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AbstractThe global population has encountered significant challenges throughout history due to infectious diseases. To comprehensively study these dynamics, a novel deterministic mathematical model, TCD IL2 Z, is developed for the early detection and treatment of lung cancer. This model incorporates IL2 cytokine and anti-PD-L1 inhibitors, enhancing the immune system’s anticancer response within five epidemiological compartments. The TCD IL2Z model is analyzed qualitatively and quantitatively, emphasizing local stability given the limited data-a critical component of epidemic modeling. The model is systematically validated by examining essential elements such as equilibrium points, the reproduction number (R0), stability, and sensitivity analysis. Next-generation techniques based on R0 that track disease transmission rates across the sub-compartments are fed into the system. At the same time, sensitivity analysis helps model how a particular parameter affects the dynamics of the system. The stability on the global level of such therapy agents retrogrades individuals with immunosuppression or treated with IL2 and anti-PD-L1 inhibitors admiring the Lyapunov functions’ applications. NSFD scheme based on the implicit method is used to find the exact value and is compared with Euler’s method and RK4, which guarantees accuracy. Thus, the simulations were conducted in the MATLAB environment. These simulations present the general symptomatic and asymptomatic consequences of lung cancer globally when detected in the middle and early stages, and measures of anticancer cells are implemented including boosting the immune system for low immune individuals. In addition, such a result provides knowledge about real-world control dynamics with IL2 and anti-PD-L1 inhibitors. The studies will contribute to the understanding of disease spread patterns and will provide the basis for evidence-based intervention development that will be geared toward actual outcomes. [ABSTRACT FROM AUTHOR]

In this paper, the existing Susceptible-Infected-Recovered-Deceased (SIRD) compartmental epidemiologic process model is modified for forecasting the coronavirus effect in India. The data from India was studied for weekly fatalities, weekly infected, weekly recovered, new cases, infected and recovered individuals, Reproductive Number R0, recovery rate, death rate, and coefficient of transmission from 30 January 2020 to 31 July 2021. SARS Coronavirus 2 (SARS-CoV-2) is the Covid strain that causes Covid sickness (COVID-19), a respiratory ailment that triggered the outbreak of COVID-19 at the beginning of December 2019. We aim to provide a hybrid SIRD model for predicting the COVID-19 outbreak. In the proposed method, to improve the exploration ability of the Grey Wolf Optimizer (GWO) or to avoid stagnation in the swarm, a modified Grey Wolf Optimization Algorithm is used to optimize the initial value of Infected individuals. The modified SIRD model is further applied to get the predicted values. The data is examined on weekly basis to prevent noise. Depending on the fact, that the precise mode of transmission is highly dependent on how and when different precautions such as isolation, confinement, and other preventative measures were implemented, we put together our projections concerning satisfactory speculations based on genuine realities. The experimental results show the various trends observed in the pandemic in terms of number of peaks, increasing trend, decreasing trend, and continuous trend for infected individuals, weekly change in number of cases, weekly deaths, weekly infected, and weekly recoeverd cases of Covid-19. The proposed modified SIRD model could be a valuable tool for assessing the impact of government measures on COVID-19 outbreak. [ABSTRACT FROM AUTHOR]

Simple Summary: Diseases in the swine industry can cause major economic and health issues. This review examines R0 estimates, which measure how efficiently respiratory diseases spread among pigs and compares transmission risks within and between farms. Seven diseases were studied: Aujeszky's disease, PPRSV, Circovirus, Influenza A, Encephalomyocarditis Virus, Classical Swine Fever, and African Swine Fever. Data from research articles showed varying R0 values, with higher transmission rates within herds for some diseases. Effective disease control requires prompt detection, response to outbreaks, and continuous monitoring to reduce its impact on the swine industry. Diseases in the swine industry can cause significant economic and health impacts. This review examines R0 estimates for respiratory diseases in pigs, assessing variations and comparing transmission risks within and between farms. A literature search of three databases aggregated peer-reviewed research articles on swine viral respiratory diseases' R0 values. The study focused on seven diseases: Aujeszky's disease (AD), Porcine Reproductive and Respiratory Syndrome Virus (PRRSV), Circovirus, Influenza A (IA), Encephalomyocarditis Virus (EV), Classical Swine Fever (CSF), and African Swine Fever (ASF). R0 values were estimated for transmission within and between herds/farms using various methods, from complex mathematical models to simple calculations. Data primarily came from disease surveillance and laboratory experiments. The median R0 for within-herd and between-herd transmission was 10 and 3.31 for AD, 2.78 and 1.14 for PRRSV, 5.9 and 0.89 for Circovirus, 1.75 and 1.6 for CSF, and 3.94 and 3.15 for ASF. For IA and EV, only within-herd R0 values were estimated at 8.65 and 1.3, respectively. Diseases with high R0 values highlight the need for prompt detection and response to outbreaks. Continuous monitoring and evaluation of pathogen transmissibility are crucial for enhancing disease surveillance and reducing the impact of livestock diseases. [ABSTRACT FROM AUTHOR]

In this paper, the existing Susceptible-Infected-Recovered-Deceased (SIRD) compartmental epidemiologic process model is modified for forecasting the coronavirus effect in India. The data from India was studied for weekly fatalities, weekly infected, weekly recovered, new cases, infected and recovered individuals, Reproductive Number [Formula: see text], recovery rate, death rate, and coefficient of transmission from 30 January 2020 to 31 July 2021. SARS Coronavirus 2 (SARS-CoV-2) is the Covid strain that causes Covid sickness (COVID-19), a respiratory ailment that triggered the outbreak of COVID-19 at the beginning of December 2019. We aim to provide a hybrid SIRD model for predicting the COVID-19 outbreak. In the proposed method, to improve the exploration ability of the Grey Wolf Optimizer (GWO) or to avoid stagnation in the swarm, a modified Grey Wolf Optimization Algorithm is used to optimize the initial value of Infected individuals. The modified SIRD model is further applied to get the predicted values. The data is examined on weekly basis to prevent noise. Depending on the fact, that the precise mode of transmission is highly dependent on how and when different precautions such as isolation, confinement, and other preventative measures were implemented, we put together our projections concerning satisfactory speculations based on genuine realities. The experimental results show the various trends observed in the pandemic in terms of number of peaks, increasing trend, decreasing trend, and continuous trend for infected individuals, weekly change in number of cases, weekly deaths, weekly infected, and weekly recoeverd cases of Covid-19. The proposed modified SIRD model could be a valuable tool for assessing the impact of government measures on COVID-19 outbreak.

