On a temporal model for the Chikungunya disease: modeling, theory and numerics

Global stability analysis and modelling onchocerciasis transmission dynamics with control measures

Background: Onchocerciasis infection is one of the neglected tropical diseases targeted for eradication by 2030. The disease is usually transmitted to humans through the bites of black flies. These black flies mostly breed near well-oxygenated fast-running water bodies. The disease is common in mostly remote agricultural villages near rivers and streams. Objective: In this study, a deterministic model describing the infection dynamics of human onchocerciasis disease with control measures is presented. Methods: We derived the model's reproductive number and used a stability theorem of a Metzler matrix to show that disease-free equilibrium is both locally and globally asymptotically stable whenever the reproductive number is less than one. Parameter contribution was conducted using sensitivity analysis. The model endemic equation is shown to be a cubic polynomial in the presence of infected immigrants and a quadratic form in their absence. Results: When the inflow of infected immigrants is null, the model endemic equation may admit a unique equilibrium if the reproductive number is greater than one, or admits multiple endemic equilibria if the reproductive number is less than unity. We carried out a sensitivity analysis to identify the significant parameters that contribute to onchocerciasis spread. Conclusion: Onchocerciasis disease can be eradicated if the importation of infected immigrants is properly monitored. The integration of the One Health concept in the public health system is key in tackling the emergence and spread of diseases.

Analysis and Bayesian estimation of a model for Chikungunya dynamics with relapse: An outbreak in Acapulco, Mexico

Chikungunya is a vector-borne viral disease transmitted by Aedes aegypti and Aedes albopictus mosquitoes. It does not have any specific treatment, and there is no vaccine. Recent epidemiological data have indicated that a relapse of the infection can occur within three months of the initial infection; however, until now, mathematical models for the spread of the disease have not considered this factor. We propose a mathematical model for the transmission of the Chikungunya virus that considers relapse. We calculated the basic reproductive number $ (R_0) $ of the disease by using the next-generation operator method. We proved the existence of a forward bifurcation. We determined the existence and the global stability of the equilibrium points by using the Lyapunov function method. We fitted the model to data from an outbreak in 2015 in Acapulco, Mexico to estimate the model parameters and $ R_0 $ with the Bayesian approach via a Hamiltonian Monte Carlo method. In the local sensitivity analysis, we found that the fraction of infected individuals who become asymptomatic has a strong impact on the basic reproductive number and makes some control measures insufficient. The impact of the fraction of infected individuals who become asymptomatic should be considered in Chikungunya control strategies.

Analysis of the dynamics of a vector-borne infection with the effect of imperfect vaccination from a fractional perspective

The burden of vector-borne infections is significant, particularly in low- and middle-income countries where vector populations are high and healthcare infrastructure may be inadequate. Further, studies are required to investigate the key factors of vector-borne infections to provide effective control measure. This study focuses on formulating a mathematical framework to characterize the spread of chikungunya infection in the presence of vaccines and treatments. The research is primarily dedicated to descriptive study and comprehension of dynamic behaviour of chikungunya dynamics. We use Banach's and Schaefer's fixed point theorems to investigate the existence and uniqueness of the suggested chikungunya framework resolution. Additionally, we confirm the Ulam-Hyers stability of the chikungunya system. To assess the impact of various parameters on the dynamics of chikungunya, we examine solution pathways using the Laplace-Adomian method of disintegration. Specifically, to visualise the impacts of fractional order, vaccination, bite rate and treatment computer algorithms are employed on the infection level of chikungunya. Our research identified the framework's essential input settings for managing chikungunya infection. Notably, the intensity of chikungunya infection can be reduced by lowering mosquito bite rates in the affected area. On the other hand, vaccination, memory index or fractional order, and treatment could be used as efficient controlling variables.

Assessing the impact of serostatus-dependent immunization on mitigating the spread of dengue virus

Dengue is the most rapidly spreading mosquito-borne disease that poses great threats to public health. We propose a compartmental model with primary and secondary infection and targeted vaccination to assess the impact of serostatus-dependent immunization on mitigating the spread of dengue virus. We derive the basic reproduction number and investigate the stability and bifurcations of the disease-free equilibrium and endemic equilibria. The existence of a backward bifurcation is proved and is used to explain the threshold dynamics of the transmission. We also carry out numerical simulations and present bifurcation diagrams to reveal rich dynamics of the model such as bi-stability of the equilibria, limit cycles, and chaos. We prove the uniform persistence and global stability of the model. Sensitivity analysis suggests that mosquito control and protection from mosquito bites are still the key measures of controlling the spread of dengue virus, though serostatus-dependent immunization is implemented. Our findings provide insightful information for public health in mitigating dengue epidemics through vaccination.

Review of Importance of Weather and Environmental Variables in Agent-Based Arbovirus Models

The study sought to review the works of literature on agent-based modeling and the influence of climatic and environmental factors on disease outbreak, transmission, and surveillance. Thus, drawing the influence of environmental variables such as vegetation index, households, mosquito habitats, breeding sites, and climatic variables including precipitation or rainfall, temperature, wind speed, and relative humidity on dengue disease modeling using the agent-based model in an African context and globally was the aim of the study. A search strategy was developed and used to search for relevant articles from four databases, namely, PubMed, Scopus, Research4Life, and Google Scholar. Inclusion criteria were developed, and 20 articles met the criteria and have been included in the review. From the reviewed works of literature, the study observed that climatic and environmental factors may influence the arbovirus disease outbreak, transmission, and surveillance. Thus, there is a call for further research on the area. To benefit from arbovirus modeling, it is crucial to consider the influence of climatic and environmental factors, especially in Africa, where there are limited studies exploring this phenomenon.

Mathematical modeling in perspective of vector-borne viral infections: a review

Background

Viral diseases are highly widespread infections caused by viruses. These viruses are passing from one human to other humans through a certain medium. The medium might be mosquito, animal, reservoir and food, etc. Here, the population of both human and mosquito vectors are important.

Main body of the abstract

The main objectives are here to introduce the historical perspective of mathematical modeling, enable the mathematical modeler to understand the basic mathematical theory behind this and present a systematic review on mathematical modeling for four vector-borne viral diseases using the deterministic approach. Furthermore, we also introduced other mathematical techniques to deal with vector-borne diseases. Mathematical models could help forecast the infectious population of humans and vectors during the outbreak.

Short conclusion

This study will be helpful for mathematical modelers in vector-borne diseases and ready-made material in the review for future advancement in the subject. This study will not only benefit vector-borne conditions but will enable ideas for other illnesses.

