Net Reproduction Number Research Articles

Modeling insect growth regulators for pest management.

Insect growth regulators (IGRs) have been developed as effective control measures against harmful insect pests to disrupt their normal development. This study is to propose a mathematical model to evaluate the cost-effectiveness of IGRs for pest management. The key features of the model include the temperature-dependent growth of insects and realistic impulsive IGRs releasing strategies. The impulsive releases are carefully modeled by counting the number of implements during an insect's temperature-dependent development duration, which introduces a surviving probability determined by a product of terms corresponding to each release. Dynamical behavior of the model is illustrated through dynamical system analysis and a threshold-type result is established in terms of the net reproduction number. Further numerical simulations are performed to quantitatively evaluate the effectiveness of IGRs to control populations of harmful insect pests. It is interesting to observe that the time-changing environment plays an important role in determining an optimal pest control scheme with appropriate release frequencies and time instants.

Global dynamics of discrete mathematical models of tuberculosis

In this paper, we develop discrete models of Tuberculosis (TB). This includes SEI endogenous and exogenous models without treatment. These models are then extended to a SEIT model with treatment. We develop two types of net reproduction numbers, one is the traditional R 0 which is based on the disease-free equilibrium, and a new net reproduction number R 0 ( E ∗ ) based on the endemic equilibrium. It is shown that the disease-free equilibrium is globally asymptotically stable if R 0 ≤ 1 and unstable if R 0 > 1 . Moreover, the endemic equilibrium is locally asymptotically stable if R 0 ( E ∗ ) < 1 < R 0 .

Modeling the population dynamics and movement of Zebra mussels

Zebra mussels have caused significant damage in many lakes and rivers. By using a hybrid population model with discrete-time equations and ordinary differential equations, we represent the zebra mussel's life cycle, growth, and population movement. The dynamics of the larvae (unsettled and settled larvae) are represented during the summer months in a system of two ordinary differential equations, while the juvenile, small adult, and large adult stages are represented by a discrete model with yearly time steps. The goal is to investigate the effects of zebra mussel movement between three different spatial locations and possible control measures. Zebra mussel data and temperature values from three locations in the Hudson River over several years were used to estimate model parameters. We investigate the stability and net reproductive number for our model. We illustrate numerically the hybrid population model for several scenarios of movement and cleaning boats to remove mussels.

The impact of dispersal and allee effects on tick invasion: a spatially-explicit discrete-time modelling approach

We develop a spatially-explicit discrete-time model that describes tick population dynamics and incorporates the developmental stages for an individual tick. The model allows for two types of movements across patches: (1) active tick movement and (2) movement of ticks through a host. We analyse the dynamics of the model under a nonlinear fecundity term that exhibits an Allee effect. We show that the system has bounded solutions and, under certain conditions on the parameters, is monotone. Using the next generation matrix approach, we define the net reproductive number of the multi-patch model, R ( 0 ) , and establish conditions under which R ( 0 ) determines the local and global asymptotic stability of the extinction equilibrium. We then show that the model exhibits rich dynamics including a monostable equilibrium, multi-stable equilibria, and cycles. Finally, we perform some numerical studies to further examine how dispersal and Allee effects impact tick survival and system stability.

A stage-structured predator-prey model with Crowley-Martin functional response

&lt;p style='text-indent:20px;'&gt;A stage-structured predator-prey model with Crowley-Martin functional response is formulated and analyzed to investigate the impaction of predator maturity delay and predator interference on the dynamics of the system. It is shown that the net reproduction number of the system determines its threshold dynamics: the system is permanent if and only if the net reproduction number is larger than one unit, otherwise the predators go extinct; Moreover, given that the system is permanent, the unique coexistence equilibrium is shown to be globally asymptotically stable provided that the predator's interference is large enough; Numerical simulations are also performed to explore the effects of predator maturity delay and predator's interference on the stability of interior equilibrium. It is indicated that an increase of maturity delay of the predator will enlarge its extinction risk and may also enrich dynamics of the system in the sense of bringing stability switches of the coexistence equilibrium; and that an increase of predator's interference may lead to stability switch of coexistence equilibrium from unstable to stable, implying that a large predator's interference can be stabilizing.&lt;/p&gt;

