An Sveir Model for Assessing Potential Impact of an Imperfect Anti-SARS Vaccine

The control of severe acute respiratory syndrome (SARS), a fatal contagious viral disease that spread to over 32 countries in 2003, was based on quarantine of latently infected individuals and isolation of individuals with clinical symptoms of SARS. Owing to the recent ongoing clinical trials of some candidate anti-SARS vaccines, this study aims to assess, via mathematical modelling, the potential impact of a SARS vaccine, assumed to be imperfect, in curtailing future outbreaks. A relatively simple deterministic model is designed for this purpose. It is shown, using Lyapunov function theory and the theory of compound matrices, that the dynamics of the model are determined by a certain threshold quantity known as the control reproduction number (Rv). If Rv ≤ 1, the disease will be eliminated from the community; whereas an epidemic occurs if Rv \u3e 1. This study further shows that an imperfect SARS vaccine with infection-blocking efficacy is always beneficial in reducing disease spread within the community, although its overall impact increases with increasing efficacy and coverage. In particular, it is shown that the fraction of individuals vaccinated at steady-state and vaccine efficacy play equal roles in reducing disease burden, and the vaccine must have efficacy of at least 75% to lead to effective control of SARS (assuming R0 = 4). Numerical simulations are used to explore the severity of outbreaks when Rv \u3e 1

Modeling the impact of quarantine during an outbreak of Ebola virus disease

The quarantine of people suspected of being exposed to an infectious agent is one of the most basic public health measure that has historically been used to combat the spread of communicable diseases in human communities. This study presents a new deterministic model for assessing the population-level impact of the quarantine of individuals suspected of being exposed to disease on the spread of the 2014–2015 outbreaks of Ebola viral disease. It is assumed that quarantine is imperfect (i.e., individuals can acquire infection during quarantine). In the absence of quarantine, the model is shown to exhibit global dynamics with respect to the disease-free and its unique endemic equilibrium when a certain epidemiological threshold (denoted by $\mathcal{R}_0$) is either less than or greater than unity. Thus, unlike the full model with imperfect quarantine (which is known to exhibit the phenomenon of backward bifurcation), the version of the model with no quarantine does not undergo a backward bifurcation. Using data relevant to the 2014–2015 Ebola transmission dynamics in the three West African countries (Guinea, Liberia and Sierra Leone), uncertainty analysis of the model show that, although the current level and effectiveness of quarantine can lead to significant reduction in disease burden, they fail to bring the associated quarantine reproduction number ($\mathcal{R}_0^Q$) to a value less than unity (which is needed to make effective disease control or elimination feasible). This reduction of $\mathcal{R}_0^Q$ is, however, very possible with a modest increase in quarantine rate and effectiveness. It is further shown, via sensitivity analysis, that the parameters related to the effectiveness of quarantine (namely the parameter associated with the reduction in infectiousness of infected quarantined individuals and the contact rate during quarantine) are the main drivers of the disease transmission dynamics. Overall, this study shows that the singular implementation of a quarantine intervention strategy can lead to the effective control or elimination of Ebola viral disease in a community if its coverage and effectiveness levels are high enough

The computation of reproduction numbers for the environment-host-environmen cholera transmission dynamics

This study presents a new model for the environment-host-environment transmission dynamics of V. cholerae in a community with an interconnected aquatic pond–river water network. For the case when the human host is the sole target of anti-cholera control and the volume of water in the pond is maximum, the disease-free equilibrium of the model is shown to be globally asymptotically stable whenever a certain epidemiological threshold, known as the basic reproduction number, is less than unity. The epidemiological implication of this result is that cholera can be eliminated from the community if the control strategies implemented can bring (and maintain) the basic reproduction number to a value less than unity. Four scenarios, that represent different interpretations of the role of the V. cholerea pathogen within the environment, were studied. The corresponding basic reproduction numbers were shown to exhibit the same threshold property with respect to the value unity (i.e., if one is less (equal, greater) than unity, then the three others are also less (equal, greater) than unity. Further, it was shown that for the case where anti-cholera control is focused on the human host population, the associated type reproduction number of the model (corresponding to each of the four transmission scenarios considered) is unique. The implication of this result is that the estimate of the effort needed for disease elimination (i.e., the required herd immunity threshold) is unique, regardless of which of the four transmission scenarios is considered. However, when any of the other two bacterial population types in the aquatic environment (i.e., bacterial in the pond or river) is the focus of the control efforts, this study shows that the associated type reproduction number is not unique. Extensive numerical simulations of the model, using a realistic set of parameters from the published literature, show that the community-wide implementation of a strategy that focus on improved water quality, sanitation, and hygiene (known as WASH-only strategy), using the current estimated coverage of 50% and efficacy of 60%, is unable to lead to the elimination of the disease. Such elimination is attainable if the coverage and efficacy are increased (e.g., to 80% and 90%, respectively). Further, elimination can be achieved using a strategy that focuses on oral rehydration therapy and the use of antibiotics to treat the infected humans (i.e., treatment-only strategy) for moderate effectiveness and coverage levels. The combined hybrid WASH-treatment strategy provides far better population-level impact vis a vis disease elimination. This study ranks the three interventions in the following order of population-level effectiveness: combined WASH-treatment, followed by treatment-only and then WASH-only strategy.Gruppo Nazionale per la Fisica Matematica (GNFM), the Istituto Nazionale di Alta Matematica Francesco Severi (INdAM) of Italy, the Simons Foundation and the National Science Foundation.https://www.worldscientific.com/worldscinet/jbs2021-02-13hj2020Mathematics and Applied Mathematic