Approximate Solutions for a Class of Predator–Prey Systems with Nonstandard Finite Difference Schemes

In this paper, we construct new nonstandard finite difference schemes to approximate a set of positive solutions for the predator–prey model, which contains different functional responses. The organization of the denominator of the discrete derivative and nonlocal approximations of nonlinear terms are employed to design the new schemes. The approach results in significant qualitative improvements in how the numerical solution behaves. We establish that the proposed nonstandard finite difference methods are elementary stable and satisfy the positivity requirement. In addition, the instances of applying PESN methods to some predator–prey systems using the Beddington–DeAngelis and Nicholson–Bailey functional responses are provided here. Finally, some numerical comparisons are presented to illustrate our findings. Our results indicate that the proposed methods are very suitable for the symmetric model of predator–prey.

A bio-mathematical approach to control the Anopheles mosquito using sterile males technology

Initiative for this study is taken to solve the mathematical model which is base-forming with population dynamics of the Anopheles mosquito using an advanced computational intelligence scheme named as genetic algorithm (GA), artificial neural network (ANN). This ANN is a famous global search method, active set (AS) scheme known as a quick local refinement, i.e. ANN-GA-AS. An error-based fitness function is optimized which is made by using the sense of the differential system and boundary conditions for solving the Anopheles mosquito control model. The ability of the stochastic ANN-GA-AS approach to solve the population dynamics of the Anopheles mosquito is examined to check the exactness, efficiency, precision, and consistency of the scheme. The numerical outcomes of the Anopheles mosquito control model through the ANN-GA-AS approach are compared with the reference Adams numerical results to show the significance of the designed scheme. Moreover, statistical considerations using the “semi-interquartile range”, “Theil’s inequality coefficient”, and “mean absolute deviation” have been applied to validate the precision and accuracy of the obtained results.

Estimating chikungunya virus transmission parameters and vector control effectiveness highlights key factors to mitigate arboviral disease outbreaks

Background

Viruses transmitted by Aedes mosquitoes have greatly expanded their geographic range in recent decades. They are considered emerging public health threats throughout the world, including Europe. Therefore, public health authorities must be prepared by quantifying the potential magnitude of virus transmission and the effectiveness of interventions.

Methodology

We developed a mathematical model with a vector-host structure for chikungunya virus transmission and estimated model parameters from epidemiological data of the two main autochthonous chikungunya virus transmission events that occurred in Southern France, in Montpellier (2014) and in Le Cannet-des-Maures (2017). We then performed simulations of the model using these estimates to forecast the magnitude of the foci of transmission as a function of the response delay and the moment of virus introduction.

Conclusions

The results of the different simulations underline the relative importance of each variable and can be useful to stakeholders when designing context-based intervention strategies. The findings emphasize the importance of, and advocate for early detection of imported cases and timely biological confirmation of autochthonous cases to ensure timely vector control measures, supporting the implementation and the maintenance of sustainable surveillance systems.

Dengue, chikungunya and Zika viruses have expanded their geographic range during recent decades and are now considered emerging threats in temperate areas. In particular, autochthonous transmissions of chikungunya virus (CHIKV) have regularly been observed in Europe since 2010. The increase in international travel and trade appear to be major factors, encouraging both a circulation of these viruses on a global scale and the dispersion of one of their main vectors, Aedes albopictus. This trend is likely to increase significantly in the future and improved preparedness and response strategies are essential to manage these emerging risks. In this respect of decision support, we developed a mathematical model for CHIKV transmission. We first estimated key model parameters of CHIKV transmission and vector control effectiveness, using data from the two main CHIKV transmission events which have already occurred in mainland France. The model was then used to forecast the magnitude of outbreaks as a function of the delay in implementing control measures, and from the moment of virus introduction during the mosquito vector season. This work will help provide stakeholders in public health with a greater understanding of the dynamics of CHIKV transmission, and with evidence for the implementation of sustainable surveillance systems.

Dynamics of a Fractional-Order Chikungunya Model with Asymptomatic Infectious Class

In this paper, a nonlinear fractional-order chikungunya disease model that incorporates asymptomatic infectious individuals is proposed and analyzed. The main interest of this work is to investigate the role of memory effects on the dynamics of chikungunya. Qualitative analysis of the model's equilibria showed that there exists a threshold quantity which governs persistence and extinction of the disease. Model parameters were estimated based on the 2015 weekly reported cases in Colombia. The Adams-Bashforth-Moulton method was used to numerically solve the proposed model. We investigated the role of asymptomatic infectious patients on short- and long-term dynamics of the diseases. We also determined threshold levels for the efficacy of preventative strategies that results in effective management of the disease. We believe that our model can provide invaluable insights for public health authorities to predict the effect of chikungunya transmission and analyze its underlying factors and to guide new control efforts.

Sterile insect technique with accidental releases of sterile females. Impact on mosquito-borne diseases control when viruses are circulating

The sterile insect technique (SIT) is a technique to control some vectors of diseases by releasing sterile males. However, during these releases, sterilized females can be (accidentally) released and since only females are vectors of diseases, it is important to study their impact when arthropod viruses are circulating. To that aim, we develop and study an entomological-epidemiological model, considering either permanent or periodic releases. Qualitative analyses of the continuous and periodic models are conducted. We highlight a critical sterile males release rate, Λ_M^crit, above which the control of wild population is always effective, using massive releases. Estimating the basic reproduction number of the epidemiological model, R₀², we show that if it is above a certain threshold, R_0,∗², that depends on the basic offspring number, N, and the release rate of sterile females, the epidemiological risk can only be controlled using (very) massive releases. Otherwise, we can estimate the basic reproduction number of the SIT epidemiological model, R_0,SIT², that shapes the stability property of the (periodic) disease-free equilibrium. We show that it might be possible to take R_0,SIT² below 1 using non-massive, but large enough, releases. However, practically, it seems more efficient to consider massive releases, followed by small releases once the vector population is small enough. In addition to SIT, we also recommend mechanical control, i.e. the reduction of breeding sites, that greatly improves the efficacy of SIT, in terms of duration or size of the releases. Our results reveal that outside an epidemic period, the release of sterile females is not an issue, as long as the sterile males release rate is greater than Λ_M^crit. Within an epidemic period, we show that sterile females releases do not really impact the SIT efficiency, as long as the release rate, Λ_F, is lower than a critical value, Λ_F^crit, that depends on the mosquito and epidemiological threshold parameters, N, and R₀². To illustrate numerically our theoretical results, we consider Dengue parameters. We estimate all thresholds and also the effective reproduction number, R_eff², and highlight the importance of early permanent or periodic SIT control to prevent or mitigate the risk of a Dengue epidemic, with and without sterile females releases.