Visceral Leishmaniasis remains a significant public health challenge in eastern Sudan despite extensive control efforts. This study employs MCMC Bayesian inference techniques to fit a mathematical model for studying visceral Leishmaniasis transmission dynamics with interventions. The research focuses on evaluation of control programs to adapt to the dynamic nature of visceral Leishmaniasis transmission. We analyze 22 years of cumulative visceral Leishmaniasis cases from eastern Sudan, an endemic region for visceral Leishmaniasis, and assessed the effectiveness of interventions implemented thus far. The results reveal that visceral Leishmaniasis is prevalent, with reported cases representing less than 20% of community infections. Improved surveillance and diagnostics are necessary for accurately estimating the disease burden. The effectiveness of intervention strategies for vector control for reducing VL transmission in the region is found to be limited. Furthermore, the model predicts visceral Leishmaniasis cases will continue to increase in the near future, underscoring the need adaptable initiatives to reduce the disease burden. [ABSTRACT FROM AUTHOR]

Among women of reproductive age, PCOS (polycystic ovarian syndrome) is one of the most prevalent endocrine illnesses. In addition to decreasing female fertility, this condition raises the risk of cardiovascular disease, diabetes, dyslipidemia, obesity, psychiatric disorders and other illnesses. In this paper, we constructed a fractional order model for polycystic ovarian syndrome by using a novel approach with the memory effect of a fractional operator. The study population was divided into four groups for this reason: Women who are at risk for infertility, PCOS sufferers, infertile women receiving therapy (gonadotropin and clomiphene citrate), and improved infertile women. We derived the basic reproductive number, and by utilizing the Jacobian matrix and the Routh-Hurwitz stability criterion, it can be shown that the free and endemic equilibrium points are both locally stable. Using a two-step Lagrange polynomial, solutions were generated in the generalized form of the power law kernel in order to explore the influence of the fractional operator with numerical simulations, which shows the impact of the sickness on women due to the effect of different parameters involved.

The world is aiming to eliminate malaria by 2030. The introduction of the pilot project on malaria vaccination for children in Kenya, Ghana, and Malawi presents a significant thrust to the elimination efforts. In this work, a susceptible, infectious and recovered (SIR) human-vector interaction mathematical model for malaria was formulated. The model was extended to include a compartment of vaccinated humans and an influx of infected immigrants. Qualitative and quantitative analysis was performed on the model. When there was no influx of infected immigrants, the model had a disease-free equilibrium point that was globally asymptotically stable when a threshold known as the basic reproductive number denoted by $ R_0 $ was less than one. When there was an influx of infected immigrants, the model had endemic equilibrium points only. Parameter sensitivity analysis on $ R_0 $ was performed and results showed that strategies must be implemented to reduce contact between mosquitoes and humans. Results from different vaccine coverage indicated that in the absence of an influx of infected immigrants, it is possible to achieve a malaria-free society when more children get vaccinated and the influx of infected humans is avoided. The analysis of the optimal control model showed that the combined use of vaccination, personal protective equipment, and treatment is the best way to curb malaria incidence, provided the influx of infected humans is completely stopped.

The aim of the current study is to reduce marijuana use among the general population. Because marijuana is an illegal narcotic with numerous negative health effects, it continues to pose a severe threat to public health in emerging nations. In this article, a modified mathematical model of the non-users, experimental users, recreational users, and addict's (NERA) model for marijuana consumption is established by incorporating a new compartment that represents the individuals who are being moved to jail by police intervention. The overall population of humans is divided into five main components: the non-smoker's compartment, experimental smoker's compartment, recreational smoker's compartment, addicted smoker's compartment, and prisoner's compartment. The novelty of this work is to modify the NERA model for marijuana consumption and validate the modified model. Furthermore, with the help of sensitivity analysis, control strategies for marijuana consumption in the population are addressed. The invariant region and the basic reproductive number (R0) are those parts that are needed for the validation of the proposed model. For the numerical simulation of the given model, the 4th-order Runge Kutta method will be used with the help of MATLAB to examine how the control strategies will play a role in marijuana consumption.

Soon after a mask mandate was relaxed (March 1, 2023), the first post–COVID-19 influenza season in Hong Kong lasted 12 weeks. After other preventive measures were accounted for, mask wearing was associated with an estimated 25% reduction in influenza transmission. Influenza resurgence probably resulted from relaxation of mask mandates and other measures.

Among women of reproductive age, PCOS (polycystic ovarian syndrome) is one of the most prevalent endocrine illnesses. In addition to decreasing female fertility, this condition raises the risk of cardiovascular disease, diabetes, dyslipidemia, obesity, psychiatric disorders and other illnesses. In this paper, we constructed a fractional order model for polycystic ovarian syndrome by using a novel approach with the memory effect of a fractional operator. The study population was divided into four groups for this reason: Women who are at risk for infertility, PCOS sufferers, infertile women receiving therapy (gonadotropin and clomiphene citrate), and improved infertile women. We derived the basic reproductive number, and by utilizing the Jacobian matrix and the Routh-Hurwitz stability criterion, it can be shown that the free and endemic equilibrium points are both locally stable. Using a two-step Lagrange polynomial, solutions were generated in the generalized form of the power law kernel in order to explore the influence of the fractional operator with numerical simulations, which shows the impact of the sickness on women due to the effect of different parameters involved. [ABSTRACT FROM AUTHOR]