Mathematical assessment of the role of vector insecticide resistance and feeding/resting behavior on malaria transmission dynamics: Optimal control analysis

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.The large-scale use of insecticide-treated bednets (ITNs) and indoor residual spraying (IRS), over the last two decades, has resulted in a dramatic reduction of malaria incidence globally. However, the effectiveness of these interventions is now being threatened by numerous factors, such as resistance to insecticide in the mosquito vector and their preference to feed and rest outdoors or early in the evening (when humans are not protected by the bednets). This study presents a new deterministic model for assessing the population-level impact of mosquito insecticide resistance on malaria transmission dynamics. A notable feature of the model is that it stratifies the mosquito population in terms of type (wild or resistant to insecticides) and feeding preference (indoor or outdoor). The model is rigorously analysed to gain insight into the existence and asymptotic stability properties of the various disease-free equilibria of the model namely the trivial disease-free equilibrium, the non-trivial resistant-only boundary disease-free equilibrium and a non-trivial disease-free equlibrium where both the wild and resistant mosquito geneotypes co-exist). Simulations of the model, using data relevant to malaria transmission dynamics in Ethiopia (a malaria-endemic nation), show that the use of optimal ITNs alone, or in combination with optimal IRS, is more effective than the singular implementation of an optimal IRS-only strategy. Further, when the effect of the fitness cost of insecticide resistance with respect to fecundity (i.e., assuming a decrease in the baseline birth rate of new resistant-type adult female mosquitoes) is accounted for, numerical simulations of the model show that the combined optimal ITNs-IRS strategy could lead to the effective control of the disease, and insecticide resistance effectively managed during the first 8 years of the 15-year implementation period of the insecticides-based anti-malaria control measures in the community.National Institute for Mathematical and Biological SynthesisNSF Award # EF-0832858The University of Tennessee, Knoxvill

Weather-driven malaria transmission model with gonotrophic and sporogonic cycles

Malaria is mainly a tropical disease and its transmission cycle is heavily influenced by environment: The life-cycles of the Anopheles mosquito vector and Plasmodium parasite are both strongly affected by ambient temperature, while suitable aquatic habitat is necessary for immature mosquito development. Therefore, how global warming may affect malaria burden is an active question, and we develop a new ordinary differential equations-based malaria transmission model that explicitly considers the temperature-dependent Anopheles gonotrophic and Plasmodium sporogonic cycles. Mosquito dynamics are coupled to infection among a human population with symptomatic and asymptomatic disease carriers, as well as temporary immunity. We also explore the effect of incorporating diurnal temperature variations upon transmission. Rigorous analysis of the model show that the non-trivial disease-free equilibrium is locallyasymptotically stable when the associated reproduction number is less than unity (this equilibrium is globally-asymptotically for a special case with no density-dependent larval and disease-induced host mortality). Numerical simulations of the model, for the case where the ambient temperature is held constant, suggest a nonlinear, hyperbolic relationship between the reproduction number and clinical malaria burden. Moreover, malaria burden peaks at 29.5 oC when daily ambient temperature is held constant, but this peak decreases with increasing daily temperature variation, to about 23–25 oC. Malaria burden also varies nonlinearly with temperature, such that small temperature changes influent disease mainly at marginal temperatures, suggesting that in areas where malaria is highly endemic, any response to global warming may be highly nonlinear and most typically minimal, while in areas of more marginal malaria potential (such as the East African highlands), increasing temperatures may translate nearly linearly into increased disease potential. Finally, we observe that while explicitly modelling the stages of the Plasmodium sporogonic cycle is essential, explicitly including the stages of the Anopheles gonotrophic cycle is of minimal importance.National Institute for Mathematical and Biological Synthesis (NIMBioS) is an Institute sponsored by the National Science Foundation, the U.S. Department of Homeland Security, and the U.S. Department of Agriculture through NSF Award #EF-0832858, with additional support from The University of Tennessee, Knoxville.http://www.tandfonline.com/loi/tjbd20am2020Mathematics and Applied Mathematic

Will vaccine-derived protective immunity curtail COVID-19 variants in the US?