Mathematical analysis and optimal control for Chikungunya virus with two routes of infection with nonlinear incidence rate

Chikungunya fever, caused by Chikungunya virus (CHIKV) and transmitted to humans by infected Aedes mosquitoes, has posed a global threat in several countries. In this paper, we investigated a modified within-host Chikungunya virus (CHIKV) infection model with antibodies where two routes of infection are considered. In a first step, the basic reproduction number [Formula: see text] was calculated and the local and global stability analysis of the steady states is carried out using the local linearization and the Lyapunov method. It is proven that the CHIKV-free steady-state [Formula: see text] is globally asymptotically stable when [Formula: see text], and the infected steady-state [Formula: see text] is globally asymptotically stable when [Formula: see text]. In a second step, we applied an optimal strategy in order to optimize the infected compartment and to maximize the uninfected one. For this, we formulated a nonlinear optimal control problem. Existence of the optimal solution was discussed and characterized using some adjoint variables. Thus, an algorithm based on competitive Gauss–Seidel-like implicit difference method was applied in order to resolve the optimality system. The theoretical results are confirmed by some numerical simulations.

Basic Reproduction Number of Chikungunya Virus Transmitted by Aedes Mosquitoes

We estimated the weighted mean basic reproduction number (R₀) of chikungunya virus based on outbreak size. R₀ was 3.4 (95% CI 2.4–4.2) and varied for 2 primary chikungunya mosquito vectors: 4.1 (95% CI 1.5–6.6) for Aedes aegypti and 2.8 (95% CI 1.8–3.8) for Ae. albopictus.

Megacities as drivers of national outbreaks: The 2017 chikungunya outbreak in Dhaka, Bangladesh

BACKGROUND

Several large outbreaks of chikungunya have been reported in the Indian Ocean region in the last decade. In 2017, an outbreak occurred in Dhaka, Bangladesh, one of the largest and densest megacities in the world. Population mobility and fluctuations in population density are important drivers of epidemics. Measuring population mobility during outbreaks is challenging but is a particularly important goal in the context of rapidly growing and highly connected cities in low- and middle-income countries, which can act to amplify and spread local epidemics nationally and internationally.

METHODS

We first describe the epidemiology of the 2017 chikungunya outbreak in Dhaka and estimate incidence using a mechanistic model of chikungunya transmission parametrized with epidemiological data from a household survey. We combine the modeled dynamics of chikungunya in Dhaka, with mobility estimates derived from mobile phone data for over 4 million subscribers, to understand the role of population mobility on the spatial spread of chikungunya within and outside Dhaka during the 2017 outbreak.

RESULTS

We estimate a much higher incidence of chikungunya in Dhaka than suggested by official case counts. Vector abundance, local demographics, and population mobility were associated with spatial heterogeneities in incidence in Dhaka. The peak of the outbreak in Dhaka coincided with the annual Eid holidays, during which large numbers of people traveled from Dhaka to other parts of the country. We show that travel during Eid likely resulted in the spread of the infection to the rest of the country.

CONCLUSIONS

Our results highlight the impact of large-scale population movements, for example during holidays, on the spread of infectious diseases. These dynamics are difficult to capture using traditional approaches, and we compare our results to a standard diffusion model, to highlight the value of real-time data from mobile phones for outbreak analysis, forecasting, and surveillance.

Optimal voluntary and mandatory insect repellent usage and emigration strategies to control the chikungunya outbreak on Reunion Island

In 2005, a chikungunya virus outbreak devastated the tropical island of Reunion, infecting a third of the total population. Motivated by the Reunion Island case study, we investigate the theoretic potential for two intervention measures under both voluntary and mandatory protocols to control a vector-borne disease when there is risk of the disease becoming endemic. The first measure uses insect repellent to prevent mosquito bites, while the second involves emigrating to the neighboring Mauritius Island to avoid infection. There is a threshold on the cost of using repellent above which both voluntary and mandatory regimes find it optimal to forgo usage. Below that threshold, mandatory usage protocols will eradicate the disease; however, voluntary adoption leaves the disease at a small endemic level. Emigrating from the island to avoid infection results in a tragedy-of-the-commons effect: while being potentially beneficial to specific susceptible individuals, the remaining islanders paradoxically face a higher risk of infection. Mandated relocation of susceptible individuals away from the epidemic is viable only if the cost of this relocation is several magnitudes lower than the cost of infection. Since this assumption is unlikely to hold for chikungunya, it is optimal to discourage such emigration for the benefit of the entire population. An underlying assumption about the conservation of human-vector encounter rates in mosquito biting behavior informs our conclusions and may warrant additional experimental verification.

Onchocerciasis dynamics: modelling the effects of treatment, education and vector control

A deterministic model of onchocerciasis disease dynamics is considered in a community partitioned into compartments based on the disease status. Public health education is offered in the community during the implementation of mass treatment using ivermectin drugs. Also, larviciding and trapping strategies are implemented in the vector population with the aim of controlling population growth of black flies. We fit the model to the data to check the suitability of the model. Expressions are derived for the influence on the reproduction numbers of these strategies. Numerical results show that the dynamics of onchocerciasis and the growth of black flies are best controlled when the four strategies are implemented simultaneously. Also, the results suggest that for the elimination of the disease in the society there is a need for finding another drug which will be implemented to ineligible human as well as killing the adult worms instead of ivermectin.

The Mayaro virus and its potential epidemiological consequences in Colombia: an exploratory biomathematics analysis

Background

Mayaro virus (Togaviridae) is an endemic arbovirus of the Americas with epidemiological similarities with the agents of other more prominent diseases such as dengue (Flaviviridae), Zika (Flaviviridae), and chikungunya (Togaviridae). It is naturally transmitted in a sylvatic/rural cycle by Haemagogus spp., but, potentially, it could be incorporated and transmitted in an urban cycle by Aedes aegypti, a vector widely disseminated in the Americas.

Methods

The Mayaro arbovirus dynamics was simulated mathematically in the colombian population in the eight biogeographical provinces, bearing in mind the vector’s population movement between provinces through passive transport via truck cargo. The parameters involved in the virus epidemiological dynamics, as well as the vital rates of Ae. aegypti in each of the biogeographical provinces were obtained from the literature. These data were included in a meta-population model in differential equations, represented by a model structured by age for the dynamic population of Ae. aegypti combined with an epidemiological SEI/SEIR-type model. In addition, the model was incorporated with a term of migration to represent the connectivity between the biogeographical provinces.

Results

The vital rates and the development cycle of Ae. aegypti varied between provinces, having greater biological potential between 23 °C and 28 °C in provinces of Imerí, biogeographical Chocó, and Magdalena, with respect to the North-Andean Moorland (9.33–21.38 °C). Magdalena and Maracaibo had the highest flow of land cargo. The results of the simulations indicate that Magdalena, Imerí, and biogeographical Chocó would be the most affected regarding the number of cases of people infected by Mayaro virus over time.