Epidemiological characteristics and transmission dynamics of the outbreak caused by the SARS-CoV-2 Omicron variant in Shanghai, China: A descriptive study

SummaryBackgroundIn early March 2022, a major outbreak of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) Omicron variant spread rapidly throughout Shanghai, China. Here we aimed to provide a description of the epidemiological characteristics and spatiotemporal transmission dynamics of the Omicron outbreak under the population-based screening and lockdown policies implemented in Shanghai.MethodsWe extracted individual information on SARS-CoV-2 infections reported between January 1 and May 31, 2022, and on the timeline of the adopted non-pharmaceutical interventions. The epidemic was divided into three phases: i) sporadic infections (January 1–February 28), ii) local transmission (March 1–March 31), and iii) city-wide lockdown (April 1 to May 31). We described the epidemic spread during these three phases and the subdistrict-level spatiotemporal distribution of the infections. To evaluate the impact on the transmission of SARS-CoV-2 of the adopted targeted interventions in Phase 2 and city-wide lockdown in Phase 3, we estimated the dynamics of the net reproduction number (Rt).FindingsA surge in imported infections in Phase 1 triggered cryptic local transmission of the Omicron variant in early March, resulting in the largest outbreak in mainland China since the original wave. A total of 626,000 SARS-CoV-2 infections were reported in 99.5% (215/216) of the subdistricts of Shanghai until the end of May. The spatial distribution of the infections was highly heterogeneous, with 37% of the subdistricts accounting for 80% of all infections. A clear trend from the city center towards adjacent suburban and rural areas was observed, with a progressive slowdown of the epidemic spread (from 463 to 244 meters/day) prior to the citywide lockdown. During Phase 2, Rt remained well above 1 despite the implementation of multiple targeted interventions. The citywide lockdown imposed on April 1 led to a marked decrease in transmission, bringing Rt below the epidemic threshold in the entire city on April 14 and ultimately leading to containment of the outbreak.InterpretationOur results highlight the risk of widespread outbreaks in mainland China, particularly under the heightened pressure of imported infections. The targeted interventions adopted in March 2022 were not capable of halting transmission, and the implementation of a strict, prolonged city-wide lockdown was needed to successfully contain the outbreak, highlighting the challenges for containing Omicron outbreaks.FundingKey Program of the National Natural Science Foundation of China (82130093); Shanghai Rising-Star Program (22QA1402300).

Analysis of the Geographic Transmission Differences of COVID-19 in China Caused by Population Movement and Population Density.

The coronavirus disease (COVID-19) has led to a global pandemic and caused huge healthy and economic losses. Non-pharmaceutical interventions, especially contact tracing and social distance restrictions, play a vital role in the control of COVID-19. Understanding the spatial impact is essential for designing such a control policy. Based on epidemic data of the confirmed cases after the Wuhan lockdown, we calculate the invasive reproduction numbers of COVID-19 in the different regions of China. Statistical analysis indicates a significant positive correlation between the reproduction numbers and the population input sizes from Wuhan, which indicates that the large-scale population movement contributed a lot to the geographic spread of COVID-19 in China. Moreover, there is a significant positive correlation between reproduction numbers and local population densities, which shows that the higher population density intensifies the spread of disease. Considering that in the early stage, there were sequential imported cases that affected the estimation of reproduction numbers, we classify the imported cases and local cases through the information of epidemiological data and calculate the net invasive reproduction number to quantify the local spread of the epidemic. The results are applied to the design of border control policy on the basis of vaccination coverage.

A discrete tick population dynamics model with continuous and seasonal birth breeding

In this paper, we formulate a discrete two-stage model with two types of birth mechanisms, continuous and seasonal. We divide tick population into two subgroups, i.e. immature and mature. We also consider diapause as an important adaptive process for ticks in respond to climate change in both stages. We derive a formula for the inherent net reproductive numbers and explore their stability analysis. When breeding is continuous, there exists a unique globally asymptotically stable positive fixed point provided that the inherent net reproductive number is larger than one; the extinction fixed point is globally asymptotically stable if the inherent net reproductive number is less than one. When breeding is seasonal with 2-periodic birth function, there exists a unique globally asymptotically stable periodic solution provided that the inherent net reproductive number is larger than one, while the population goes to extinction if this value is less than one. For the cases with multi-periodic birth function, we use numerical simulation to compare their complex behaviors.

