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It takes into account that conscious, susceptible individuals with self‐protection cannot be infected by mosquito bites, a seven‐dimensional dengue transmission model with self‐protection, and two different standard incidence rates are proposed. Our focus is on discussing the global behavior and the optimal control of the model. We first calculate the control reproduction number Rc$$ {R}_c $$ and determine that if Rc>1$$ {R}_c&gt;1 $$, the model has a unique dengue equilibrium E∗$$ {E}&amp;#x0005E;{\ast } $$. Furthermore, we obtain the local stability of dengue‐free equilibrium E0$$ {E}_0 $$ and the dengue equilibrium E∗$$ {E}&amp;#x0005E;{\ast } $$ by using the method of proof by contradiction. By utilizing the limit system of the model and the Lyapunov direct method, we acquire that E0$$ {E}_0 $$ is globally stable if Rc<1$$ {R}_c&lt;1 $$; E0$$ {E}_0 $$ is globally attractive if Rc=1$$ {R}_c&amp;#x0003D;1 $$, and if Rc>1$$ {R}_c&gt;1 $$, the model is weakly persistent with a thorough analysis, and then E∗$$ {E}&amp;#x0005E;{\ast } $$ is globally stable. Finally, in order to minimize investment in dengue transmission, an optimal control strategy with four control variables is presented using Pontryagin's minimum principle. [ABSTRACT FROM AUTHOR]

This study focuses on formulating and analysing a COVID-19 transmission dynamics model using integer and fractional-order derivatives in the Caputo sense. The model considers two doses of vaccination, confinement, and treatment with limited resources. The control reproduction number is computed and the asymptotic stability analysis of the disease-free equilibrium is proved. We also prove the existence of at least one endemic equilibrium whenever $ \mathcal{R}_c>1 $. Using real data from Germany, we calibrate our models by performing parameter estimations. We find that the control reproduction number is approximately equal to 1.90, which implies that the disease remains endemic in Germany. We also perform global sensitivity analysis by computing partial rank correlation coefficients (PRCC) between $ \mathcal{R}_c $ (respectively compartments of infected individuals) and each model parameter. By fixing vaccine coverage at 70%, we observe that it might be more effective to increase the vaccine efficacy than increasing the numbers of vaccinated people. After that, we formulate the corresponding fractional model in the Caputo sense, proving positivity, boundedness, existence, and uniqueness of solutions. We calculate the control reproduction number of the fractional model, and prove the asymptotic stability of the DFE, and existence of at least one endemic equilibrium point. We find from numerical simulations, that for a long-term forecasting, it seems better to use a fractional derivative in the range $ \varphi\in (0,0.87] $ than using just ordinary derivatives. Indeed, for this range of the fractional-order parameter, daily detected cases are closer to those the classical model predicts. [ABSTRACT FROM AUTHOR]

The recent mpox outbreak (in 2022–2023) has different clinical and epidemiological features compared with previous outbreaks of the disease. During this outbreak, sexual contact was believed to be the primary transmission route of the disease. In addition, the community of men having sex with men (MSM) was disproportionately affected by the outbreak. This population is also disproportionately affected by HIV infection. Given that both diseases can be transmitted sexually, the endemicity of HIV, and the high sexual behavior associated with the MSM community, it is essential to understand the effect of the two diseases spreading simultaneously in an MSM population. Particularly, we aim to understand the potential effects of HIV on an mpox outbreak in the MSM population. We develop a mechanistic mathematical model of HIV and mpox co-infection. Our model incorporates the dynamics of both diseases and considers HIV treatment with anti-retroviral therapy (ART). In addition, we consider a potential scenario where HIV infection increases susceptibility to mpox, and investigate the potential impact of this mechanism on mpox dynamics. Our analysis shows that HIV can facilitate the spread of mpox in an MSM population, and that HIV treatment with ART may not be sufficient to control the spread of mpox in the population. However, we showed that a moderate use of condoms or reduction in sexual contact in the population combined with ART is beneficial in controlling mpox transmission. Based on our analysis, it is evident that effective control of HIV, specifically through substantial ART use, moderate condom compliance, and reduction in sexual contact, is imperative for curtailing the transmission of mpox in an MSM population and mitigating the compounding impact of these intertwined epidemics.

Pyrethroid-treated bed-nets (PTNs) protect individuals against malaria by blocking and repelling mosquitoes. We develop and analyze a PTNs malaria model that explicitly includes mosquito host choice (also known as feeding/biting preference) and Pyrethroid repellent effect. Our model reveals that mosquito biting/feeding preference on infectious hosts π and repellent effect r drive for the existence of both the endemic equilibrium points and the occurrence or elimination of backward bifurcation. The threshold parameters for the mosquito biting preference on infectious hosts π ∗ and repellent effect r ∗ for the occurrence and elimination of backward bifurcation are computed. Moreover, it is shown that, increasing the mosquito host choice rate or decreasing the repellent effect rate, annihilates backward bifurcation, thus facilitating the control of malaria. Furthermore, we prove that the threshold of mosquito biting preference is a monotone increasing function of the repellent effect r. We show that the model exhibits both trans-critical forward bifurcation and backward bifurcation when either the mosquito host choice π crosses a threshold value π 1 or the repellent effect r passes through a threshold repellent rate r 1 . Sufficient conditions for the global asymptotic stability of the equilibrium point are derived. On the other hand, it is established that, decreasing the mosquito biting preference or increasing the rate of the repellent effect (i.e personal protection) or the combining both actions, decreases the malaria control reproduction number R 0 . Finally, the interplay between the bed-nets treated repellent effect and mosquito host choice and its potential on the dynamics of malaria is investigated and illustrated numerically. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has not only presented a major global public health and socio-economic crisis, but has also significantly impacted human behavior towards adherence (or lack thereof) to public health intervention and mitigation measures implemented in communities worldwide. This study is based on the use of mathematical modeling approaches to assess the extent to which SARS-CoV-2 transmission dynamics is impacted by population-level changes of human behavior due to factors such as (a) the severity of transmission (such as disease-induced mortality and level of symptomatic transmission), (b) fatigue due to the implementation of mitigation interventions measures (e.g., lockdowns) over a long (extended) period of time, (c) social peer-pressure, among others. A novel behavior-epidemiology model, which takes the form of a deterministic system of nonlinear differential equations, is developed and fitted using observed cumulative SARS-CoV-2 mortality data during the first wave in the United States. The model fits the observed data, as well as makes a more accurate prediction of the observed daily SARS-CoV-2 mortality during the first wave (March 2020–June 2020), in comparison to the equivalent model which does not explicitly account for changes in human behavior. This study suggests that, as more newly-infected individuals become asymptomatically-infectious, the overall level of positive behavior change can be expected to significantly decrease (while new cases may rise, particularly if asymptomatic individuals have higher contact rate, in comparison to symptomatic individuals). [ABSTRACT FROM AUTHOR]