Conclusions

The temperature in each of the provinces influences the local population dynamics of Ae. aegypti and passive migration via transport of land cargo plays an important role on how the Mayaro virus would be disseminated in the human population. Once this arbovirus begins an urban cycle, the most-affected departments would be Antioquia, Santander, Norte de Santander, Cesar (Provinces of Magdalena), and Valle del Cauca, and Chocó (biogeographical province of Chocó), which is why vector control programmes must aim their efforts at these departments and include some type of vector control to the transport of land cargo to avoid a future Mayaro epidemic.

Modeling and simulation of the spatial population dynamics of the Aedes aegypti mosquito with an insecticide application

Background

The Aedes aegypti mosquito is the primary vector for several diseases. Its control requires a better understanding of the mosquitoes’ live cycle, including the spatial dynamics. Several models address this issue. However, they rely on many hard to measure parameters. This work presents a model describing the spatial population dynamics of Aedes aegypti mosquitoes using partial differential equations (PDEs) relying on a few parameters.

Methods

We show how to estimate model parameter values from the experimental data found in the literature using concepts from dynamical systems, genetic algorithm optimization and partial differential equations. We show that our model reproduces some analytical formulas relating the carrying capacity coefficient to experimentally measurable quantities as the maximum number of mobile female mosquitoes, the maximum number of eggs, or the maximum number of larvae. As an application of the presented methodology, we replicate one field experiment numerically and investigate the effect of different frequencies in the insecticide application in the urban environment.

Results

The numerical results suggest that the insecticide application has a limited impact on the mosquitoes population and that the optimal application frequency is close to one week.

Conclusions

Models based on partial differential equations provide an efficient tool for simulating mosquitoes’ spatial population dynamics. The reduced model can reproduce such dynamics on a sufficiently large scale.

Stability Analysis and Optimal Control for Yellow Fever Model with Vertical Transmission

In this study, a deterministic model for the transmission dynamics of yellow fever (YF) in a human-mosquito setting in the presence of control measures is constructed and rigorously analyzed. In addition to horizontal transmissions, vertical transmission within mosquito population is incorporated. Analysis of the mosquito-only component of the model shows that the reduced model has a mosquito-extinction equilibrium, which is globally-asymptotically stable whenever the basic offspring number ( N 0 ) is less than unity. The vaccinated and type reproduction numbers of the full-model are computed. Condition for global-asymptotic stability of the disease-free equilibrium of the model whenN 0 > 1 is presented. It is shown that, fractional dosing of YF vaccine does not meet YF vaccination requirements. Optimal control theory is applied to the model to characterize the controls parameters. Using Pontryagin's maximum principle and modified forward-backward sweep technique, the necessary conditions for existence of solutions to the optimal control problem is determined. Numerical simulations of the models to assess the effect of fractional vaccine dosing on the disease dynamics and global sensitivity analysis are presented.

Reviewing estimates of the basic reproduction number for dengue, Zika and chikungunya across global climate zones

BACKGROUND

Globally, dengue, Zika virus, and chikungunya are important viral mosquito-borne diseases that infect millions of people annually. Their geographic range includes not only tropical areas but also sub-tropical and temperate zones such as Japan and Italy. The relative severity of these arboviral disease outbreaks can vary depending on the setting. In this study we explore variation in the epidemiologic potential of outbreaks amongst these climatic zones and arboviruses in order to elucidate potential reasons behind such differences.

METHODOLOGY

We reviewed the peer-reviewed literature (PubMed) to obtain basic reproduction number (R₀) estimates for dengue, Zika virus, and chikungunya from tropical, sub-tropical and temperate regions. We also computed R₀ estimates for temperate and sub-tropical climate zones, based on the outbreak curves in the initial outbreak phase. Lastly we compared these estimates across climate zones, defined by latitude.

RESULTS

Of 2115 studies, we reviewed the full text of 128 studies and included 65 studies in our analysis. Our results suggest that the R₀ of an arboviral outbreak depends on climate zone, with lower R₀ estimates, on average, in temperate zones (R₀ = 2.03) compared to tropical (R₀ = 3.44) and sub-tropical zones (R₀ = 10.29). The variation in R₀ was considerable, ranging from 0.16 to 65. The largest R₀ was for dengue (65) and was estimated by the Ross-Macdonald model in the tropical zone, whereas the smallest R₀ (0.16) was for Zika virus and was estimated statistically from an outbreak curve in the sub-tropical zone.

CONCLUSIONS

The results indicate climate zone to be an important determinant of the basic reproduction number, R₀, for dengue, Zika virus, and chikungunya. The role of other factors as determinants of R₀, such as methods, environmental and social conditions, and disease control, should be further investigated. The results suggest that R₀ may increase in temperate regions in response to global warming, and highlight the increasing need for strengthening preparedness and control activities.

Modelling and Analyzing Virus Mutation Dynamics of Chikungunya Outbreaks

Chikungunya fever, caused by chikungunya virus (CHIKV) and transmitted to humans by infected Aedes mosquitoes, has posed a global threat in several countries in 2015. Recent outbreaks in La Réunion, Italy and China are related with a new variant of CHIKV with shorter extrinsic incubation period in contaminated mosquitoes, but the role of this new variant on the spread of chikungunya fever is unclear. We develop a mathematical model that incorporates the virus mutation dynamics in the transmission of CHIKV among mosquitoes and humans. Our numerical simulations show that a substantial virus mutation rate combined with high virus transmission probabilities from mosquito to human, could result in sustainable chikungunya fever outbreaks. Further, we apply Markov Chain Monte Carlo sampling method to fit our model to the 2007 chikungunya fever outbreak data in North-Eastern Italy where the mutant strain was detected. We conclude that the basic reproduction number might be underestimated without considering the mutation dynamics, and our estimation shows that the basic reproduction number of the 2007 Italy outbreak was [Formula: see text] = 2.035[95%Cl: 1.9424 - 2.1366]. Sensitivity analysis shows that the transmission rate of the mutant strain from mosquitoes to human is more influential on [Formula: see text] than the shortened extrinsic incubation period. We conclude that the virus mutation dynamics could play an important role in the transmission of CHIKV, and there is a crucial need to better understand the mutation mechanism.

Mathematical Modeling and Characterization of the Spread of Chikungunya in Colombia

The Chikungunya virus is the cause of an emerging disease in Asia and Africa, and also in America, where the virus was first detected in 2006. In this paper, we present a mathematical model of the Chikungunya epidemic at the population level that incorporates the transmission vector. The epidemic threshold parameter R 0 for the extinction of disease is computed using the method of the next generation matrix, which allows for insights about what are the most relevant model parameters. Using Lyapunov function theory, some sufficient conditions for global stability of the the disease-free equilibrium are obtained. The proposed mathematical model of the Chikungunya epidemic is used to investigate and understand the importance of some specific model parameters and to give some explanation and understanding about the real infected cases with Chikungunya virus in Colombia for data belonging to the year 2015. In this study, we were able to estimate the value of the basic reproduction number R 0 . We use bootstrapping and Markov chain Monte Carlo techniques in order to study parameters’ identifiability. Finally, important policies and insights are provided that could help government health institutions in reducing the number of cases of Chikungunya in Colombia.