Discrete stage-structured tick population dynamical system with diapause and control.

A discrete stage-structured tick population dynamical system with diapause is studied, and spraying acaricides as the control strategy is considered in detail. We stratify vector populations in terms of their maturity status as immature and mature subgroups. The immature subgroup is divided into two categories: normal immature and diapause immature. We compute the net reproduction number $ R_0 $ and perform a qualitative analysis. When $ R_0 < 1 $, the global asymptotic stability of tick-free fixed point is well proved by the inherent projection matrix; there exists a unique coexistence fixed point and the conditions for its asymptotic stability are obtained if and only if $ R_0 > 1; $ the model has transcritical bifurcation if $ R_0 = 1. $ Moreover, we calculate the net reproduction numbers of the model with constant spraying acaricides and periodic spraying acaricides, respectively, and compare the effects of the two methods on controlling tick populations.

Stage duration distributions and intraspecific competition: a review of continuous stage-structured models.

Stage structured models, by grouping individuals with similar demographic characteristics together, have proven useful in describing population dynamics. This manuscript starts from reviewing two widely used modeling frameworks that are in the form of integral equations and age-structured partial differential equations. Both modeling frameworks can be reduced to the same differential equation structures with/without time delays by applying Dirac and gamma distributions for the stage durations. Each framework has its advantages and inherent limitations. The net reproduction number and initial growth rate can be easily defined from the integral equation. However, it becomes challenging to integrate the density-dependent regulations on the stage distribution and survival probabilities in an integral equation, which may be suitably incorporated into partial differential equations. Further recent modeling studies, in particular those by Stephen A. Gourley and collaborators, are reviewed under the conditions of the stage duration distribution and survival probability being regulated by population density.

The early phase of the COVID-19 epidemic in Lombardy, Italy

BackgroundIn the night of February 20, 2020, the first epidemic of the novel coronavirus disease (COVID-19) outside Asia was uncovered by the identification of its first patient in Lombardy region, Italy. In the following weeks, Lombardy experienced a sudden increase in the number of ascertained infections and strict measures were imposed to contain the epidemic spread. MethodsWe analyzed official records of cases occurred in Lombardy to characterize the epidemiology of SARS-CoV-2 during the early phase of the outbreak. A line list of laboratory-confirmed cases was set up and later retrospectively consolidated, using standardized interviews to ascertained cases and their close contacts. We provide estimates of the serial interval, of the basic reproduction number, and of the temporal variation of the net reproduction number of SARS-CoV-2. ResultsEpidemiological investigations detected over 500 cases (median age: 69, IQR: 57–78) before the first COVID-19 diagnosed patient (February 20, 2020), and suggested that SARS-CoV-2 was already circulating in at least 222 out of 1506 (14.7%) municipalities with sustained transmission across all the Lombardy provinces. We estimated the mean serial interval to be 6.6 days (95% CrI, 0.7–19). Our estimates of the basic reproduction number range from 2.6 in Pavia (95% CI, 2.1–3.2) to 3.3 in Milan (95% CI, 2.9–3.8). A decreasing trend in the net reproduction number was observed following the detection of the first case. ConclusionsAt the time of first case notification, COVID-19 was already widespread in the entire Lombardy region. This may explain the large number of critical cases experienced by this region in a very short timeframe. The slight decrease of the reproduction number observed in the early days after February 20, 2020 might be due to increased population awareness and early interventions implemented before the regional lockdown imposed on March 8, 2020.

Differential impact of physical distancing strategies on social contacts relevant for the spread of SARS-CoV-2: evidence from a cross-national online survey, March–April 2020

ObjectivesWe investigate changes in social contact patterns following the gradual introduction of non-pharmaceutical interventions and their implications for infection transmission in the early phase of the pandemic.Design, setting and participantsWe...

