Modelling the transmission dynamics and control of the novel 2009 swine influenza (H1N1) pandemic

Dynamics of a two-group model for assessing the impacts of pre-exposure prophylaxis, testing and risk behaviour change on the spread and control of HIV/AIDS in an MSM population

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.

Population heterogeneity in vaccine coverage impacts epidemic thresholds and bifurcation dynamics

Population heterogeneity, especially in individuals' contact networks, plays an important role in transmission dynamics of infectious diseases. For vaccine-preventable diseases, outstanding issues like vaccine hesitancy and availability of vaccines further lead to nonuniform coverage among groups, not to mention the efficacy of vaccines and the mixing pattern varying from one group to another. As the ongoing COVID-19 pandemic transitions to endemicity, it is of interest and significance to understand the impact of aforementioned population heterogeneity on the emergence and persistence of epidemics. Here we analyze epidemic thresholds and characterize bifurcation dynamics by accounting for heterogeneity caused by group-dependent characteristics, including vaccination rate and efficacy as well as disease transmissibility. Our analysis shows that increases in the difference in vaccination coverage among groups can render multiple equilibria of disease burden to exist even if the overall basic reproductive ratio is below one (also known as backward bifurcation). The presence of other heterogeneity factors such as differences in vaccine efficacy, transmission, mixing pattern, and group size can each exhibit subtle impacts on bifurcation. We find that heterogeneity in vaccine efficacy can undermine the condition for backward bifurcations whereas homophily tends to aggravate disease endemicity. Our results have practical implications for improving public health efforts by addressing the role of population heterogeneity in the spread and control of diseases.

Comparing the transmission potential from sequence and surveillance data of 2009 North American influenza pandemic waves

Technological advancements in phylodynamic modeling coupled with the accessibility of real-time pathogen genetic data are increasingly important for understanding the infectious disease transmission dynamics. In this study, we compare the transmission potentials of North American influenza A(H1N1)pdm09 derived from sequence data to that derived from surveillance data. The impact of the choice of tree-priors, informative epidemiological priors, and evolutionary parameters on the transmission potential estimation is evaluated. North American Influenza A(H1N1)pdm09 hemagglutinin (HA) gene sequences are analyzed using the coalescent and birth-death tree prior models to estimate the basic reproduction number (R ₀ ). Epidemiological priors gathered from published literature are used to simulate the birth-death skyline models. Path-sampling marginal likelihood estimation is conducted to assess model fit. A bibliographic search to gather surveillance-based R ₀ values were consistently lower (mean ≤ 1.2) when estimated by coalescent models than by the birth-death models with informative priors on the duration of infectiousness (mean ≥ 1.3 to ≤2.88 days). The user-defined informative priors for use in the birth-death model shift the directionality of epidemiological and evolutionary parameters compared to non-informative estimates. While there was no certain impact of clock rate and tree height on the R ₀ estimation, an opposite relationship was observed between coalescent and birth-death tree priors. There was no significant difference (p = 0.46) between the birth-death model and surveillance R ₀ estimates. This study concludes that tree-prior methodological differences may have a substantial impact on the transmission potential estimation as well as the evolutionary parameters. The study also reports a consensus between the sequence-based R ₀ estimation and surveillance-based R ₀ estimates. Altogether, these outcomes shed light on the potential role of phylodynamic modeling to augment existing surveillance and epidemiological activities to better assess and respond to emerging infectious diseases.

Propagation of H1N1 virus through saliva movement in oesophagus: a mathematical model

H1N1 (Swine flu) is caused by the influenza A virus which belongs to the Orthomyxoviridae family. Influenza A is very harmful to the elderly, and people with chronic respiratory disease and cardiovascular disease. Therefore, it is essential to analyse the behaviour of virus transmission through the saliva movement in oesophagus. A mathematical paradigm is developed to study the saliva movement under the applications of transverse magnetic field. Jeffrey fluid model is considered for saliva to show the viscoelastic nature. The flow nature is considered creeping and assumptions of long wavelength and low Reynolds number are adopted for analytical solutions. The Basset-Boussinesq-Oseen equation is employed to understand the propagation of H1N1 virus through saliva under the effect of applicable forces such as gravity, virtual mass, basset force, and drag forces. The suitable data for saliva, oesophagus and H1N1 virus are taken from the existing literature for simulation of the results using MATLAB software. From the graphical results, it is observed that the susceptibility to viral infections is less because the magnetic field reduces the motion of the virus particle. Further, the chances of infections in males are more as compared to females and children due to variation in viscosity of saliva. Such findings provide an understanding of the mechanics of the virus floating through the saliva (viscoelastic fluids) in the oesophagus.