Diseases in the swine industry can cause significant economic and health impacts. This review examines R0 estimates for respiratory diseases in pigs, assessing variations and comparing transmission risks within and between farms. A literature search of three databases aggregated peer-reviewed research articles on swine viral respiratory diseases’ R0 values. The study focused on seven diseases: Aujeszky’s disease (AD), Porcine Reproductive and Respiratory Syndrome Virus (PRRSV), Circovirus, Influenza A (IA), Encephalomyocarditis Virus (EV), Classical Swine Fever (CSF), and African Swine Fever (ASF). R0 values were estimated for transmission within and between herds/farms using various methods, from complex mathematical models to simple calculations. Data primarily came from disease surveillance and laboratory experiments. The median R0 for within-herd and between-herd transmission was 10 and 3.31 for AD, 2.78 and 1.14 for PRRSV, 5.9 and 0.89 for Circovirus, 1.75 and 1.6 for CSF, and 3.94 and 3.15 for ASF. For IA and EV, only within-herd R0 values were estimated at 8.65 and 1.3, respectively. Diseases with high R0 values highlight the need for prompt detection and response to outbreaks. Continuous monitoring and evaluation of pathogen transmissibility are crucial for enhancing disease surveillance and reducing the impact of livestock diseases.

In this paper, we investigate the COVID-19 pandemic in Canada and evaluate the Canadian government policies on controlling COVID-19 outbreaks. The first case of COVID-19 was reported in Ontario on 25 January 2020. Since then, there have been over million cases by now. During this time period, the federal, provincial and local governments have implemented regulations and policies in order to control the pandemic. To evaluate these government policies, which may be done by analysing the infection rate, infection period and reproductive number of COVID-19, we approach the problem by introducing an extended susceptible-exposed-infectious-removed (SEIR) model and conduct the model inference by using the iterated filter ensemble adjustment Kalman filter (IF-EAKF) algorithm. We first divide the time period into phases according to the policy intensities in each province by segmenting the time period from 4 March 2020 to 31 October 2020 into three time phases: the exploding phase, the strict policy implementation phase, and the provincial reopening phase. We then use IF-EAKF algorithm to obtain the estimates of the model parameters. We show that the infection rate in the second phase is lower than that in both first and third phases. We also discuss the number of new COVID-19 cases under different policy intensities and different policy durations in the third wave of the pandemic.

In this paper, a novel fractional-order monkeypox epidemic model is introduced, where fractional-order derivatives in the sense of Caputo are applied to achieve more realistic results for the proposed nonlinear model. The newly developed model, which models the transmission and spread of monkeypox across the interacting populations of humans and rodents, is controlled by a 14-dimensional system of fractional-order differential equations. To comply with empirical and reported observations, the state variables of the proposed model are categorized into three main groups of state variables: the population who are at high risk of being infected, people with low infection probability, and finally, rodents who can carry and transmit the virus. The high-risk group represents individuals who might be more vulnerable to the virus due to their habits, workplace, or hygienic behaviors. The existence, uniqueness, non-negativity, and boundedness of the solution to the proposed model are proved. The next-generation matrix approach is used to determine the control monkeypox reproduction number, R0, and the equilibrium points for the proposed model are obtained. The effect of the main parameters in the model is thoroughly investigated to provide new insight into the new dynamics of the model. The region of stability of the disease-free points (DFE) is obtained in the space of parameters, and the effect of the parameters is examined. In addition, the optimal control strategy is applied to the model to provide insight into some prevention control to stop the disease from spreading and to provide new control strategies during the monkeypox outbreak. Numerical simulations are performed to validate the theoretical results of the different optimal control strategies.

The aim of the current study is to reduce marijuana use among the general population. Because marijuana is an illegal narcotic with numerous negative health effects, it continues to pose a severe threat to public health in emerging nations. In this article, a modified mathematical model of the non-users, experimental users, recreational users, and addict's (NERA) model for marijuana consumption is established by incorporating a new compartment that represents the individuals who are being moved to jail by police intervention. The overall population of humans is divided into five main components: the non-smoker's compartment, experimental smoker's compartment, recreational smoker's compartment, addicted smoker's compartment, and prisoner's compartment. The novelty of this work is to modify the NERA model for marijuana consumption a nd validate the modified model. Furthermore, with the help of sensitivity analysis, control strategies for marijuana consumption in the population are addressed. The invariant region and the basic reproductive number (R0) are those parts that are needed for the validation of the proposed model. For the numerical simulation of the given model, the 4th-order Runge Kutta method will be used with the help of MATLAB to examine how the control strategies will play a role in marijuana consumption. [ABSTRACT FROM AUTHOR]

The severe acute respiratory syndrome (SARS-CoV-2) pandemic and high hospitalization rates placed a tremendous strain on hospital resources, necessitating the use of models to predict hospital volumes and the associated resource requirements. Complex epidemiologic models have been developed and published, but many require continued adjustment of input parameters. We developed a simplified model for short-term bed need predictions that self-adjusts to changing patterns of disease in the community and admission rates. The model utilizes public health data on community new case counts for SARS-CoV-2 and projects anticipated hospitalization rates. The model was retrospectively evaluated after the second wave of SARS-CoV-2 in New York, New York (October 2020–April 2021) for its accuracy in predicting numbers of coronavirus disease 2019 (COVID-19) admissions 3, 5, 7, and 10 days into the future, comparing predicted admissions with actual admissions for each day at a large integrated health-care delivery network. The mean absolute percent error of the model was found to be low when evaluated across the entire health system, for a single region of the health system or for a single large hospital (6.1%–7.6% for 3-day predictions, 9.2%–10.4% for 5-day predictions, 12.4%–13.2% for 7-day predictions, and 17.1%–17.8% for 10-day predictions). [ABSTRACT FROM AUTHOR]