Tuberculosis (TB) remains a pressing global health concern, demanding urgent attention to mitigate its spread and impact. In this study, we present a rigorous mathematical model of TB transmission that incorporates early case detection and addresses the critical issue of treatment failure. Through the development of a system of nonlinear ordinary differential equations, we conduct comprehensive analyses to assess the dynamics of TB transmission and the efficacy of intervention strategies. Our findings underscore the urgent need for effective TB control measures. Mathematical analyses reveal that the model exhibits a TB-free equilibrium, which is globally asymptotically stable only if the control reproduction number falls below one. However, we identify a concerning phenomenon: the model demonstrates a forward bifurcation when the control reproduction number equals one, suggesting that the disease-free equilibrium loses its stability, while simultaneously, the stable unique endemic equilibrium begins to emerge. Moreover, sensitivity analysis highlights the complex interplay between case detection rates, treatment failure probabilities, and TB transmission dynamics. Contrary to expectations, increasing case detection rates and minimizing treatment failure probabilities may not consistently reduce the basic reproduction number or the size of the infected population. Instead, there exists a critical threshold for intervention effectiveness, beyond which TB transmission can be significantly curtailed. Biologically, this phenomenon may occur if there is no balance between case detection and treatment efforts. If treatment quality does not improve, then case detection will not have a significant impact, and in the worst case scenario, it can exacerbate the intervention’s negative effects. These findings underscore the urgency of implementing targeted intervention strategies to combat TB transmission effectively. Failure to meet the critical intervention threshold risks undermining TB elimination efforts and exacerbating the global TB burden. Through numerical simulations, we elucidate potential intervention scenarios necessary for achieving TB elimination goals in human populations. In conclusion, our study highlights the urgent imperative for coordinated action to control TB transmission effectively. By elucidating the dynamics of TB spread and intervention efficacy, we provide valuable insights to inform evidence-based policy decisions and accelerate progress towards TB elimination on a global scale.

Inspired by the transmission characteristics of the Coronavirus disease 2019 (COVID-19), an epidemic model with quarantine and standard incidence rate is first developed, then a novel analysis approach is proposed for finding the ultimate lower bound of the number of infected individuals, which means that the epidemic is uniformly persistent if the control reproduction number ℛ c > 1 . This approach can be applied to the related biomathematical models, and some existing works can be improved by using that. In addition, the infection-free equilibrium V0 of the model is locally asymptotically stable (LAS) if ℛ c < 1 and linearly stable if ℛ c = 1 ; while V0 is unstable if ℛ c > 1 . [ABSTRACT FROM AUTHOR]

Copyright of Journal of Central China Normal University is the property of Huazhong Normal University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Although much progress has been made in reducing the public health burden of the human immunodeficiency virus (HIV), which causes acquired immunodeficiency syndrome (AIDS), since its emergence in the 1980s (largely due to the large-scale use and availability of potent antiviral therapy, improved diagnostic and intervention and mitigation measures), HIV remains an important public health challenge globally, including in the United States. This study is based on the use of mathematical modeling approaches to assess the population-level impact of pre-exposure prophylaxis (PrEP), voluntary testing (to detect undetected HIV-infected individuals), and changes in human behavior (with respect to risk structure), on the spread and control of HIV/AIDS in an MSM (men-who-have sex-with-men) population. Specifically, a novel two-group mathematical model, which stratifies the total MSM population based on risk (low or high) of acquisition of HIV infection, is formulated. The model undergoes a PrEP-induced backward bifurcation when the control reproduction number of the model is less than one if the efficacy of PrEP to prevent a high-risk susceptible MSM individual from acquiring HIV infection is not perfect (the consequence of which is that, while necessary, having the reproduction number of the model less than one is no longer sufficient for the elimination of the disease in the MSM population). For the case where the efficacy of PrEP is perfect, this study shows that the disease-free equilibrium of the two-group model is globally-asymptotically stable when the associated control reproduction number of the model is less than one. Global sensitivity analysis was carried out to identify the main parameters of the model that have the highest influence on the value of the control reproduction number of the model (thereby, having the highest influence on the disease burden in the MSM population). Numerical simulations of the model, using a plausible range of parameter values, show that if half of the MSM population considered adhere strictly to the specified PrEP regimen (while other interventions are maintained at their baseline values), a reduction of about 22% of the new yearly HIV cases recorded at the peak of the disease could be averted (compared to the worst-case scenario where PrEP-based intervention is not implemented in the MSM population). The yearly reduction at the peak increases to about 50% if the PrEP coverage in the MSM population increases to 80%. This study showed, based on the parameter values used in the simulations, that the prospects of elimination of HIV/AIDS in the MSM community are promising if high-risk susceptible individuals are no more than 15% more likely to acquire HIV infection, in comparison to their low-risk counterparts. Furthermore, these prospects are significantly improved if undetected HIV-infected individuals are detected within an optimal period of time. [ABSTRACT FROM AUTHOR]

The emergence of a coronavirus disease (COVID-19) pandemic caused by severe acute respiratory syndrome coronavirus (SARS-COV 2) has caused an unprecedented global societal and public health crisis. A mathematical model that incorporates an individual’s ability to resist COVID-19 infection is considered to study the dynamics of COVID-19. Detection and testing for COVID-19 in individuals who has ability to resist the infection, proper preventive measures, and timely medical care are essential in managing and controlling COVID-19 outbreak. These allows us to make quantifiable predictions about the effects of testing utilization on the COVID-19 prevalence. First, we analyze the disease-free state of the COVID-19 model, calculate the baseline control reproduction number, and obtain the local stability of disease-free equilibrium. The model is calibrated using data obtained from Nigeria Centre for Disease Control and key parameters of the model are estimated. Sensitivity analysis is carried out to investigate the influence of the parameters in curtailing the disease. Numerical simulations are then used to explore the behavior of the model solutions involving the novel variable (genetically resistant humans) and control measures. Our results suggest that strict intervention effort (early detection of genetically resistant individuals, testing and isolation of the infected individuals) is required for quick suppression of the disease.