Practical unidentifiability of a simple vector-borne disease model: Implications for parameter estimation and intervention assessment

Mathematical modeling has an extensive history in vector-borne disease epidemiology, and is increasingly used for prediction, intervention design, and understanding mechanisms. Many studies rely on parameter estimation to link models and data, and to tailor predictions and counterfactuals to specific settings. However, few studies have formally evaluated whether vector-borne disease models can properly estimate the parameters of interest given the constraints of a particular dataset. Identifiability analysis allows us to examine whether model parameters can be estimated uniquely-a lack of consideration of such issues can result in misleading or incorrect parameter estimates and model predictions. Here, we evaluate both structural (theoretical) and practical identifiability of a commonly used compartmental model of mosquito-borne disease, using the 2010 dengue epidemic in Taiwan as a case study. We show that while the model is structurally identifiable, it is practically unidentifiable under a range of human and mosquito time series measurement scenarios. In particular, the transmission parameters form a practically identifiable combination and thus cannot be estimated separately, potentially leading to incorrect predictions of the effects of interventions. However, in spite of the unidentifiability of the individual parameters, the basic reproduction number was successfully estimated across the unidentifiable parameter ranges. These identifiability issues can be resolved by directly measuring several additional human and mosquito life-cycle parameters both experimentally and in the field. While we only consider the simplest case for the model, we show that a commonly used model of vector-borne disease is unidentifiable from human and mosquito incidence data, making it difficult or impossible to estimate parameters or assess intervention strategies. This work illustrates the importance of examining identifiability when linking models with data to make predictions and inferences, and particularly highlights the importance of combining laboratory, field, and case data if we are to successfully estimate epidemiological and ecological parameters using models.

Analysis of latent CHIKV dynamics models with general incidence rate and time delays

In this paper, we study the stability analysis of latent Chikungunya virus (CHIKV) dynamics models. The incidence rate between the CHIKV and the uninfected monocytes is modelled by a general nonlinear function which satisfies a set of conditions. The model is incorporated by intracellular discrete or distributed time delays. Using the method of Lyapunov function, we established the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations.

Assessing health burden risk and control effect on dengue fever infection in the southern region of Taiwan

BACKGROUND

The high prevalence of dengue in Taiwan and the consecutive large dengue outbreaks in the period 2014-2015 suggest that current control interventions are suboptimal. Understanding the effect of control effort is crucial to inform future control strategies.

OBJECTIVES

We developed a framework to measure season-based health burden risk from 2001 to 2014. We reconstructed various intervention coverage to assess the attributable effect of dengue infection control efforts.

MATERIALS AND METHODS

A dengue-mosquito-human transmission dynamic was used to quantify the vector-host interactions and to estimate the disease epidemics. We used disability-adjusted life years (DALYs) to assess health burden risk. A temperature-basic reproduction number (R0)-DALYs relationship was constructed to examine the potential impacts of temperature on health burden. Finally, a health burden risk model linked a control measure model to evaluate the effect of dengue control interventions.

RESULTS

We showed that R0 and DALYs peaked at 25°C with estimates of 2.37 and 1387, respectively. Results indicated that most dengue cases occurred in fall with estimated DALYs of 323 (267-379, 95% CI) at 50% risk probability. We found that repellent spray had by far the largest control effect with an effectiveness of ~71% in all seasons. Pesticide spray and container clean-up have both made important contributions to reducing prevalence/incidence. Repellent, pesticide spray, container clean-up together with Wolbachia infection suppress dengue outbreak by ~90%.

CONCLUSION

Our presented modeling framework provides a useful tool to measure dengue health burden risk and to quantify the effect of dengue control on dengue infection prevalence and disease incidence in the southern region of Taiwan.

Analysis of within-host CHIKV dynamics models with general incidence rate

In this paper we study the stability analysis of two within-host Chikungunya virus (CHIKV) dynamics models. The incidence rate between the CHIKV and the uninfected monocytes is modeled by a general nonlinear function. The second model considers two types of infected monocytes (i) latently infected monocytes which do not generate CHIKV and (ii) actively infected monocytes which produce the CHIKV particles. Sufficient conditions are found which guarantee the global stability of the positive steady states. Using the Lyapunov function, we established the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations.

Comparing the effectiveness of different strains of Wolbachia for controlling chikungunya, dengue fever, and zika

Once Aedes aegypti and Aedes albopictus mosquitoes that spread Chikungunya virus, dengue virus, and Zika virus are infected with Wolbachia, they have reduced egg laying rates, reduced transmission abilities, and shorter lifespans. Since most infected mosquitoes are only infectious in the last few days of their lives, shortening a mosquito's lifespan by a day or two can greatly reduce their abilities to spread mosquito-borne viral diseases, such as Chikungunya, dengue fever, and Zika. We developed a mathematical model to compare the effectiveness of the wMel and wAlbB strains of Wolbachia for controlling the spread of these viruses. The differences among the diseases, mosquitoes, and Wolbachia strains are captured by the model parameters for the mosquito-human transmission cycle. Moreover, the model accounts for the behavior changes of infectious population created by differences in the malaise caused by these viruses. We derived the effective and basic reproduction numbers for the model that are used to estimate the number of secondary infections from the infectious populations. In the same density of Wolbachia-free Aedes aegypti or Aedes albopictus mosquitoes, we observed that wMel and wAlbB strains of Wolbachia can reduce the transmission rates of these diseases effectively.

SWITCHING VACCINATION SCHEMES FOR VECTOR-BORNE DISEASES WITH SEASONAL FLUCTUATIONS

Theory is developed for an epidemic model of a seasonally-spreading vector-borne disease using a hybrid system framework. Applicable to diseases spread by mosquitoes (e.g., chikungunya and Zika virus via Aedes albopictus), seasonal variations in transmission are modeled using switching parameters to represent term-time forcing. The vector agent is assumed to exhibit a period of incubation upon infection, modeled using a distribution. Three hybrid control strategies are analyzed in detail: switching cohort immunization, pulse vaccination at pre-specified times, and state-dependent pulse vaccination. Methods from switched systems theory are used to derive threshold disease eradication conditions involving the model parameters; convergence of solutions to a disease-free set or periodic solution is shown. A comprehensive analysis is performed to compare and contrast the different control schemes.

