coronavirus disease. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, local and global stability analysis of the disease-free equilibrium (symmetry), and sensitivity analysis. Furthermore, numerical solutions of the proposed model are obtained with the generalized Adam–Bashforth–Moulton method developed for the fractional-order model. Our analysis and solutions profile show that each of these incorporated parameters is very important in controlling the spread of COVID-19. Based on the results with different fractional-order, we observe that there seems to be a third or even fourth wave of the spike in cases of COVID-19, which is currently occurring in many countries.