Spatio-temporal dynamics of a model for the effect of variable ages at reproduction

Some species may have totally different ages at successful reproduction (ages at maturity) in population growth. For example, Ixodes ticks, a vector species responsible for many tick-borne diseases, may suspend development and undergo diapause during maturation process, which naturally introduce distinct ages at reproduction. Although the age at reproduction is a key demographic trait that is probably under high selective pressure, it is highly variable and the effect of this variability on spatial establishment and invasion is not well understood. In this study, a spatial mechanistic model, in the form of reaction diffusion equations with nonlocal terms incorporating two different ages at reproduction, is formulated and mathematically analyzed from a dynamical system point of view. Specifically, the persistence of the species in a bounded domain can be predicted by the net reproduction number and the spreading property in an unbounded domain in terms of spreading speed and traveling waves is characterized. Numerical simulations are conducted to further illustrate the impact of ages at reproduction on the net reproduction number and the spreading speed of the species, in particular for various scenarios of fitness tradeoffs of the premature survival and early reproduction.

Modeling the interplay between demography, social contact patterns, and SARS-CoV-2 transmission in the South West Shewa Zone of Oromia Region, Ethiopia

BackgroundCOVID-19 spread may have a dramatic impact in countries with vulnerable economies and limited availability of, and access to, healthcare resources and infrastructures. However, in sub-Saharan Africa, a low prevalence and mortality have been observed so far.MethodsWe collected data on individuals’ social contacts in the South West Shewa Zone (SWSZ) of Ethiopia across geographical contexts characterized by heterogeneous population density, work and travel opportunities, and access to primary care. We assessed how socio-demographic factors and observed mixing patterns can influence the COVID-19 disease burden, by simulating SARS-CoV-2 transmission in remote settlements, rural villages, and urban neighborhoods, under school closure mandate.ResultsFrom national surveillance data, we estimated a net reproduction number of 1.62 (95% CI 1.55–1.70). We found that, at the end of an epidemic mitigated by school closure alone, 10–15% of the population residing in the SWSZ would have been symptomatic and 0.3–0.4% of the population would require mechanical ventilation and/or possibly result in a fatal outcome. Higher infection attack rates are expected in more urbanized areas, but the highest incidence of critical disease is expected in remote subsistence farming settlements. School closure contributed to reduce the reproduction number by 49% and the attack rate of infections by 28–34%.ConclusionsOur results suggest that the relatively low burden of COVID-19 in Ethiopia observed so far may depend on social mixing patterns, underlying demography, and the enacted school closures. Our findings highlight that socio-demographic factors can also determine marked heterogeneities across different geographical contexts within the same region, and they contribute to understand why sub-Saharan Africa is experiencing a relatively lower attack rate of severe cases compared to high-income countries.

The effect of control measures on COVID-19 transmission in South Korea.

Countries around the world have taken control measures to mitigate the spread of COVID-19, including Korea. Social distancing is considered an essential strategy to reduce transmission in the absence of vaccination or treatment. While interventions have been successful in controlling COVID-19 in Korea, maintaining the current restrictions incurs great social costs. Thus, it is important to analyze the impact of different polices on the spread of the epidemic. To model the COVID-19 outbreak, we use an extended age-structured SEIR model with quarantine and isolation compartments. The model is calibrated to age-specific cumulative confirmed cases provided by the Korea Disease Control and Prevention Agency (KDCA). Four control measures—school closure, social distancing, quarantine, and isolation—are investigated. Because the infectiousness of the exposed has been controversial, we study two major scenarios, considering contributions to infection of the exposed, the quarantined, and the isolated. Assuming the transmission rate would increase more than 1.7 times after the end of social distancing, a second outbreak is expected in the first scenario. The epidemic threshold for increase of contacts between teenagers after school reopening is 3.3 times, which brings the net reproduction number to 1. The threshold values are higher in the second scenario. If the average time taken until isolation and quarantine reduces from three days to two, cumulative cases are reduced by 60% and 47% in the first scenario, respectively. Meanwhile, the reduction is 33% and 41%, respectively, for rapid isolation and quarantine in the second scenario. Without social distancing, a second wave is possible, irrespective of whether we assume risk of infection by the exposed. In the non-infectivity of the exposed scenario, early detection and isolation are significantly more effective than quarantine. Furthermore, quarantining the exposed is as important as isolating the infectious when we assume that the exposed also contribute to infection.