Assessment of the Probability of Autochthonous Transmission of Chikungunya Virus in Canada under Recent and Projected Climate Change

BACKGROUND

Chikungunya virus (CHIKV) is a reemerging pathogen transmitted by Aedes aegypti and Aedes albopictus mosquitoes. The ongoing Caribbean outbreak is of concern due to the potential for infected travelers to spread the virus to countries where vectors are present and the population is susceptible. Although there has been no autochthonous transmission of CHIKV in Canada, there is concern that both Ae. albopictus and CHIKV will become established, particularly under projected climate change. We developed risk maps for autochthonous CHIKV transmission in Canada under recent (1981–2010) and projected climate (2011–2040 and 2041–2070).

METHODS

The risk for CHIKV transmission was the combination of the climatic suitability for CHIKV transmission potential and the climatic suitability for the presence of Ae. albopictus; the former was assessed using a stochastic model to calculate R0 and the latter was assessed by deriving a suitability indicator (SIG) that captures a set of climatic conditions known to influence the ecology of Ae. albopictus. R₀ and SIG were calculated for each grid cell in Canada south of 60°N, for each time period and for two emission scenarios, and combined to produce overall risk categories that were mapped to identify areas suitable for transmission and the duration of transmissibility.

FINDINGS

The risk for autochthonous CHIKV transmission under recent climate is very low with all of Canada classified as unsuitable or rather unsuitable for transmission. Small parts of southern coastal British Columbia become progressively suitable with short-term and long-term projected climate; the duration of potential transmission is limited to 1–2 months of the year.

INTERPRETATION

Although the current risk for autochthonous CHIKV transmission in Canada is very low, our study could be further supported by the routine surveillance of Ae. albopictus in areas identified as potentially suitable for transmission given our uncertainty on the current distribution of this species in Canada. https://doi.org/10.1289/EHP669

Mathematical model of Zika virus with vertical transmission

Zika is a flavivirus transmitted to humans through either the bites of infected Aedes mosquitoes or sexual transmission. Zika has been linked to congenital anomalies such as microcephaly. In this paper, we analyze a new system of ordinary differential equations which incorporates human vertical transmission of Zika virus, the birth of babies with microcephaly and asymptomatically infected individuals. The Zika model is locally and globally asymptotically stable when the basic reproduction number is less than unity. Our model shows that asymptomatic individuals amplify the disease burden in the community, and the most important parameters for ZIKV spread are the death rate of mosquitoes, the mosquito biting rate, the mosquito recruitment rate, and the transmission per contact to mosquitoes and to adult humans. Scenario exploration indicates that personal-protection is a more effective control strategy than mosquito-reduction strategy. It also shows that delaying conception reduces the number of microcephaly cases, although this does little to prevent Zika transmission in the broader community. However, by coupling aggressive vector control and personal protection use, it is possible to reduce both microcephaly and Zika transmission. 2000 Mathematics Subject Classifications: 92B05, 93A30, 93C15.

A large-scale stochastic spatiotemporal model for Aedes albopictus-borne chikungunya epidemiology

Chikungunya is a viral disease transmitted to humans primarily via the bites of infected Aedes mosquitoes. The virus caused a major epidemic in the Indian Ocean in 2004, affecting millions of inhabitants, while cases have also been observed in Europe since 2007. We developed a stochastic spatiotemporal model of Aedes albopictus-borne chikungunya transmission based on our recently developed environmentally-driven vector population dynamics model. We designed an integrated modelling framework incorporating large-scale gridded climate datasets to investigate disease outbreaks on Reunion Island and in Italy. We performed Bayesian parameter inference on the surveillance data, and investigated the validity and applicability of the underlying biological assumptions. The model successfully represents the outbreak and measures of containment in Italy, suggesting wider applicability in Europe. In its current configuration, the model implies two different viral strains, thus two different outbreaks, for the two-stage Reunion Island epidemic. Characterisation of the posterior distributions indicates a possible relationship between the second larger outbreak on Reunion Island and the Italian outbreak. The model suggests that vector control measures, with different modes of operation, are most effective when applied in combination: adult vector intervention has a high impact but is short-lived, larval intervention has a low impact but is long-lasting, and quarantining infected territories, if applied strictly, is effective in preventing large epidemics. We present a novel approach in analysing chikungunya outbreaks globally using a single environmentally-driven mathematical model. Our study represents a significant step towards developing a globally applicable Ae. albopictus-borne chikungunya transmission model, and introduces a guideline for extending such models to other vector-borne diseases.

From eggs to bites: do ovitrap data provide reliable estimates of Aedes albopictus biting females?

BACKGROUND

Aedes albopictus is an aggressive invasive mosquito species that represents a serious health concern not only in tropical areas, but also in temperate regions due to its role as vector of arboviruses. Estimates of mosquito biting rates are essential to account for vector-human contact in models aimed to predict the risk of arbovirus autochthonous transmission and outbreaks, as well as nuisance thresholds useful for correct planning of mosquito control interventions. Methods targeting daytime and outdoor biting Ae. albopictus females (e.g., Human Landing Collection, HLC) are expensive and difficult to implement in large scale schemes. Instead, egg-collections by ovitraps are the most widely used routine approach for large-scale monitoring of the species. The aim of this work was to assess whether ovitrap data can be exploited to estimate numbers of adult biting Ae. albopictus females and whether the resulting relationship could be used to build risk models helpful for decision-makers in charge of planning of mosquito-control activities in infested areas.

METHOD

Ovitrap collections and HLCs were carried out in hot-spots of Ae. albopictus abundance in Rome (Italy) along a whole reproductive season. The relationship between the two sets of data was assessed by generalized least square analysis, taking into account meteorological parameters.

RESULT

The mean number of mosquito females/person collected by HLC in 15' (i.e., females/HLC) and the mean number of eggs/day were 18.9 ± 0.7 and 39.0 ± 2.0, respectively. The regression models found a significant positive relationship between the two sets of data and estimated an increase of one biting female/person every five additional eggs found in ovitraps. Both observed and fitted values indicated presence of adults in the absence of eggs in ovitraps. Notably, wide confidence intervals of estimates of biting females based on eggs were observed. The patterns of exotic arbovirus outbreak probability obtained by introducing these estimates in risk models were similar to those based on females/HLC (R0 > 1 in 86% and 40% of sampling dates for Chikungunya and Zika, respectively; R0 < 1 along the entire season for Dengue). Moreover, the model predicted that in this case-study scenario an R0 > 1 for Chikungunya is also to be expected when few/no eggs/day are collected by ovitraps.