Huanglongbing infection (HLB) or citrus greening and more rarely yellow shoot disease is a fatal bacterial disease of citrus. Our objective in this study is to propose a mathematical model to predict the outbreak of Huanglongbing (HLB) infection with Logistic growth in psyllid insect vectors to predict the transmission of this disease among citrus. Indeed, we considered the periodic environment to model the seasonality of the spread of the disease. In this regard, an explicit expression of the reproductive number R 0 is obtained, which has been used for analyzing the behavior of the model in the cases when R 0 > 1 and R 0 < 1. The mathematical findings are supported using numerical illustrations. [ABSTRACT FROM AUTHOR]

IntroductionSeveral indicators were employed to manage the COVID-19 pandemic. In this study, our objective was to compare the instantaneous reproductive number and the epidemic growth rate in the Spanish population.MethodsData on daily numbers of cases, admissions into hospitals, admissions into ICUs, and deaths due to COVID-19 in Spain from March 2020 to March 2022 were obtained. The four “pandemic state indicators”, which are daily numbers of cases, admissions into hospitals, admissions into ICUs, and deaths due to COVID-19 in Spain from March 2020 to March 2022 were obtained from the Instituto de Salud Carlos III. The epidemic growth rate was estimated as the derivative of the natural logarithm of daily cases with respect to time. Both the reproductive number and the growth rate, as “pandemic trend indicators,” were evaluated according to their capacity to anticipate waves as “pandemic state indicators.”ResultsUsing both the reproductive number and the epidemic growth rate, we were able to anticipate most COVID-19 waves. In most waves, the more severe the presentation of COVID-19, the more effective the pandemic trend indicators would be.ConclusionBesides daily number of cases or other measures of disease frequency, the epidemic growth rate and the reproductive number have different roles in measuring the trend of an epidemic. Naïve interpretations and the use of any indicator as a unique value to make decisions should be discouraged.

In this paper, a novel fractional-order monkeypox epidemic model is introduced, where fractional-order derivatives in the sense of Caputo are applied to achieve more realistic results for the proposed nonlinear model. The newly developed model, which models the transmission and spread of monkeypox across the interacting populations of humans and rodents, is controlled by a 14-dimensional system of fractional-order differential equations. To comply with empirical and reported observations, the state variables of the proposed model are categorized into three main groups of state variables: the population who are at high risk of being infected, people with low infection probability, and finally, rodents who can carry and transmit the virus. The high-risk group represents individuals who might be more vulnerable to the virus due to their habits, workplace, or hygienic behaviors. The existence, uniqueness, non-negativity, and boundedness of the solution to the proposed model are proved. The next-generation matrix approach is used to determine the control monkeypox reproduction number, R 0 , and the equilibrium points for the proposed model are obtained. The effect of the main parameters in the model is thoroughly investigated to provide new insight into the new dynamics of the model. The region of stability of the disease-free points (DFE) is obtained in the space of parameters, and the effect of the parameters is examined. In addition, the optimal control strategy is applied to the model to provide insight into some prevention control to stop the disease from spreading and to provide new control strategies during the monkeypox outbreak. Numerical simulations are performed to validate the theoretical results of the different optimal control strategies. [ABSTRACT FROM AUTHOR]

The relationship between air quality and the spread of Covid-19 has been proven to be sometimes positive and sometimes negative in previous studies. A research gap was seen in Iran regarding the impact of air quality on the spread of Covid-19. Thus, this study examined the relationship between the reproductive number of Covid-19 with the air quality index and meteorological factors. The reproductive number is an index to explain the spread of a viral disease. The air quality index related to each of the pollutants NO2, O3, CO, PM2.5, PM10, and the criterion pollutant were utilized in this study. Meteorological factors, including temperature, relative humidity, precipitation, air pressure, and wind speed were used. The data were obtained weekly and at Tehran province. The dependence of variables was determined using Pearson and Spearman correlation coefficients. The examined relationships were then estimated by regression. Each independent variable was tested in a distinct regression because of the limitations of the study. The linear and curvature regressions were performed according to the dispersion of variables and statistical assumptions. The best model was fitted based on statistical significance and regression coefficient of determination. The results of correlation tests showed the dependence of reproductive number with PM10, PM2.5, SO2 and relative humidity. Regression tests also confirmed the relationship between the reproductive number (dependent variable) and each of the independent variables PM10 (coefficient of determination 0.274), PM2.5 (coefficient of determination 0.358), SO2 (coefficient of determination 0.359), and relative humidity (determination coefficient 0.213). The results indicated that an increase in PM10, PM2.5, SO2 and decrease in relative humidity was associated with an increase in spread of Covid-19. [ABSTRACT FROM AUTHOR]

Phylodynamic methods have lately played a key role in understanding the spread of infectious diseases. During the coronavirus disease (COVID-19) pandemic, large scale genomic surveillance has further increased the potential of dynamic inference from viral genomes. With the continual emergence of novel severe acute respiratory syndrome coronavirus type 2 (SARS-CoV-2) variants, explicitly allowing transmission rate differences between simultaneously circulating variants in phylodynamic inference is crucial. In this study, we present and empirically validate an extension to the BEAST2 package birth–death skyline model (BDSKY), BDSKY |$\lambda $|⁠ , which introduces a scaling factor for the transmission rate between independent, jointly inferred trees. In an extensive simulation study, we show that BDSKY |$\lambda $| robustly infers the relative transmission rates under different epidemic scenarios. Using publicly available genome data of SARS-CoV-2, we apply BDSKY |$\lambda $| to quantify the transmission advantage of the Omicron over the Delta variant in Berlin, Germany. We find the overall transmission rate of Omicron to be scaled by a factor of two with pronounced variation between the individual clusters of each variant. These results quantify the transmission advantage of Omicron over the previously circulating Delta variant, in a crucial period of pre-established non-pharmaceutical interventions. By inferring variant- as well as cluster-specific transmission rate scaling factors, we show the differences in transmission dynamics for each variant. This highlights the importance of incorporating lineage-specific transmission differences in phylodynamic inference. [ABSTRACT FROM AUTHOR]