The COVID-19 epidemic has been spreading around the world for nearly three years, and asymptomatic infections have exacerbated the spread of the epidemic. To analyse and evaluate the role of asymptomatic infections in the spread of the epidemic, we establish an improved COVID-19 infectious disease dynamics model. We fit the epidemic data in the four time periods corresponding to the selected 614G, Alpha, Delta and Omicron variants and obtain the proportion of asymptomatic persons among the infected persons gradually increased and with the increase of the detection ratio, the cumulative number of cases has dropped significantly, but the decline in the proportion of asymptomatic infections is not obvious. Therefore, in view of the hidden transmission of asymptomatic infections, the cooperation between various epidemic prevention and control policies is required to effectively curb the spread of the epidemic. [ABSTRACT FROM AUTHOR]

Numerous prevention intervention strategies have been developed to curtail the spread of pulmonary tuberculosis to susceptible populations. However, pulmonary tuberculosis continues to claim many lives worldwide. In this paper, a deterministic mathematical model incorporating an asymptomatic infectious population, considering vaccine efficacy, and vaccination rate, has been formulated. The model includes asymptomatic infectious individuals since they spread infections incessantly to susceptible populations without being noticed, thus contributing to the high transmission rate. Sensitivity and numerical analysis have been conducted to investigate the impact of varying vaccine efficacy and vaccination rates on the transmission of pulmonary tuberculosis infections from the asymptomatic infectious population. The sensitivity and numerical results show that an increase in vaccine efficacy reduces the asymptomatic infectious population and subsequently lowers the transmission rate of infections. Moreover, an increase in vaccine efficacy was shown to reduce the control reproduction number due to asymptomatic infectious individuals, thereby decreasing the transmission of pulmonary tuberculosis to susceptible populations. Further results indicate that an increase in vaccination rate reduces the control reproduction number due to asymptomatic infectious individuals, consequently lowering the rate of infection transmission. These findings emphasize the need to develop a vaccine of higher efficacy to reduce infection transmission to susceptible populations by the asymptomatic infectious individuals. Additionally, the results underscore the importance of increasing vaccination rates to eradicate pulmonary tuberculosis from the population.

Monkeypox (Mpox) is a viral disease primarily affecting animals that can occasionally be transmitted to humans. While it can cause a rash and flu-like symptoms, it is generally less severe than smallpox. Awareness of the disease, proper preventive measures, and timely medical care are essential in managing and controlling Mpox outbreaks. We develop a new compartmentalized mathematical model to study the impact of intense awareness on the control and mitigation of the Mpox disease. The model captures the dynamics of humans and hosts (mammals) in transmitting Mpox disease while the human susceptible population was stratified into two subgroups of aware and unaware individuals. The model is analytically analyzed, and the simulation shows the prospect of an effective public awareness campaign program in reducing the cumulative incidence (new cases) of Mpox disease. Furthermore, the results suggest the need for consistency and continuous awareness program, adhering to public health measures to increase awareness of the Mpox disease.

In this work, in order to evaluate the immediate and long-term impacts of vaccination on the transmission dynamics of TF, we develop a compartmental mathematical model which takes into account vaccination and medically hygienic compartments for the dynamics of TF transmission in a population. Based on the positivity and boundedness of the model solutions, the model is shown to be mathematically well posed. The next generation matrix method is used to determine the control reproduction number, R0π, of the model. It is shown that the model has a unique disease-free equilibrium, which is proved to be locally asymptotically stable when R0π is less than unity. Further analysis suggests that the model admits a unique endemic equilibrium when R0π is greater than unity. To investigate the effect of the model parameters on the transmission and spread of the disease in the population, sensitivity analysis is conducted. The dynamics of TF spread within the populations under the varying effects of some key sensitive parameters, such as the effective diseases transmission rate in human, bacteria shedding rate from symptomatic infectious humans, vaccine efficacy, decay rate of bacteria from the environment and recovery rate of symptomatic infectious humans, is further studied using numerical simulations. The study suggests some measures that can be put in place to guide against the menace of TF in the population.

SARS COV-2 (Covid-19) has imposed a monumental socio-economic burden worldwide, and its impact still lingers. We propose a deterministic model to describe the transmission dynamics of Covid-19, emphasizing the effects of vaccination on the prevailing epidemic. The proposed model incorporates current information on Covid-19, such as reinfection, waning of immunity derived from the vaccine, and infectiousness of the pre-symptomatic individuals into the disease dynamics. Moreover, the model analysis reveals that it exhibits the phenomenon of backward bifurcation, thus suggesting that driving the model reproduction number below unity may not suffice to drive the epidemic toward extinction. The model is fitted to real-life data to estimate values for some of the unknown parameters. In addition, the model epidemic threshold and equilibria are determined while the criteria for the stability of each equilibrium solution are established using the Metzler approach. A sensitivity analysis of the model is performed based on the Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficients (PRCCs) approaches to illustrate the impact of the various model parameters and explore the dependency of control reproduction number on its constituents parameters, which invariably gives insight on what needs to be done to contain the pandemic effectively. The foregoing notwithstanding, the contour plots of the control reproduction number concerning some of the salient parameters indicate that increasing vaccination coverage and decreasing vaccine waning rate would remarkably reduce the value of the reproduction number below unity, thus facilitating the possible elimination of the disease from the population. Finally, the model is solved numerically and simulated for different scenarios of disease outbreaks with the findings discussed.