A BEHAVIORAL CHANGE MODEL TO ASSESS VACCINATION-INDUCED RELAXATION OF SOCIAL DISTANCING DURING AN EPIDEMIC

The success of mass vaccination campaigns may be jeopardized by human risky behaviors. For example, high level of vaccination coverage may induce early relaxation of social distancing. In this paper, we focus on the mutual influence between the decline in prevalence, due to the rise in the overall immunization coverage, and the consequent decrease in the compliance to social distancing measures. We consider an epidemic model where both the vaccination rate and the disease transmission rate are influenced by human behavior, which in turn depends on the current and past information about the spread of the disease. We highlight the impact of the information-related parameters on the transient and asymptotic behavior of the system that is on the early stage of the epidemic and its final outcome. Among the main results, we evidence that sustained oscillations may be triggered by the behavioral memory in the prevalence-dependent vaccination rate. However, the relaxation of social distancing may induce a switch from a cyclic regime to damped oscillations.

First two months of the 2019 Coronavirus Disease (COVID-19) epidemic in China: real-time surveillance and evaluation with a second derivative model

Background

Similar to outbreaks of many other infectious diseases, success in controlling the novel 2019 coronavirus infection requires a timely and accurate monitoring of the epidemic, particularly during its early period with rather limited data while the need for information increases explosively.

Methods

In this study, we used a second derivative model to characterize the coronavirus epidemic in China with cumulatively diagnosed cases during the first 2 months. The analysis was further enhanced by an exponential model with a close-population assumption. This model was built with the data and used to assess the detection rate during the study period, considering the differences between the true infections, detectable and detected cases.

Results

Results from the second derivative modeling suggest the coronavirus epidemic as nonlinear and chaotic in nature. Although it emerged gradually, the epidemic was highly responsive to massive interventions initiated on January 21, 2020, as indicated by results from both second derivative and exponential modeling analyses. The epidemic started to decelerate immediately after the massive actions. The results derived from our analysis signaled the decline of the epidemic 14 days before it eventually occurred on February 4, 2020. Study findings further signaled an accelerated decline in the epidemic starting in 14 days on February 18, 2020.

Conclusions

The coronavirus epidemic appeared to be nonlinear and chaotic, and was responsive to effective interventions. The methods used in this study can be applied in surveillance to inform and encourage the general public, public health professionals, clinicians and decision-makers to take coordinative and collaborative efforts to control the epidemic.

Control strategy design for the anti-HBV mathematical model

Currently, the anti-viral therapy has been extensively utilised to reduce the viral burden and switch off certain infectious sources for hepatitis B virus (HBV) infected patients in clinical treatment. Several pieces of existing evidence have demonstrated that large-scale coverage with anti-viral therapy has obtained a certain great contribution in hygiene and disease control. In this study, an anti-HBV mathematical model is considered and its control strategy of the drug treatment is designed. Based on the Lyapunov theory, this study derives three main theorems to propose three different control strategies, respectively, for drug treatments [inline-formula removed] and [inline-formula removed], such that all states of the anti-HBV model can finally converge to the infection-free equilibrium point [inline-formula removed] asymptotically. Especially, the designed drug treatment [inline-formula removed] or [inline-formula removed] is not a fixed value, but it is time-varying and dependent on states. In Theorem 1, the single drug treatment [inline-formula removed] without [inline-formula removed] is synthesised. Theorem 2 considers the single drug treatment [inline-formula removed] without [inline-formula removed]. In Theorem 3, the combination therapy of [inline-formula removed] and [inline-formula removed] is designed. Finally, there are several simulations to show that the proposed combination therapy is much more effective to cure HBV infected patients than the drug treatment with solely single [inline-formula removed] or single [inline-formula removed].