In this work, we aim to propose a hybrid fractional-order model for investigation and observation of the tuberculosis (TB) disease involving constant-proportional Caputo (CPC) operator. We treat the proposed model's positivity, boundedness, well-posedness, and biological viability with a reproductive number. We prove the existence and uniqueness of the solutions to the proposed model using the fixed-point theorem. For the proposed model, Ulam Hyres' stability is also presented. To evaluate the fractional integral operator, we use different techniques to invert the proportional-caputo (PC) and constant-proportional caputo (CPC) operators. We also use our suggested model's fractional differential equations to derive the eigenfunctions of the CPC operator. There is a detailed discussion of additional analysis of the CPC and Hilfer generalized proportional operators. To solve the suggested model, we employ the Laplace Adomian Decomposition (LADM) technique. Fractional order enhances the dynamics of the epidemic model and has a significant impact on the persistence and extinction of the infection. We see that the CPC operator yields excellent results when applied to the TB version's mathematical modelling. The suggested strategy is a straightforward, useful, and practical plan for resolving and comprehending a range of non-linear physical models. This study serves as an illustration of the application of fractional derivatives in epidemiology. [ABSTRACT FROM AUTHOR]

Cases of COVID-19 and its variant omicron are raised all across the world. The most lethal form and effect of COVID-19 are the omicron version, which has been reported in tens of thousands of cases daily in numerous nations. FollowingWHO (World health organization) records on 30 December 2021, the cases of COVID-19 were found to be maximum for which boarding individuals were found 1,524,266, active, recovered, and discharge were found to be 82,402 and 34,258,778, respectively. While there were 160,989 active cases, 33,614,434 cured cases, 456,386 total deaths, and 605,885,769 total samples tested. So far, 1,438,322,742 individuals have been vaccinated. The coronavirus or COVID-19 is inciting panic for several reasons. It is a new virus that has affected the whole world. Scientists have introduced certain ways to prevent the virus. One can lower the danger of infection by reducing the contact rate with other persons. Avoiding crowded places and social events withmany people reduces the chance of one being exposed to the virus. The deadly COVID-19 spreads speedily. It is thought that the upcoming waves of this pandemicwill be evenmore dreadful. Mathematicians have presented severalmathematical models to study the pandemic and predict future dangers. The need of the hour is to restrict the mobility to control the infection from spreading. Moreover, separating affected individuals from healthy people is essential to control the infection. We consider the COVID-19 model in which the population is divided into five compartments. The present model presents the population's diffusion effects on all susceptible, exposed, infected, isolated, and recovered compartments. The reproductive number, which has a key role in the infectious models, is discussed. The equilibrium points and their stability is presented. For numerical simulations, finite difference (FD) schemes like nonstandard finite difference (NSFD), forward in time central in space (FTCS), and Crank Nicolson (CN) schemes are implemented. Some core characteristics of schemes like stability and consistency are calculated. [ABSTRACT FROM AUTHOR]

Mosquito-borne viruses are emerging or re-emerging globally, afflicting millions of people around the world. Aedes aegypti, the yellow fever mosquito, is the principal vector of dengue, Zika, and chikungunya viruses, and has well-established populations across tropical and subtropical urban areas of the Americas, including the southern United States. While intense arboviral epidemics have occurred in Mexico and further south in the Americas, local transmission in the United States has been minimal. Here, we study Ae. aegypti and Culex quinquefasciatus host feeding patterns and vertebrate host communities in residential environments of South Texas to identify host-utilization relative to availability. Only 31% of Ae. aegypti blood meals were derived from humans, while 50% were from dogs and 19% from other wild and domestic animals. In Cx. quinquefasciatus, 67% of blood meals were derived from chicken, 22% came from dogs, 9% from various wild avian species, and 2% from other mammals including one human, one cat, and one pig. We developed a model for the reproductive number, R0, for Zika virus (ZIKV) in South Texas relative to northern Mexico using human disease data from Tamaulipas, Mexico. We show that ZIKV R0 in South Texas communities could be greater than one if the risk of human exposure to Ae. aegypti bites in these communities is at least 60% that of Northern Mexico communities. The high utilization of non-human vertebrates and low risk of human exposure in South Texas diminishes the outbreak potential for human-amplified urban arboviruses transmitted by Ae. aegypti.

The aim of this paper is to study the existence and the asymptotic stability of solutions for an epidemiologically emerging reaction-diffusion model. We show that the model has two types of equilibrium points to resolve the proposed system for a fairly broad class of nonlinearity that describes the transmission of an infectious disease between individuals. The model is analyzed by using the basic reproductive number R0{R}_{0}. Finally, we present the numerical examples simulations that clarifies and confirms the results of the study throughout the paper.

Background: The time-varying reproduction number, R t , is commonly used to monitor the transmissibility of an infectious disease during an epidemic, but standard methods for estimating R t seldom account for the impact of overdispersion on transmission. Methods: We developed a negative binomial framework to estimate R t and a time-varying dispersion parameter (k t ). We applied the framework to COVID-19 incidence data in Hong Kong in 2020 and 2021. We conducted a simulation study to compare the performance of our model with the conventional Poisson-based approach. Results: Our framework estimated an R t peaking around 4 (95% credible interval = 3.13, 4.30), similar to that from the Poisson approach but with a better model fit. Our approach further estimated k t <0.5 at the start of both waves, indicating appreciable heterogeneity in transmission. We also found that k t decreased sharply to around 0.4 when a large cluster of infections occurred. Conclusions: Our proposed approach can contribute to the estimation of R t and monitoring of the time-varying dispersion parameters to quantify the role of superspreading. [ABSTRACT FROM AUTHOR]