China is one of the countries in the world carrying a heavy burden of tuberculosis. Due to the unbalanced economic development, the number of people working in other parts of country is huge, and the mobility of personnel has exacerbated the increase in tuberculosis cases. Most patients affected by this are in their middle and young ages. It is having a great impact among the family and society. Therefore, research on how to control this disease is absolutely necessary. The population is divided into two categories such as local population and the immigrant population. A pulmonary tuberculosis dynamic model with population heterogeneity is established. We calculate the basic reproductive number and the controlled reproductive number, and discuss the two types of population under the constraints given by the amount of vaccine and the optimal immunization ratio obtained is (0. 1 1 8 , 0. 1 0 7) , which can reduce the effective reproduction number from 5.85 to 0.227. It is understood that immunizing the local population will control the spread of the epidemic to a large extent, and we simulate the final scale of infection after immunization under the optimal immunization ratio. It can take a minimum of at least 10 years to reduce the spread of this disease, but to eliminate it forever, it needs at least a minimum of 100 years. [ABSTRACT FROM AUTHOR]

Since the beginning of March 2022, the epidemic due to the Omicron variant has developed rapidly in Jilin Province. To figure out the key controlling factors and validate the model to show the success of the Zero-COVID policy in the province, we constructed a Recursive Zero-COVID Model quantifying the strength of the control measures, and defined the control reproduction number as an index for describing the intensity of interventions. Parameter estimation and sensitivity analysis were employed to estimate and validate the impact of changes in the strength of different measures on the intensity of public health preventions qualitatively and quantitatively. The recursive Zero-COVID model predicted that the dates of elimination of cases at the community level of Changchun and Jilin Cities to be on April 8 and April 17, respectively, which are consistent with the real situation. Our results showed that the strict implementation of control measures and adherence of the public are crucial for controlling the epidemic. It is also essential to strengthen the control intensity even at the final stage to avoid the rebound of the epidemic. In addition, the control reproduction number we defined in the paper is a novel index to measure the intensity of the prevention and control measures of public health.

Contact tracing is an important intervention measure to control infectious diseases. We present a new approach that borrows the edge dynamics idea from network models to track contacts included in a compartmental SIR model for an epidemic spreading in a randomly mixed population. Unlike network models, our approach does not require statistical information of the contact network, data that are usually not readily available. The model resulting from this new approach allows us to study the effect of contact tracing and isolation of diagnosed patients on the control reproduction number and number of infected individuals. We estimate the effects of tracing coverage and capacity on the effectiveness of contact tracing. Our approach can be extended to more realistic models that incorporate latent and asymptomatic compartments.

Mumps is a viral contagious disease associated with puffy cheeks and tender and swollen jaw. It spreads through direct contact with saliva or respiratory droplets from the mouth, nose or throat of infected persons. In this work, we present a mathematical model which describes the dynamics of the disease in a human population. The model incorporates isolation and treatment of infected individuals as a control measure. It is shown that the disease-free equilibrium (DFE) is locally and globally asymptotically stable when the control reproduction number Rc is less than one. It is also shown that the model has a unique endemic equilibrium which exists when Rc > 1. The existence of a unique endemic equilibrium confirms the global stability of the DFE, and the absence of backward bifurcation in the model. Optimal control analysis is performed on the model to obtain the proportion of infected humans to be isolated for optimal control of the disease. Plots are presented to show the dynamics of the disease in the presence of the control measures. [ABSTRACT FROM AUTHOR]

For an infectious disease such as COVID-19, we present a new four-stage vaccination model (unvaccinated, dose 1 + 2, booster, repeated boosters), which examines the impact of vaccination coverage, vaccination rate, generation interval, control reproduction number, vaccine efficacies and rates of waning immunity upon the dynamics of infection. We derive a single equation that allows computation of equilibrium prevalence and incidence of infection, given knowledge about these parameters and variable values. Based upon a 20-compartment model, we develop a numerical simulation of the associated differential equations. The model is not a forecasting or even predictive one, given the uncertainty about several biological parameter values. Rather, it is intended to aid a qualitative understanding of how equilibrium levels of infection may be impacted upon, by the parameters of the system. We examine one-at-a-time sensitivity analysis around a base case scenario. The key finding which should be of interest to policymakers is that while factors such as improved vaccine efficacy, increased vaccination rates, lower waning rates and more stringent non-pharmaceutical interventions might be thought to improve equilibrium levels of infection, this might only be done to good effect if vaccination coverage on a recurrent basis is sufficiently high.

Copyright of Journal of Xinyang Normal University Natural Science Edition is the property of Journal of Xinyang Normal University Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Contact tracing is an important intervention measure to control infectious diseases. We present a new approach that borrows the edge dynamics idea from network models to track contacts included in a compartmental SIR model for an epidemic spreading in a randomly mixed population. Unlike network models, our approach does not require statistical information of the contact network, data that are usually not readily available. The model resulting from this new approach allows us to study the effect of contact tracing and isolation of diagnosed patients on the control reproduction number and number of infected individuals. We estimate the effects of tracing coverage and capacity on the effectiveness of contact tracing. Our approach can be extended to more realistic models that incorporate latent and asymptomatic compartments. [ABSTRACT FROM AUTHOR]

The large-scale infection of COVID-19 has led to a significant impact on lives and economies around the world and has had considerable impact on global public health. Social distancing, mask wearing and contact tracing have contributed to containing or at least mitigating the outbreak, but how public awareness influences the effectiveness and efficiency of such approaches remains unclear. In this study, we developed a discrete compartment dynamic model to mimic and explore how media reporting and the strengthening containment strategies can help curb the spread of COVID-19 using Shaanxi Province, China, as a case study. The targeted model is parameterized based on multi-source data, including the cumulative number of confirmed cases, recovered individuals, the daily number of media-reporting items and the imported cases from the rest of China outside Shaanxi from January 23 to April 11, 2020. We carried out a sensitivity analysis to investigate the effect of media reporting and imported cases on transmission. The results revealed that reducing the intensity of media reporting, which would result in a significant increasing of the contact rate and a sizable decreasing of the contact-tracing rate, could aggravate the outbreak severity by increasing the cumulative number of confirmed cases. It also demonstrated that diminishing the imported cases could alleviate the outbreak severity by reducing the length of the epidemic and the final size of the confirmed cases; conversely, delaying implementation of lockdown strategies could prolong the length of the epidemic and magnify the final size. These findings suggest that strengthening media coverage and timely implementing of lockdown measures can significantly reduce infection.