DISCUSSION

This work provides the first evidence of the possibility to predict mean number of adult biting Ae. albopictus females based on mean number of eggs and to compute the threshold of eggs/ovitrap associated to epidemiological risk of arbovirus transmission in the study area. Overall, however, the large confidence intervals in the model predictions represent a caveat regarding the reliability of monitoring schemes based exclusively on ovitrap collections to estimate numbers of biting females and plan control interventions.

Imported chikungunya cases in an area newly colonised by Aedes albopictus: mathematical assessment of the best public health strategy

We aimed to identify the optimal strategy that should be used by public health authorities against transmission of chikungunya virus in mainland France. The theoretical model we developed, which mimics the current surveillance system, predicted that without vector control (VC), the probability of local transmission after introduction of viraemic patients was around 2%, and the number of autochthonous cases between five and 15 persons per hectare, depending on the number of imported cases. Compared with this baseline, we considered different strategies (VC after clinical suspicion of a case or after laboratory confirmation, for imported or autochthonous cases): Awaiting laboratory confirmation for suspected imported cases to implement VC had no significant impact on the epidemiological outcomes analysed, mainly because of the delay before entering into the surveillance system. However, waiting for laboratory confirmation of autochthonous cases before implementing VC resulted in more frequent outbreaks. After analysing the economic cost of such strategies, our study suggested implementing VC immediately after the notification of a suspected autochthonous case as the most efficient strategy in settings where local transmission has been proven. Nevertheless, we identified that decreasing reporting time for imported cases should remain a priority.

The Role of Hyalomma Truncatum on the Dynamics of Rift Valley Fever: Insights from a Mathematical Epidemic Model

To date, our knowledge of Rift Valley fever (RVF) disease spread and maintenance is still limited, as flooding, humid weather and presence of biting insects such as mosquitoes, have not completely explained RVF outbreaks. We propose a model that includes livestock, mosquitoes and ticks compartments structured according to their questing and feeding behaviour in order to study the possible role of ticks on the dynamics of RVF. To quantify disease transmission at the initial stage of the epidemic, we derive an explicit formula of the basic reproductive number, [Formula: see text]. Using the concept of Metzler matrix, we state necessary conditions for global asymptotic stability of the disease-free equilibrium. Results suggest that although host-ticks interactions may serve as disease reservoirs or disease amplifiers, the Aedes reproductive number should be kept under unity if disease post-epizootics activities are to be controlled. Results of both local and global sensitivity analysis of selected model parameters indicate that [Formula: see text] is more sensitive to the ticks attachment and detachment rates, probability of transmission from ticks to host and from host to ticks, length of infection in livestock and ticks death rate. Furthermore, when comparing the mean value of [Formula: see text] with that from previous studies which did not include ticks we found that our [Formula: see text] is very much larger resulting in an increase in the exponential phase of an outbreak. These findings suggest that if ticks are capable of transmitting the virus, they may be contributing to disease outbreaks and endemicity.

Ajuste de la fuerza de infección del dengue

Objetivo Plantear un modelo matemático hospedero vector para el ajuste de la fuerza de infección del dengue en una población variable con crecimiento logístico y ciclo de vida del mosquito con tasa de ovoposición periódica, considerando inmunidad a un serotipo.Métodos El modelo matemático propuesto está representado por ocho ecuaciones diferenciales a las que se les calcula la fuerza de infección por el método de las redes libres de escala.Resultados Se presenta una simulación del modelo matemático resuelto mediante un algoritmo implementado en el software MATLAB con datos obtenidos de la literatura. En la simulación se puede observar el crecimiento de la fuerza de infección del dengue a través del tiempo, donde esta varía de acuerdo al cambio de algunos parámetros.Conclusiones La fuerza de la infección aumenta en el tiempo, es decir, la tasa de nuevos casos crece, mostrando la necesidad de prevención en las personas, mediante el uso de telas metálicas, mosquiteros, repelentes, ropa adecuada entre otras medidas; control químico como larvicidas y adulticidas contra el vector, como también la eliminación de criaderos que interrumpan su ciclo de vida

Defining the Risk of Zika and Chikungunya Virus Transmission in Human Population Centers of the Eastern United States

The recent spread of mosquito-transmitted viruses and associated disease to the Americas motivates a new, data-driven evaluation of risk in temperate population centers. Temperate regions are generally expected to pose low risk for significant mosquito-borne disease; however, the spread of the Asian tiger mosquito (Aedes albopictus) across densely populated urban areas has established a new landscape of risk. We use a model informed by field data to assess the conditions likely to facilitate local transmission of chikungunya and Zika viruses from an infected traveler to Ae. albopictus and then to other humans in USA cities with variable human densities and seasonality. Mosquito-borne disease occurs when specific combinations of conditions maximize virus-to-mosquito and mosquito-to-human contact rates. We develop a mathematical model that captures the epidemiology and is informed by current data on vector ecology from urban sites. The model demonstrates that under specific but realistic conditions, fifty-percent of introductions by infectious travelers to a high human, high mosquito density city could initiate local transmission and 10% of the introductions could result in 100 or more people infected. Despite the propensity for Ae. albopictus to bite non-human vertebrates, we also demonstrate that local virus transmission and human outbreaks may occur when vectors feed from humans even just 40% of the time. Inclusion of human behavioral changes and mitigations were not incorporated into the models and would likely reduce predicted infections. This work demonstrates how a conditional series of non-average events can result in local arbovirus transmission and outbreaks of human disease, even in temperate cities.

The impact of rainfall and temperature on the spatial progression of cases during the chikungunya re-emergence in Thailand in 2008-2009

BACKGROUND

In 2008, chikungunya virus (CHIKV) re-emerged in Thailand after more than a decade of absence. Cases first appeared in the extreme southern region of the country and advanced northward approx. 300 km over the next 18 months. The spatial advance of CHIKV cases appeared to occur at two rates, initially progressing slowly and then increasing in speed. We hypothesize that climatic variation affected the transmission of CHIKV in the country.

METHODS

To determine the effect of climate on CHIKV transmission, we evaluated models where climate affects the transmission rate from mosquitoes to humans; extrinsic incubation period; fertility rate of mosquitoes; and the mortality rate of mosquito larvae. We compared these models to models that did not include climate effects.

RESULTS

The inclusion of climate data greatly improved model fit with models assuming climate affected the fertility rate of mosquitoes providing the best fit to data.

CONCLUSION

These results suggest that climatic variation contributed to the slower rate of incidence observed in March 2009. Overall, a gradient in transmission probability and mortality and fertility rates of mosquito is observed over the entire area with the most southern districts experiencing the most efficient transmission.