A "Public Health Emergency of International Concern (PHEIC)" monkeypox outbreak was declared by the World Health Organization on 23 June 2022. More than 16,000 monkeypox cases were reported in more than 75 countries across six regions as of July 25. The Bayesian SIR (Susceptible–Infected–Recovered) model with the directed acyclic graphic method was used to estimate the basic/effective reproductive number (R0/Re) and to assess the epidemic spread of monkeypox across the globe. The maximum estimated R0/Re was 1.16 (1.15–1.17), 1.20 (1.20–1.20), 1.34 (1.34–1.35), 1.33 (1.33–1.33) and 2.52 (2.41–2.66) in the United States, Spain, Brazil, the United Kingdom and the Democratic Republic of the Congo, respectively. The values of R0/Re were below 1 after August 2022. The estimated infectious time before isolation ranged from 2.05 to 2.74 days. The PHEIC of the global spreading of human monkeypox has been contained so as to avoid a pandemic in the light of the reasoning-based epidemic model assessment. [ABSTRACT FROM AUTHOR]

BACKGROUND: Estimation of temporal changes in human immunodeficiency virus (HIV) transmission patterns can help to elucidate the impact of preventive strategies and public health policies. METHODS: Portuguese HIV-1 subtype B and G pol genetic sequences were appended to global reference data sets to identify country-specific transmission clades. Bayesian birth-death models were used to estimate subtype-specific effective reproductive numbers (Re). Discrete trait analysis (DTA) was used to quantify mixing among transmission groups. RESULTS: We identified 5 subtype B Portuguese clades (26-79 sequences) and a large monophyletic subtype G Portuguese clade (236 sequences). We estimated that major shifts in HIV-1 transmission occurred around 1999 (95% Bayesian credible interval [BCI], 1998-2000) and 2000 (95% BCI, 1998-2001) for subtypes B and G, respectively. For subtype B, Re dropped from 1.91 (95% BCI, 1.73-2.09) to 0.62 (95% BCI,.52-.72). For subtype G, Re decreased from 1.49 (95% BCI, 1.39-1.59) to 0.72 (95% BCI, .63-.8). The DTA suggests that people who inject drugs (PWID) and heterosexuals were the source of most (>80%) virus lineage transitions for subtypes G and B, respectively. CONCLUSIONS: The estimated declines in Re coincide with the introduction of highly active antiretroviral therapy and the scale-up of harm reduction for PWID. Inferred transmission events across transmission groups emphasize the importance of prevention efforts for bridging populations.

This paper proposes a simple mathematical model that represents the dynamics of youth play for adolescents from 11 to 18 years. This model is defined by a system of 3 differential equations, which are based on continuous processes. The specification of the classes of our model is based on the group classification of the state of gravity of the problem given in [10]. Then we proceed to find the equilibrium points of the system and its analysis. For our numerical simulation we estimate all the parameters of the model using the research work [6] and we apply the Runge kutta algorithm of order 4. As a result and conclusion it is determined that the problem with the game is endemic among young people. In addition, the prevalence of problems with the game is lower in students aged 15 to 18 than in students aged 11 to 14.

Purpose: Nursing homes and long-term care facilities have experienced severe outbreaks and elevated mortality rates of COVID-19. When available, vaccination at-scale has helped drive a rapid reduction in severe cases. However, vaccination coverage remains incomplete among residents and staff, such that additional mitigation and prevention strategies are needed to reduce the ongoing risk of transmission. One such strategy is that of "shield immunity", in which immune individuals modulate their contact rates and shield uninfected individuals from potentially risky interactions.Methods: Here, we adapt shield immunity principles to a network context, by using computational models to evaluate how restructured interactions between staff and residents affect SARS-CoV-2 epidemic dynamics.Results: First, we identify a mitigation rewiring strategy that reassigns immune healthcare workers to infected residents, significantly reducing outbreak sizes given weekly testing and rewiring (48% reduction in the outbreak size). Second, we identify a preventative prewiring strategy in which susceptible healthcare workers are assigned to immunized residents. This preventative strategy reduces the risk and size of an outbreak via the inadvertent introduction of an infectious healthcare worker in a partially immunized population (44% reduction in the epidemic size). These mitigation levels derived from network-based interventions are similar to those derived from isolating infectious healthcare workers.Conclusions: This modeling-based assessment of shield immunity provides further support for leveraging infection and immune status in network-based interventions to control and prevent the spread of COVID-19. [ABSTRACT FROM AUTHOR]

We considered an SEIHR mathematical model to investigate the dynamics of COVID-19. Real data of COVID-19 confirmed cases are fitted to the model. The basic reproductive number is approximated to be R 0 ≈ 2.16. The most globally sensitive parameter of the basic reproductive number is the incubation period of coronavirus. The Atangana Baleanu fractional derivative in Caputo sense (ABC) representation of the model is formulated, and a numerical approximation developed by Toufik and Atangana is used. It is shown that decreasing the fractional-order leads to decreasing the infection of the virus in the infected compartments. [ABSTRACT FROM AUTHOR]

COVID-19 became a household name globally in the year 2020 after it was first discovered in Wuhan, China in December 2019. It is a global pandemic that shut the economy of all nations in the larger part of year 2020 by forcing a compulsory holiday on mankind due to its threat of mass death. The menace of this pandemic was combated with the total arsenal in human capacity. One of such weapons is case detection that leads to either self-isolation or quarantine. This weapon helps to reduce the number of new cases that may arise from undetected asymptomatic/symptomatic carriers within a population. In this article, the dynamics of COVID-19 transmission were studied by developing a mathematical model incorporating case detection, the impact of sensitization, and role of early diagnosis in curbing the spread of this disease. The basic properties in terms of existence, uniqueness, and boundedness of solution for the formulated model were discussed. Also, the model was found to exhibit two equilibrium states which are categorised as the disease-free (DFE) and pandemic equilibrium states. The reproductive number for the model was computed and used to establish the stability analysis for both equilibrium states. Center manifold theory was employed to assess the bifurcation analysis of the model and the result shows that the model exhibits forward bifurcation when the reproductive number is greater than and equal to 1.