Acute respiratory illness caused by human adenovirus have been increasing in morbidity and mortality in recent years. Currently, isolation of symptomatic infected individuals is the primary means of controlling outbreaks in closed spaces such as schools and military camps. However, the disease is still spreading despite the implementation of control measures. To reveal the underlying mechanism of this phenomenon, we propose a dynamic model that considers invisible transmission and isolated confirmed cases. By calculating and analyzing the control reproduction number, it is found that asymptomatic infected individuals play an important role in the spread of the epidemic. Therefore, in the absence of specific vaccines, non-pharmaceutical interventions such as quarantine of exposed individuals are effective means to mitigate severity. The results show that the earlier the control of invisible transmission is implemented, the lower the peak and the shorter the duration of the outbreak. These findings will provide the theoretical basis and recommendations for prevention and control of human adenovirus transmission in closed spaces.

A time-delayed dengue virus transmission model has been developed, which takes into account vaccination failure and the presence of exposed mosquitoes. This model also incorporates the survival probability of infected individuals during the incubation period to provide a clearer understanding of how latency affects the control reproduction number R c. Furthermore, by employing the Lyapunov functional approach, we establish the global asymptotic stability of equilibria in relation to R c. The results indicate that the disease-free equilibrium T 0 is globally asymptotically stable if and only if R c ≤ 1 , whereas the endemic equilibrium T ∗ is globally asymptotically stable if and only if R c > 1. [ABSTRACT FROM AUTHOR]

Background: The pandemic coronavirus disease 2019 (COVID-19) has spread and caused enormous and serious damages to many countries worldwide. One of the most typical interventions is the social distancing such as lockdown that would contribute to reduce the number of contacts among undiagnosed individuals. However, prolongation of the period of such a restrictive intervention could hugely affect the social and economic systems, and the outbreak will come back if the strong social distancing policy will end earlier due to the economic damage. Therefore, the social distancing policy should be followed by massive testing accompanied with quarantine to eradicate the infection. Methods: In this paper, we construct a mathematical model and discuss the effect of massive testing with quarantine, which would be less likely to affect the social and economic systems, and its efficacy has been proved in South Korea, Taiwan, Vietnam and Hong Kong. Results: By numerical calculation, we show that the control reproduction number is monotone decreasing and convex downward with respect to the testing rate, which implies that the improvement of the testing rate would highly contribute to reduce the epidemic size if the original testing rate is small. Moreover, we show that the recurrence of the COVID-19 epidemic in Japan could be possible after the lifting of the state of emergency if there is no massive testing and quarantine. Conclusions: If we have entered into an explosive phase of the epidemic, the massive testing could be a strong tool to prevent the disease as long as the positively reacted individuals will be effectively quarantined, no matter whether the positive reaction is pseudo or not. Since total population could be seen as a superposition of smaller communities, we could understand how testing and quarantine policy might be powerful to control the disease.

Abstract Background In December 2019, an outbreak of coronavirus disease (later named as COVID-19) was identified in Wuhan, China and, later on, detected in other parts of China. Our aim is to evaluate the effectiveness of the evolution of interventions and self-protection measures, estimate the risk of partial lifting control measures and predict the epidemic trend of the virus in the mainland of China excluding Hubei province based on the published data and a novel mathematical model. Methods A novel COVID-19 transmission dynamic model incorporating the intervention measures implemented in China is proposed. COVID-19 daily data of the mainland of China excluding Hubei province, including the cumulative confirmed cases, the cumulative deaths, newly confirmed cases and the cumulative recovered cases between 20 January and 3 March 2020, were archived from the National Health Commission of China (NHCC). We parameterize the model by using the Markov Chain Monte Carlo (MCMC) method and estimate the control reproduction number (R c ), as well as the effective daily reproduction ratio- R e (t), of the disease transmission in the mainland of China excluding Hubei province. Results The estimation outcomes indicate that R c is 3.36 (95% CI: 3.20–3.64) and R e (t) has dropped below 1 since 31 January 2020, which implies that the containment strategies implemented by the Chinese government in the mainland of China are indeed effective and magnificently suppressed COVID-19 transmission. Moreover, our results show that relieving personal protection too early may lead to a prolonged disease transmission period and more people would be infected, and may even cause a second wave of epidemic or outbreaks. By calculating the effective reproduction ratio, we prove that the contact rate should be kept at least less than 30% of the normal level by April, 2020. Conclusions To ensure the pandemic ending rapidly, it is necessary to maintain the current integrated restrict interventions and self-protection measures, including travel restriction, quarantine of entry, contact tracing followed by quarantine and isolation and reduction of contact, like wearing masks, keeping social distance, etc. People should be fully aware of the real-time epidemic situation and keep sufficient personal protection until April. If all the above conditions are met, the outbreak is expected to be ended by April in the mainland of China apart from Hubei province.

Abstract Public health interventions have been implemented to mitigate the spread of coronavirus disease 2019 (COVID-19) in Ontario, Canada; however, the quantification of their effectiveness remains to be done and is important to determine if some of the social distancing measures can be relaxed without resulting in a second wave. We aim to equip local public health decision- and policy-makers with mathematical model-based quantification of implemented public health measures and estimation of the trend of COVID-19 in Ontario to inform future actions in terms of outbreak control and de-escalation of social distancing. Our estimates confirm that (1) social distancing measures have helped mitigate transmission by reducing daily infection contact rate, but the disease transmission probability per contact remains as high as 0.145 and case detection rate was so low that the effective reproduction number remained higher than the threshold for disease control until the closure of non-essential business in the Province; (2) improvement in case detection rate and closure of non-essential business had resulted in further reduction of the effective control number to under the threshold. We predict the number of confirmed cases according to different control efficacies including a combination of reducing further contact rates and transmission probability per contact. We show that improved case detection rate plays a decisive role to reduce the effective reproduction number, and there is still much room in terms of improving personal protection measures to compensate for the strict social distancing measures.