Vector-borne diseases models with residence times - A Lagrangian perspective

A multi-patch and multi-group modeling framework describing the dynamics of a class of diseases driven by the interactions between vectors and hosts structured by groups is formulated. Hosts' dispersal is modeled in terms of patch-residence times with the nonlinear dynamics taking into account the effective patch-host size. The residence times basic reproduction number R₀ is computed and shown to depend on the relative environmental risk of infection. The model is robust, that is, the disease free equilibrium is globally asymptotically stable (GAS) if R₀≤1 and a unique interior endemic equilibrium is shown to exist that is GAS whenever R₀>1 whenever the configuration of host-vector interactions is irreducible. The effects of patchiness and groupness, a measure of host-vector heterogeneous structure, on the basic reproduction number R₀, are explored. Numerical simulations are carried out to highlight the effects of residence times on disease prevalence.

Human behaviors: A threat to mosquito control?

In this work, we consider a simple theoretical model that enables us to take into account private human decisions that may interfere with public mosquito control. The model reflects the trade-off between perceived costs and observed efficacy. Our theoretical results emphasize that households may reduce their protective behavior in response to mechanical elimination techniques piloted by a public agent, leading to an increase in the total number of mosquitoes in the surrounding environment and generating a barrier for vector-borne diseases control. Our study is sufficiently generic to be applied to different arboviral diseases. It also shows that vector-control models and strategies have to take into account individual behaviors.

Dengue and chikungunya: modelling the expansion of mosquito-borne viruses into naïve populations

With the recent global spread of a number of mosquito-borne viruses, there is an urgent need to understand the factors that contribute to the ability of viruses to expand into naïve populations. Using dengue and chikungunya viruses as case studies, we detail the necessary components of the expansion process: presence of the mosquito vector; introduction of the virus; and suitable conditions for local transmission. For each component we review the existing modelling approaches that have been used to understand recent emergence events or to assess the risk of future expansions. We identify gaps in our knowledge that are related to each of the distinct aspects of the human-mosquito transmission cycle: mosquito ecology; human-mosquito contact; mosquito-virus interactions; and human-virus interactions. Bridging these gaps poses challenges to both modellers and empiricists, but only through further integration of models and data will we improve our ability to better understand, and ultimately control, several infectious diseases that exert a significant burden on human health.

Mathematical Model of Three Age-Structured Transmission Dynamics of Chikungunya Virus

We developed a new age-structured deterministic model for the transmission dynamics of chikungunya virus. The model is analyzed to gain insights into the qualitative features of its associated equilibria. Some of the theoretical and epidemiological findings indicate that the stable disease-free equilibrium is globally asymptotically stable when the associated reproduction number is less than unity. Furthermore, the model undergoes, in the presence of disease induced mortality, the phenomenon of backward bifurcation, where the stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the associated reproduction number is less than unity. Further analysis of the model indicates that the qualitative dynamics of the model are not altered by the inclusion of age structure. This is further emphasized by the sensitivity analysis results, which shows that the dominant parameters of the model are not altered by the inclusion of age structure. However, the numerical simulations show the flaw of the exclusion of age in the transmission dynamics of chikungunya with regard to control implementations. The exclusion of age structure fails to show the age distribution needed for an effective age based control strategy, leading to a one size fits all blanket control for the entire population.

Large-Scale Modelling of the Environmentally-Driven Population Dynamics of Temperate Aedes albopictus (Skuse)

The Asian tiger mosquito, Aedes albopictus, is a highly invasive vector species. It is a proven vector of dengue and chikungunya viruses, with the potential to host a further 24 arboviruses. It has recently expanded its geographical range, threatening many countries in the Middle East, Mediterranean, Europe and North America. Here, we investigate the theoretical limitations of its range expansion by developing an environmentally-driven mathematical model of its population dynamics. We focus on the temperate strain of Ae. albopictus and compile a comprehensive literature-based database of physiological parameters. As a novel approach, we link its population dynamics to globally-available environmental datasets by performing inference on all parameters. We adopt a Bayesian approach using experimental data as prior knowledge and the surveillance dataset of Emilia-Romagna, Italy, as evidence. The model accounts for temperature, precipitation, human population density and photoperiod as the main environmental drivers, and, in addition, incorporates the mechanism of diapause and a simple breeding site model. The model demonstrates high predictive skill over the reference region and beyond, confirming most of the current reports of vector presence in Europe. One of the main hypotheses derived from the model is the survival of Ae. albopictus populations through harsh winter conditions. The model, constrained by the environmental datasets, requires that either diapausing eggs or adult vectors have increased cold resistance. The model also suggests that temperature and photoperiod control diapause initiation and termination differentially. We demonstrate that it is possible to account for unobserved properties and constraints, such as differences between laboratory and field conditions, to derive reliable inferences on the environmental dependence of Ae. albopictus populations.

Estimating dengue type reproduction numbers for two provinces of Sri Lanka during the period 2013-14

Dengue is an endemic disease in the southeast Asian country Sri Lanka. Two seasonal peaks of dengue incidence were observed every year since 2002 onwards. In this study, we formulate a 2-strain dengue model for analyzing the monthly seasonal dengue incidence data from 2 provinces of Sri Lanka during the period April 2013 to September 2014. The seasonality is incorporated in the model in terms of mosquito biting rate, which we assume to be time periodic. We estimated 2 primary reproduction numbers and the basic reproduction number in a periodic environment using dengue incidence data from the western and the central provinces of Sri Lanka. We also estimated different time-average type reproduction numbers from the model using the data from these 2 provinces. Using univariate sensitivity analysis, we measured the sensitivity of the time average reproduction number ([Formula: see text]) When we vary different parameters of the proposed dengue model, we find the transmission probability of human susceptibility to strain-I infection and the mosquito mortality rate parameters are the most sensitive parameters in dengue transmission in these 2 provinces.

Temperature Characterization of Different Urban Microhabitats of Aedes albopictus (Diptera Culicidae) in Central-Northern Italy

Aedes albopictus (Skuse) is an invasive mosquito species that has spread to many countries in temperate regions bordering the Mediterranean basin, where it is becoming a major public health concern. A good knowledge of the thermal features of the most productive breeding sites for Ae. albopictus is crucial for a better estimation of the mosquitoes' life cycle and developmental rates. In this article, we address the problem of predicting air temperature in three microhabitats common in urban and suburban areas and the air and water temperature inside an ordinary catch basin, which is considered the most productive breeding site for Ae. albopictus in Italy. Temperature differences were statistically proven between the three microhabitats and between the catch basin external and internal temperature. The impacts on the developmental rates for each life stage of Ae. albopictus were tested through a parametric function of the temperature, and the aquatic stages resulted as being the most affected using the specific temperature inside a typical catch basin instead of a generic air temperature. The impact of snow cover on the catch basin internal temperature, and consequently on the mortality of diapausing eggs, was also evaluated. These data can be useful to improve epidemiological models for a better prediction of Ae. albopictus seasonal and population dynamics in central-northern Italian urban areas.