Introduction: COVID is a new disease; understanding the transmission dynamics and epidemiological characteristics may help in developing the effective control measures. The study is done 1. To determine the various factors influencing the acquisition of COVID-19 infection among high-risk contacts 2. To estimate the secondary attack rate among high-risk contacts 3. To determine the factors in COVID index cases influencing their secondary attack rate. Methodology: Unmatched case control study was conducted from March to August 2020 among 139 COVID index cases in Madurai district from March–May (Reference period) and their 50 COVID positive (cases), 551 COVID negative (controls) high-risk contacts. Case investigation form* and contact tracing Proforma*were used to collect data. Chi-square test and independent sample t test were used to find out the association. Univariate* and Multivariate logistic regression* were used to predict the risk of various factors in acquisition of COVID infection with the help of adjusted and unadjusted odds ratio. P value < 0.05 was considered statistically significant. Results: Male contacts (P = 0.005, OR = 2.520), overcrowding (P = 0.007, OR = 3.810), and duration of exposure to index case (for 4-7 days P = 0.014, OR = 2.902, for >7 days P = 0.001, OR = 6.748 and for > 12 hours/day P = 0.000, OR = 5.543) were significant factors predicted to be associated with acquisition of COVID infection among high-risk contacts. Reproductive number (R0)* estimated was 1.3. Secondary attack rate (SAR)* estimated among high-risk contacts was 8.32%. Index cases whose outcome was death (P = 0.026); symptomatic index cases (P = 0.000), cases with fever (P = 0.001); sorethroat (P = 0.019); breathlessness (P = 0.010); cough (P = 0.006) and running nose (P = 0.002) had significantly higher mean SAR than their counterparts. Conclusion: Contacts with above said risk factors who were found to be more prone to infection could be given special focus to prevent the transmission in them.

In this paper, we studied a two-patch age-structured model of tuberculosis in a context where the migration is not controlled. Motivated by the fact that no author has highlighted the impact of migration on the dynamics of transmission of tuberculosis. Each subpopulation is subdivided into five compartments: susceptible; latent, vaccinated, infective and treated. After the determination of the reproductive numbers ℜ(ψ, ρ) and ℜ0(ρ), we established the conditions of the global and local stability of the equilibrium point without disease. It has been shown that there is only one point of endemic equilibrium. Numerical simulations show that uncontrolled migration negatively influences the dynamics of tuberculosis. [ABSTRACT FROM AUTHOR]

Invasive pest establishment is a pervasive threat to global ecosystems, agriculture, and public health. The recent establishment of the invasive spotted lanternfly in the northeastern United States has proven devastating to farms and vineyards, necessitating urgent development of population dynamical models and effective control practices. In this paper, we propose a stage-age-structured system of PDEs to model insect pest populations, in which underlying dynamics are dictated by ambient temperature through rates of development, fecundity, and mortality. The model incorporates diapause and non-diapause pathways, and is calibrated to experimental and field data on the spotted lanternfly. We develop a novel moving mesh method for capturing age-advection accurately, even for coarse discretization parameters. We define a one-year reproductive number ( R 0 ) from the spectrum of a one-year solution operator, and study its sensitivity to variations in the mean and amplitude of the annual temperature profile. We quantify assumptions sufficient to give rise to the low-rank structure of the solution operator characteristic of part of the parameter domain. We discuss establishment potential as it results from the pairing of a favorable R 0 value and transient population survival, and address implications for pest control strategies. [ABSTRACT FROM AUTHOR]

Background & Objectives: In late December 2019, an outbreak of severe acute respiratory syndrome coronavirus 2 (SARS COV-2) occurred in the city of Wuhan, the capital of the Hubei province in the central part of the People’s Republic of China (Ren et al., 2020). In Saudi Arabia, the first case of COVID-19 was reported in March 2, 2020. In March 8, 2020, the Saudi authorities adopted the lockdown strategy to contain the disease. The aim of this study was to determine the effectiveness of the various phases of the lockdown strategy in Saudi Arabia and its impact on the basic reproductive number (R0) of the COVID-19 outbreak. Material and Methods: The timeline of the COVID-19 outbreak in Saudi Arabia was divided into three-time intervals. Google Mobility Community Reports (2020) was used to estimate the changes in community mobility during the various phases of the lockdown. The basic reproductive number (R0) of the COVID-19 outbreak was calculated daily using the Susceptible, Infected and Recovered (SIR) model based on the Saudi Ministry of Health (MOH) daily reports. This is a standard system to determine the spread of the virus on the basis of infection rate, quarantine rate as well as confirmation rate. The mean values of the calculated R0 during each interval were compared using one-way ANOVA test. Results: There was no statistically significant difference between the mean values of the different phases of the lockdown (P > 0.05). Moreover, mean R0 value of the second interval was 0.09 higher than the initial interval with free community mobility. Furthermore, the mean R0 values of the third interval with the full lockdown was 0.28 higher than the initial interval. Conclusion: Early implementation of lockdown strategy combined with other social distancing strategies help in containing infectious outbreaks in their early phases. Continuous assessment of such strategies’ effectiveness provides decision makers with precious information needed to justify their application when considering their economic impact.

The effective reproductive number Re is a key indicator of the growth of an epidemic. Since the start of the SARS-CoV-2 pandemic, many methods and online dashboards have sprung up to monitor this number through time. However, these methods are not always thoroughly tested, correctly placed in time, or are overly confident during high incidence periods. Here, we present a method for timely estimation of Re, applied to COVID-19 epidemic data from 170 countries. We thoroughly evaluate the method on simulated data, and present an intuitive web interface for interactive data exploration. We show that, in early 2020, in the majority of countries the estimated Re dropped below 1 only after the introduction of major non-pharmaceutical interventions. For Europe the implementation of non-pharmaceutical interventions was broadly associated with reductions in the estimated Re. Globally though, relaxing non-pharmaceutical interventions had more varied effects on subsequent Re estimates. Our framework is useful to inform governments and the general public on the status of epidemics in their country, and is used as the official source of Re estimates for SARS-CoV-2 in Switzerland. It further allows detailed comparison between countries and in relation to covariates such as implemented public health policies, mobility, behaviour, or weather data.