Dengue is a vector-borne disease with an increasing incidence worldwide, and it is transmitted by the bites of mosquitoes infected with dengue viruses. This viral infection persistently affects economic sectors and public health. Hence, this paper analyzes an optimal control model of dengue infection with partial immune and asymptomatic individuals. We introduced four time-dependent control measures, thus treated bednets, treatment (prophylactics), insecticides, and vaccination. There is a threshold parameter RC; when RCis less than or equal to one, the disease-free equilibrium exists, and when RCis greater than one, the endemic equilibrium exists. The equilibrium points are globally asymptotically stable using Lyapunov functions. We notice that the control reproduction number, RC,is dependent on the initial number of mosquito population, Nv0, and that of the initial human population, Nh0. It is also noticed that, RCincreases whenever Nv0increases, with constant Nh0. We obtain the adjoint system of the proposed optimal control problem. The optimized system is then solved numerically using Runge–Kutta fourth-order scheme. We performed a cost-effectiveness analysis by proposing five strategies for the optimal control problem. We then calculated the efficacy ratio (ER), infection averted ratio (IAR), average cost-effectiveness ratio (ACER), and the incremental cost-effectiveness ratio (ICER). These results show that the use of vaccination and treatment has the least incremental cost-effectiveness ratio and is consequently more cost-effective (cost-saving). However, in terms of infection averted, the combined use of treated bednets, vaccination, treatment, and insecticides is just as good as vaccination and treatment only.

In this paper, a model of mumps transmission with quarantine measure is proposed and then the control reproduction number ℛ c of the model is obtained. This model admits a unique endemic equilibrium P* if and only if Rc > 1, while the disease-free equilibrium P0 always exists. By using the technique of constructing Lyapunov functions and the generalized Lyapunov-LaSalle theorem, we first show that the equilibrium P0 is globally asymptotically stable (GAS) if Rc ≤ 1; second, we prove that the equilibrium P* is GAS if Rc > 1. Our results reveal that mumps can be eliminated from the community for ℛ c ≤ 1 and it will be persistent for ℛ c > 1 , and quarantine measure can also effectively control the mumps transmission. [ABSTRACT FROM AUTHOR]

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Objectives: Firstly, according to the characteristics of COVID-19 epidemic and the control measures of the government of Shaanxi Province, a general population epidemic model is established. Then, the control reproduction number of general population epidemic model is obtained. Based on the epidemic model of general population, the epidemic model of general population and college population is further established, and the control reproduction number is also obtained. Methods: For the established epidemic model, firstly, the expression of the control reproduction number is obtained by using the next generation matrix. Secondly, the real-time reported data of COVID-19 in Shaanxi Province is used to fit the epidemic model, and the parameters in the model are estimated by least square method and MCMC. Thirdly, the Latin hypercube sampling method and partial rank correlation coefficient (PRCC) are adopted to analyze the sensitivity of the model. Conclusions: The control reproduction number remained at 3 from January 23 to January 31, then gradually decreased from 3 to slightly greater than 0.2 by using the real-time reports on the number of COVID-19 infected cases from Health Committee of Shaanxi Province in China. In order to further control the spread of the epidemic, the following measures can be taken: (i) reducing infection by wearing masks, paying attention to personal hygiene and limiting travel; (ii) improving isolation of suspected patients and treatment of symptomatic individuals. In particular, the epidemic model of the college population and the general population is established, and the control reproduction number is given, which will provide theoretical basis for the prevention and control of the epidemic in the colleges. [ABSTRACT FROM AUTHOR]

Infectious disease outbreaks sometimes overwhelm healthcare facilities. A recent case occurred in West Africa in 2014 when an Ebola virus outbreak overwhelmed facilities in Sierra Leone, Guinea and Liberia. In such scenarios, how many patients can hospitals admit to minimize disease burden? This study considers what type of hospital admission policy during a hypothetical Ebola outbreak can better serve the community, if overcrowding degrades the hospital setting. Our result shows that which policy minimizes loss to the community depends on the initial estimation of the control reproduction number, $R_0$. When the outbreak grows extremely fast ($R_0$$ \gg $1) it is better (in terms of total disease burden) to stop admitting patients after reaching the carrying capacity because overcrowding in the hospital makes the hospital setting ineffective at containing infection, but when the outbreak grows only a little faster than the system's ability to contain it ($R_0 \gtrsim 1$), it is better to admit patients beyond the carrying capacity because limited overcrowding still reduces infection more in the community. However, when $R_0$ is no more than a little greater than 1 (for our parameter values, 1.012), both policies result the same because the number of patients never exceeds the maximum capacity.

Background: The pandemic coronavirus disease 2019 (COVID-19) has spread and caused enormous and serious damages to many countries worldwide. One of the most typical interventions is the social distancing such as lockdown that would contribute to reduce the number of contacts among undiagnosed individuals. However, prolongation of the period of such a restrictive intervention could hugely affect the social and economic systems, and the outbreak will come back if the strong social distancing policy will end earlier due to the economic damage. Therefore, the social distancing policy should be followed by massive testing accompanied with quarantine to eradicate the infection. Methods: In this paper, we construct a mathematical model and discuss the effect of massive testing with quarantine, which would be less likely to affect the social and economic systems, and its efficacy has been proved in South Korea, Taiwan, Vietnam and Hong Kong. Results: By numerical calculation, we show that the control reproduction number is monotone decreasing and convex downward with respect to the testing rate, which implies that the improvement of the testing rate would highly contribute to reduce the epidemic size if the original testing rate is small. Moreover, we show that the recurrence of the COVID-19 epidemic in Japan could be possible after the lifting of the state of emergency if there is no massive testing and quarantine. Conclusions: If we have entered into an explosive phase of the epidemic, the massive testing could be a strong tool to prevent the disease as long as the positively reacted individuals will be effectively quarantined, no matter whether the positive reaction is pseudo or not. Since total population could be seen as a superposition of smaller communities, we could understand how testing and quarantine policy might be powerful to control the disease. [ABSTRACT FROM AUTHOR]