Multiple effective vaccines are currently being deployed to combat the COVID-19 pandemic, and are viewed as the major factor in marked reductions of disease burden in regions with moderate to high vaccination coverage. The effectiveness of COVID-19 vaccination programs is, however, significantly threatened by the emergence of new SARS-COV-2 variants that, in addition to being more transmissible than the wild-type (original) strain, may at least partially evade existing vaccines. A two-strain (one wildtype, one variant) and two-group (vaccinated or otherwise) mechanistic mathematical model is designed and used to assess the impact of the vaccine-induced cross-protective efficacy on the spread the COVID-19 pandemic in the United States. Rigorous analysis of the model shows that, in the absence of any co-circulating SARS-CoV-2 variant, the vaccine-derived herd immunity threshold needed to eliminate the wild-type strain can be achieved if 59% of the US population is fully-vaccinated with either the Pfizer or Moderna vaccine. This threshold increases to 76% if the wild-type strain is co-circulating with the Alpha variant (a SARS-CoV-2 variant that is 56% more transmissible than the wild-type strain). If the wild-type strain is co-circulating with the Delta variant (which is estimated to be 100% more transmissible than the wild-type strain), up to 82% of the US population needs to be vaccinated with either of the aforementioned vaccines to achieve the vaccine-derived herd immunity. Global sensitivity analysis of the model reveal the following four parameters as the most influential in driving the value of the reproduction number of the variant strain (hence, COVID-19 dynamics) in the US: (a) the infectiousness of the co-circulating SARS-CoV-2 variant, (b) the proportion of individuals fully vaccinated (using Pfizer or Moderna vaccine) against the wild-type strain, (c) the cross-protective efficacy the vaccines offer against the variant strain and (d) the modification parameter accounting for the reduced infectiousness of fully-vaccinated individuals experiencing breakthrough infection. Specifically, numerical simulations of the model show that future waves or surges of the COVID-19 pandemic can be prevented in the US if the two vaccines offer moderate level of cross-protection against the variant (at least 67%). This study further suggests that a new SARS-CoV-2 variant can cause a significant disease surge in the US if (i) the vaccine coverage against the wild-type strain is low (roughly <66%) (ii) the variant is much more transmissible (e.g., 100% more transmissible), than the wild-type strain, or (iii) the level of cross-protection offered by the vaccine is relatively low (e.g., less than 50%). A new SARS-CoV-2 variant will not cause such surge in the US if it is only moderately more transmissible (e.g., the Alpha variant, which is 56% more transmissible) than the wild-type strain, at least 66% of the population of the US is fully vaccinated, and the three vaccines being deployed in the US (Pfizer, Moderna, and Johnson & Johnson) offer a moderate level of cross-protection against the variant.The Simons Foundation and the National Science Foundation.http://www.keaipublishing.com/idmam2022Mathematics and Applied Mathematic

Cross-immunity-induced backward bifurcation for a model of transmission dynamics of two strains of influenza

A new deterministic model for the transmission dynamics of two strains of in- uenza is designed and used to qualitatively assess the role of cross-immunity on the transmission process. It is shown that incomplete cross-immunity could in- duce the phenomenon of backward bifurcation when the associated reproduction number is less than unity. The model undergoes competitive exclusion (where Strain i drives out Strain j to extinction whenever R0i > 1 > R0j ; i; j = 1; 2; i ̸= j). For the case where infection with one strain confers complete im- munity against infection with the other strain, it is shown that the disease-free equilibrium of the model is globally-asymptotically stable whenever the repro- duction number is less than unity. In the absence of cross-immunity, the model can have a continuum of co-existence endemic equilibria (which is shown to be globally-asymptotically stable for a special case). When infection with one strain confers incomplete immunity against the other. Numerical simulations of the model show that the two strains co-exist, with Strain i dominating (but not driving out Strain j), whenever R0i > R0j > 1.http://www.elsevier.com/locate/nonrwaam201

Mathematics of a single-locus model for assessing the impacts of pyrethroid resistance and temperature on population abundance of malaria mosquitoes

Please read abstract in the article.http://www.keaipublishing.com/en/journals/infectious-disease-modelling/Mathematics and Applied Mathematic