Converging and emerging threats to health security

Advances in biological sciences have outpaced regulatory and legal frameworks for biosecurity. Simultaneously, there has been a convergence of scientific disciplines such as synthetic biology, data science, advanced computing and many other technologies, which all have applications in health. For example, advances in cybercrime methods have created ransomware attacks on hospitals, which can cripple health systems and threaten human life. New kinds of biological weapons which fall outside of traditional Cold War era thinking can be created synthetically using genetic code. These convergent trajectories are dramatically expanding the repertoire of methods which can be used for benefit or harm. We describe a new risk landscape for which there are few precedents, and where regulation and mitigation are a challenge. Rapidly evolving patterns of technology convergence and proliferation of dual-use risks expose inadequate societal preparedness. We outline examples in the areas of biological weapons, antimicrobial resistance, laboratory security and cybersecurity in health care. New challenges in health security such as precision harm in medicine can no longer be addressed within the isolated vertical silo of health, but require cross-disciplinary solutions from other fields. Nor can they cannot be managed effectively by individual countries. We outline the case for new cross-disciplinary approaches in risk analysis to an altered risk landscape.

Evaluation of Influenza Vaccination Efficacy: A Universal Epidemic Model

By means of a designed epidemic model, we evaluated the influence of seasonal vaccination coverage as well as a potential universal vaccine with differing efficacy on the aftermath of seasonal and pandemic influenza. The results of the modeling enabled us to conclude that, to control a seasonal influenza epidemic with a reproduction coefficient R₀ ≤ 1.5, a 35% vaccination coverage with the current seasonal influenza vaccine formulation is sufficient, provided that other epidemiology measures are regularly implemented. Increasing R₀ level of pandemic strains will obviously require stronger intervention. In addition, seasonal influenza vaccines fail to confer protection against antigenically distinct pandemic influenza strains. Therefore, the necessity of a universal influenza vaccine is clear. The model predicts that a potential universal vaccine will be able to provide sufficient reliable (90%) protection against pandemic influenza only if its efficacy is comparable with the effectiveness of modern vaccines against seasonal influenza strains (70%–80%); given that at least 40% of the population has been vaccinated in advance, ill individuals have been isolated (observed), and a quarantine has been introduced. If other antiepidemic measures are absent, a vaccination coverage of at least 80% is required.

Mathematical analysis of swine influenza epidemic model with optimal control

A deterministic model is designed and used to analyze the transmission dynamics and the impact of antiviral drugs in controlling the spread of the 2009 swine influenza pandemic. In particular, the model considers the administration of the antiviral both as a preventive as well as a therapeutic agent. Rigorous analysis of the model reveals that its disease-free equilibrium is globally asymptotically stable under a condition involving the threshold quantity-reproduction number R c . The disease persists uniformly ifR c > 1 and the model has a unique endemic equilibrium under certain condition. The model undergoes backward bifurcation if the antiviral drugs are completely efficient. Uncertainty and sensitivity analysis is presented to identify and study the impact of critical model parameters on the reproduction number. A time dependent optimal treatment strategy is designed using Pontryagin's maximum principle to minimize the treatment cost and the infected population. Finally the reproduction number is estimated for the influenza outbreak and model provides a reasonable fit to the observed swine (H1N1) pandemic data in Manitoba, Canada, in 2009.

Modelling effectiveness of herd level vaccination against Q fever in dairy cattle

Q fever is a worldwide zoonosis caused by the bacterium Coxiella burnetii. The control of this infection in cattle is crucial: infected ruminants can indeed encounter reproductive disorders and represent the most important source of human infection. In the field, vaccination is currently advised in infected herds but the comparative effectiveness of different vaccination protocols has never been explored: the duration of the vaccination programme and the category of animals to be vaccinated have to be determined. Our objective was to compare, by simulation, the effectiveness over 10 years of three different vaccination strategies in a recently infected dairy cattle herd.A stochastic individual-based epidemic model coupled with a model of herd demography was developed to simulate three temporal outputs (shedder prevalence, environmental bacterial load and number of abortions) and to calculate the extinction rate of the infection. For all strategies, the temporal outputs were predicted to strongly decrease with time at least in the first years of vaccination. However, vaccinating only three years was predicted inadequate to stabilize these dynamic outputs at a low level. Vaccination of both cows and heifers was predicted as being slightly more effective than vaccinating heifers only. Although the simulated extinction rate of the infection was high for both scenarios, the outputs decreased slower when only heifers were vaccinated.Our findings shed new light on vaccination effectiveness related to Q fever. Moreover, the model can be further modified for simulating and assessing various Q fever control strategies such as environmental and hygienic measures.