Dynamics of a periodic tick-borne disease model with co-feeding and multiple patches.

By extending a mechanistic model for the tick-borne pathogen systemic transmission with the consideration of seasonal climate impacts, host movement as well as the co-feeding transmission route, this paper proposes a novel modeling framework for describing the spatial dynamics of tick-borne diseases. The net reproduction number for tick growth and basic reproduction number for disease transmission are derived, which predict the global dynamics of tick population growth and disease transmission. Numerical simulations not only verify the analytical results, but also characterize the contribution of co-feeding transmission route on disease prevalence in a habitat and the effect of host movement on the spatial spreading of the pathogen.

Epidemiological characteristics of COVID-19 cases and estimates of the reproductive numbers 1 month into the epidemic, Italy, 28 January to 31 March 2020.

BackgroundOn 20 February 2020, a locally acquired coronavirus disease (COVID-19) case was detected in Lombardy, Italy. This was the first signal of ongoing transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in the country. The number of cases in Italy increased rapidly and the country became the first in Europe to experience a SARS-CoV-2 outbreak.AimOur aim was to describe the epidemiology and transmission dynamics of the first COVID-19 cases in Italy amid ongoing control measures.MethodsWe analysed all RT-PCR-confirmed COVID-19 cases reported to the national integrated surveillance system until 31 March 2020. We provide a descriptive epidemiological summary and estimate the basic and net reproductive numbers by region.ResultsOf the 98,716 cases of COVID-19 analysed, 9,512 were healthcare workers. Of the 10,943 reported COVID-19-associated deaths (crude case fatality ratio: 11.1%) 49.5% occurred in cases older than 80 years. Male sex and age were independent risk factors for COVID-19 death. Estimates of R0 varied between 2.50 (95% confidence interval (CI): 2.18–2.83) in Tuscany and 3.00 (95% CI: 2.68–3.33) in Lazio. The net reproduction number Rt in northern regions started decreasing immediately after the first detection.ConclusionThe COVID-19 outbreak in Italy showed a clustering onset similar to the one in Wuhan, China. R0 at 2.96 in Lombardy combined with delayed detection explains the high case load and rapid geographical spread. Overall, Rt in Italian regions showed early signs of decrease, with large diversity in incidence, supporting the importance of combined non-pharmacological control measures.

Estimation of the net reproductive number of COVID-19 in Iran

Estimation of the net reproductive number of COVID-19 in Iran

Impact of a Nationwide Lockdown on SARS-CoV-2 Transmissibility, Italy.

On March 11, 2020, Italy imposed a national lockdown to curtail the spread of severe acute respiratory syndrome coronavirus 2. We estimate that, 14 days after lockdown, the net reproduction number had dropped below 1 and remained stable at »0.76 (95% CI 0.67–0.85) in all regions for >3 of the following weeks.

The contribution of asymptomatic SARS-CoV-2 infections to transmission on the Diamond Princess cruise ship.

A key unknown for SARS-CoV-2 is how asymptomatic infections contribute to transmission. We used a transmission model with asymptomatic and presymptomatic states, calibrated to data on disease onset and test frequency from the Diamond Princess cruise ship outbreak, to quantify the contribution of asymptomatic infections to transmission. The model estimated that 74% (70-78%, 95% posterior interval) of infections proceeded asymptomatically. Despite intense testing, 53% (51-56%) of infections remained undetected, most of them asymptomatic. Asymptomatic individuals were the source for 69% (20-85%) of all infections. The data did not allow identification of the infectiousness of asymptomatic infections, however low ranges (0-25%) required a net reproduction number for individuals progressing through presymptomatic and symptomatic stages of at least 15. Asymptomatic SARS-CoV-2 infections may contribute substantially to transmission. Control measures, and models projecting their potential impact, need to look beyond the symptomatic cases if they are to understand and address ongoing transmission.