The generation interval (the time between infection of primary and secondary cases) and its often used proxy, the serial interval (the time between symptom onset of primary and secondary cases) are critical parameters in understanding infectious disease dynamics. Because it is difficult to determine who infected whom, these important outbreak characteristics are not well understood for many diseases. We present a novel method for estimating transmission intervals using surveillance or outbreak investigation data that, unlike existing methods, does not require a contact tracing data or pathogen whole genome sequence data on all cases. We start with an expectation maximization algorithm and incorporate relative transmission probabilities with noise reduction. We use simulations to show that our method can accurately estimate the generation interval distribution for diseases with different reproductive numbers, generation intervals, and mutation rates. We then apply our method to routinely collected surveillance data from Massachusetts (2010-2016) to estimate the serial interval of tuberculosis in this setting. [ABSTRACT FROM AUTHOR]

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The COVID-19 pandemic has placed an unprecedented burden on public health and strained the worldwide economy. The rapid spread of COVID-19 has been predominantly driven by aerosol transmission, and scientific research supports the use of face masks to reduce transmission. However, a systematic and quantitative understanding of how face masks reduce disease transmission is still lacking. We used epidemic data from the Diamond Princess cruise ship to calibrate a transmission model in a high-risk setting and derive the reproductive number for the model. We explain how the terms in the reproductive number reflect the contributions of the different infectious states to the spread of the infection. We used that model to compare the infection spread within a homogeneously mixed population for different types of masks, the timing of mask policy, and compliance of wearing masks. Our results suggest substantial reductions in epidemic size and mortality rate provided by at least 75% of people wearing masks (robust for different mask types). We also evaluated the timing of the mask implementation. We illustrate how ample compliance with moderate-quality masks at the start of an epidemic attained similar mortality reductions to less compliance and the use of high-quality masks after the epidemic took off. We observed that a critical mass of 84% of the population wearing masks can completely stop the spread of the disease. These results highlight the significance of a large fraction of the population needing to wear face masks to effectively reduce the spread of the epidemic. The simulations show that early implementation of mask policy using moderate-quality masks is more effective than a later implementation with high-quality masks. These findings may inform public health mask-use policies for an infectious respiratory disease outbreak (such as one of COVID-19) in high-risk settings.

A “Public Health Emergency of International Concern (PHEIC)” monkeypox outbreak was declared by the World Health Organization on 23 June 2022. More than 16,000 monkeypox cases were reported in more than 75 countries across six regions as of July 25. The Bayesian SIR (Susceptible–Infected–Recovered) model with the directed acyclic graphic method was used to estimate the basic/effective reproductive number (R0/Re) and to assess the epidemic spread of monkeypox across the globe. The maximum estimated R0/Re was 1.16 (1.15–1.17), 1.20 (1.20–1.20), 1.34 (1.34–1.35), 1.33 (1.33–1.33) and 2.52 (2.41–2.66) in the United States, Spain, Brazil, the United Kingdom and the Democratic Republic of the Congo, respectively. The values of R0/Re were below 1 after August 2022. The estimated infectious time before isolation ranged from 2.05 to 2.74 days. The PHEIC of the global spreading of human monkeypox has been contained so as to avoid a pandemic in the light of the reasoning-based epidemic model assessment.

Omicron, the latest SARS-CoV-2 Variant of Concern (VOC), first appeared in Africa in November 2021. At present, the question of whether a new VOC will out-compete the currently predominant variant is important for governments seeking to determine if current surveillance strategies and responses are appropriate and reasonable. Based on both virus genomes and daily-confirmed cases, we compare the additive differences in growth rates and reproductive numbers ( R 0 ) between VOCs and their predominant variants through a Bayesian framework and phylo-dynamics analysis. Faced with different variants, we evaluate the effects of current policies and vaccinations against VOCs and predominant variants. The model also predicts the date on which a VOC may become dominant based on simulation and real data in the early stage. The results suggest that the overall additive difference in growth rates of B.1.617.2 and predominant variants was 0.44 (95% confidence interval, 95% CI: −0.38, 1.25) in February 2021, and that the VOC had a relatively high R 0 . The additive difference in the growth rate of BA.1 in the United Kingdom was 6.82 times the difference between Delta and Alpha, and the model successfully predicted the dominating process of Alpha, Delta and Omicron. Current vaccination strategies remain similarly effective against Delta compared to the previous variants. Our model proposes a reliable Bayesian framework to predict the spread trends of VOCs based on early-stage data, and evaluates the effects of public health policies, which may help us better prepare for the upcoming Omicron variant, which is now spreading at an unprecedented speed. [ABSTRACT FROM AUTHOR]

Many researchers began doing studies about pandemic COVID-19 which began to spread from Wuhan, China in 2019 to all around the world and so far, numerous researches have been done around the world to control this contagious disease. In this paper, we proposed a MSIlIhR-V mathematical model to study the spreading of pandemic COVID-19. This paper is aimed to study the vaccination effect in the control of the disease propagation rate. Another goal of this paper is to find the maximum number of susceptible people, minimum number of infected people, and the best value for number of vaccination people. The Jacobian matrix was obtained in the virus absenteeism equilibrium point for the proposed dynamical system. The spectral radius method was applied to find the analytical formula for the reproductive number. Reproductive number is one of the most benefit and important tools to study of epidemic model's stability and instability. In the following, by adding a controller to the model and also using the optimal control strategy, model performance was improved. To validate of the proposed models with controller and without controller we use the real data of COVID-19 from 4 January, 2021 up to 14 June, 2021 in Iran. Maple and MATLAB software's will be used for programming. We will use Maple software for analytical parts and MATLAB software for numerical and simulation parts. [ABSTRACT FROM AUTHOR]