A deterministic model for the effects on disease prevalence of the most advanced pre-erythrocytic vaccine against malaria is proposed and studied. The model includes two vaccinated classes that correspond to initially vaccinated and booster dose vaccinated individuals. These two classes are structured by time-since-initial-vaccination (vaccine-age). This structure is a novelty for vector–host models; it allows us to explore the effects of parameters that describe timed and delayed delivery of a booster dose, and immunity waning on disease prevalence. Incorporating two vaccinated classes can predict more accurately threshold vaccination coverages for disease eradication under multi-dose vaccination programs. We derive a vaccine-age-structured control reproduction number ℛ and establish conditions for the existence and stability of equilibria to the system. The model is bistable when ℛ < 1. In particular, it exhibits a backward (sub-critical) bifurcation, indicating that ℛ = 1 is no longer the threshold value for disease eradication. Thus, to achieve eradication we must identify and implement control measures that will reduce ℛ to a value smaller than unity. Therefore, it is crucial to be cautious when using ℛ to guide public health policy, although it remains a key quantity for decision making. Our results show that if the booster vaccine dose is administered with delay, individuals may not acquire its full protective effect, and that incorporating waning efficacy into the system improves the accuracy of the model outcomes. This study suggests that it is critical to follow vaccination schedules closely, and anticipate the consequences of delays in those schedules. [ABSTRACT FROM AUTHOR]

Public health interventions have been implemented to mitigate the spread of coronavirus disease 2019 (COVID-19) in Ontario, Canada; however, the quantification of their effectiveness remains to be done and is important to determine if some of the social distancing measures can be relaxed without resulting in a second wave. We aim to equip local public health decision- and policy-makers with mathematical model-based quantification of implemented public health measures and estimation of the trend of COVID-19 in Ontario to inform future actions in terms of outbreak control and de-escalation of social distancing. Our estimates confirm that (1) social distancing measures have helped mitigate transmission by reducing daily infection contact rate, but the disease transmission probability per contact remains as high as 0.145 and case detection rate was so low that the effective reproduction number remained higher than the threshold for disease control until the closure of non-essential business in the Province; (2) improvement in case detection rate and closure of non-essential business had resulted in further reduction of the effective control number to under the threshold. We predict the number of confirmed cases according to different control efficacies including a combination of reducing further contact rates and transmission probability per contact. We show that improved case detection rate plays a decisive role to reduce the effective reproduction number, and there is still much room in terms of improving personal protection measures to compensate for the strict social distancing measures. [ABSTRACT FROM AUTHOR]

More than 20 outbreaks of Ebola virus disease have occurred in Africa since 1976, and yet no adequate treatment is available. Hence, prevention, control measures and supportive treatment remain the only means to avoid the disease. Among these measures, contact tracing occupies a prominent place. In this paper, we propose a simple mathematical model that incorporates imperfect contact tracing, quarantine and hospitalization (or isolation). The control reproduction number ℛ c of each sub-model and for the full model are computed. Theoretically, we prove that when ℛ c is less than one, the corresponding model has a unique globally asymptotically stable disease-free equilibrium. Conversely, when ℛ c is greater than one, the disease-free equilibrium becomes unstable and a unique globally asymptotically stable endemic equilibrium arises. Furthermore, we numerically support the analytical results and assess the efficiency of different control strategies. Our main observation is that, to eradicate EVD, the combination of high contact tracing (up to 90%) and effective isolation is better than all other control measures, namely: (1) perfect contact tracing, (2) effective isolation or full hospitalization, (3) combination of medium contact tracing and medium isolation. [ABSTRACT FROM AUTHOR]

Objective: The objective of this study is to develop a mathematical model for the COVID-19 pandemic including vaccination, the transmissibility of the virus-pathogen dose-response relationship, vaccine efficiency, and vaccination rate., Methods: The Runge-Kutta (RK-45) method was applied to solve the proposed model with MATLAB code and the calculated results show the dynamics of the individuals in each compartment. The data of total death due to the COVID-19 pandemic in the case of the USA were collected from GitHub and the re-use of this data needs no ethical clearance. The control reproduction number was used to assess the dose-response relationship and critical vaccination coverage., Results: We have calculated the probability of infection and the infection risk against the different exposure doses and the virus copies, respectively. The results show that the probability of infection increases with the increasing exposure dose for certain virus copies and the risk of infection decreases with the increasing of virus copies for a certain exposure dose. The results also show that the critical vaccination coverage demands increase with an increase in transmission rate and decrease with increasing vaccine efficacy., Conclusions: It was seen that the critical vaccination coverage corresponding to an increased transmission rate rise sharply in the beginning and then reached a threshold. Moreover, the real data of the total death cases in the USA were compared with the fitted curved of the model which validated the proposed model. Vaccination against COVID-19 is essential to control the pandemic, and achieving high vaccine uptake in the population can reduce the pandemic as fast as possible., Competing Interests: The authors declare no conflicts of interest. All the authors have equally agreed to publish the final version of the manuscript., (© 2023 Elsevier España, S.L.U. All rights reserved.)

We develop a mathematical model to closely mimic the integrated program of impulsive vector control (every Friday afternoon since the initiation of the program) and continuous patient treatment and isolation implemented in the Guangdong Province of China during its 2014 dengue outbreak. We fitted the data of accumulated infections and used the parameterized model to carry out a retrospective analysis to estimate the basic reproduction number 1.7425 (95% CI 1.4443–2.0408), the control reproduction number 0.1709, and the mosquito-killing ratios 0.1978, 0.2987, 0.6158 and 0.5571 on October 3, 10, 17 and 24, respectively. This suggests that integrated intervention is highly effective in controlling the dengue outbreak. We also simulated outbreak outcomes under different variations of the implemented interventions. We showed that skipping one Friday for vector control would not result in raising the control reproduction number to the threshold value 1 but would lead to significant increase in the accumulated infections at the end of the outbreak. The findings indicate that quick and persistent impulsive implementation of vector control result in an effective reduction in the control reproduction number and hence lead to significant decline of new infections. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model is proposed and analyzed for Hepatitis C virus (HCV) infection transmissions. In this model, both of chronic primary infection and possibility of reinfection are considered. Two thresholds of basic reproduction number R 0 and control reproduction number R c are derived. We get the sufficient conditions for the existence of infection-free equilibrium and endemic equilibrium. The sufficient conditions for the local and global stability of the equilibria are also obtained. Some numerical simulations are performed to prove the theoretical results. At last, some discussions are presented. [ABSTRACT FROM AUTHOR]

This paper presents a statistical study of a deterministic model for the transmissiondynamics and control of severe acute respiratory syndrome (SARS). The effect of themodel parameters on the dynamics of the disease is analyzed using sensitivity anduncertainty analyses. The response (or output) of interest is the control reproductionnumber, which is an epidemiological threshold governing the persistence or eliminationof SARS in a given population. The compartmental model includes parameters associatedwith control measures such as quarantine and isolation of asymptomatic and symptomaticindividuals. One feature of our analysis is the incorporation of time-dependentfunctions into the model to reflect the progressive refinement of these SARS controlmeasures over time. Consequently, the model contains continuous time-varying inputs andoutputs. In this setting, sensitivity and uncertainty analytical techniques are used inorder to analyze the impact of the uncertainty in the parameter estimates on the resultsobtained and to determine which parameters have the largest impact on driving thedisease dynamics.

The emergence of mutant strains of COVID-19 reduces the effectiveness of vaccines in preventing infection, but remains effective in preventing severe illness and death. This paper established a heterogeneous mixing model of age groups with pharmaceutical and non-pharmaceutical interventions by analyzing the transmission mechanism of breakthrough infection caused by the heterogeneity of protection period under the action of vaccine-preventable infection with the original strain. The control reproduction number R c of the system is analyzed, and the existence and stability of equilibrium are given by the comparison principle. Numerical simulation was conducted to evaluate the vaccination program and intervention measures in the customized scenario, demonstrating that the group-3 coverage rate p 3 plays a key role in R c. It is proposed that accelerating the rate of admission and testing is conducive to epidemic control by further fitting data of COVID-19 transmission in real scenarios. The findings provide a general modeling idea for the emergence of new vaccines to prevent infection by mutant strains, as well as a solid theoretical foundation for mainland China to formulate future vaccination strategies for new vaccines. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics". • A modeling framework of heterogeneous mixing for COVID-19 with NPIs and vaccines. • Breakthrough infection and vaccines to reduce infection were incorporated into model. • Dynamical properties are analyzed, including threshold and stabilities of equilibria. • The vaccination strategies in custom scenario were explored with multiple indicators. [ABSTRACT FROM AUTHOR]

We develop a mathematical model for the dynamics of malaria with a varying population for which new individuals are recruited through immigration and births. In the model, we assume that non‐immune travellers move to endemic regions with sprays, smear themselves with jelly that is repellent to mosquitoes on arrival in malarious regions, others take long term antimalarials, and pregnant women and infants receive full treatment doses at intervals even when they are not sick from malaria (commonly referred to as intermittent preventive therapy). We introduce more features that describe the dynamics of the disease for the control strategies that protect the above vulnerable groups. The model analysis is done and equilibrium points are analyzed to establish their local and global stability. The threshold of the disease, the control reproduction number, is established for which the disease can be eliminated. First Published Online: 14 Oct 2010

W.O. Kermack and A.G. McKendrick introduced in their fundamental paper, A Contribution to the Mathematical Theory of Epidemics, published in 1927, a deterministic model that captured the qualitative dynamic behavior of single infectious disease outbreaks. A Kermack–McKendrick discrete-time general framework, motivated by the emergence of a multitude of models used to forecast the dynamics of epidemics, is introduced in this manuscript. Results that allow us to measure quantitatively the role of classical and general distributions on disease dynamics are presented. The case of the geometric distribution is used to evaluate the impact of waiting-time distributions on epidemiological processes or public health interventions. In short, the geometric distribution is used to set up the baseline or null epidemiological model used to test the relevance of realistic stage-period distribution on the dynamics of single epidemic outbreaks. A final size relationship involving the control reproduction number, a function of transmission parameters and the means of distributions used to model disease or intervention control measures, is computed. Model results and simulations highlight the inconsistencies in forecasting that emerge from the use of specific parametric distributions. Examples, using the geometric, Poisson and binomial distributions, are used to highlight the impact of the choices made in quantifying the risk posed by single outbreaks and the relative importance of various control measures. [ABSTRACT FROM AUTHOR]

Abstract: A multigroup SIR epidemiological model is used to study the effects of group-targeted vaccination strategies on disease control and prevention. The model takes into consideration both proportionate and preferential mixing patterns between groups. We show that the dynamical behaviors of the model are determined by the control reproduction number and, under certain conditions, by the type-reproduction number T 1v . These reproduction numbers provide criteria for evaluating control strategies including targeted vaccination programs and reduction of interactions between groups. We also illustrate how these reproduction numbers can be used to examine the influence of population heterogeneities such as group preferences, activity levels, and mixing patterns. Criteria are also established for disease eradication from the entire network of populations by applying vaccination strategies in one or some sub-populations. [Copyright &y& Elsevier]

Abstract: Compartmental models for influenza that include control by vaccination and antiviral treatment are formulated. Analytic expressions for the basic reproduction number, control reproduction number and the final size of the epidemic are derived for this general class of disease transmission models. Sensitivity and uncertainty analyses of the dependence of the control reproduction number on the parameters of the model give a comparison of the various intervention strategies. Numerical computations of the deterministic models are compared with those of recent stochastic simulation influenza models. Predictions of the deterministic compartmental models are in general agreement with those of the stochastic simulation models. [Copyright &y& Elsevier]

We develop a mathematical model for the dynamics of malaria with a varying population for which new individuals are recruited through immigration and births. In the model, we assume that non-immune travellers move to endemic regions with sprays, smear themselves with jelly that is repellent to mosquitoes on arrival in malarious regions, others take long term antimalarials, and pregnant women and infants receive full treatment doses at intervals even when they are not sick from malaria (commonly referred to as intermittent preventive therapy). We introduce more features that describe the dynamics of the disease for the control strategies that protect the above vulnerable groups. The model analysis is done and equilibrium points are analyzed to establish their local and global stability. The threshold of the disease, the control reproduction number, is established for which the disease can be eliminated. [ABSTRACT FROM AUTHOR]