Vector-host Model Research Articles

A dynamical study of a fuzzy epidemic model of Mosquito-Borne Disease

Numerical models help us to understand the transmission dynamics of infectious diseases. Since vectors transmit many diseases, vector host models are very important. The transmission dynamics of Dengue fever with an incubation period of the virus with fuzzy parameters have been analyzed in this article. Sometimes it is very difficult and almost impossible to collect numerical data as a fixed value. Due to the lack of precise numerical data for the parameters, the fuzzy model is considered here. Fuzzy theory is a very powerful mathematical tool for dealing with imprecision and uncertainties. In this article, the chance of the occurrence of dengue infection βh(a), the recovery rate r(a) and the mortality rate of the human population μh(a) due to dengue fever are considered fuzzy numbers. The stability of equilibrium points of the model has been determined and a reproduction number has been derived respectively in a fuzzy sense. A numerical model is designed for the studied model having fuzzy parameters and some numerical experiments are performed which indicate that the proposed method shows positivity, stability, and convergence at each time step size. Hence the method preserves the essential features of the dynamic epidemic models.

A direct comparison of methods for assessing the threat from emerging infectious diseases in seasonally varying environments

Seasonal variations in environmental conditions lead to changing infectious disease epidemic risks at different times of year. The probability that early cases initiate a major epidemic depends on the season in which the pathogen enters the population. The instantaneous epidemic risk (IER) can be tracked. This quantity is straightforward to calculate, and corresponds to the probability of a major epidemic starting from a single case introduced at time t=t0, assuming that environmental conditions remain identical from that time onwards (i.e. for all t≥t0). However, the threat when a pathogen enters the population in fact depends on changes in environmental conditions occurring within the timescale of the initial phase of the outbreak. For that reason, we compare the IER with a different metric: the case epidemic risk (CER). The CER corresponds to the probability of a major epidemic starting from a single case entering the population at time t=t0, accounting for changes in environmental conditions after that time. We show how the IER and CER can be calculated using different epidemiological models (the stochastic Susceptible-Infectious-Removed model and a stochastic host-vector model that is parameterised using temperature data for Miami) in which transmission parameter values vary temporally. While the IER is always easy to calculate numerically, the adaptable method we provide for calculating the CER for the host-vector model can also be applied easily and solved using widely available software tools. In line with previous research, we demonstrate that, if a pathogen is likely to either invade the population or fade out on a fast timescale compared to changes in environmental conditions, the IER closely matches the CER. However, if this is not the case, the IER and the CER can be significantly different, and so the CER should be used. This demonstrates the need to consider future changes in environmental conditions carefully when assessing the risk posed by emerging pathogens.

Predicting the Spread of Vector-Borne Diseases in a Warming World

Predicting how climate warming affects vector borne diseases is a key research priority. The prevailing approach uses the basic reproductive number (R0) to predict warming effects. However, R0 is derived under assumptions of stationary thermal environments; using it to predict disease spread in non-stationary environments could lead to erroneous predictions. Here, we develop a trait-based mathematical model that can predict disease spread and prevalence for any vector borne disease under any type of non-stationary environment. We parameterize the model with trait response data for the Malaria vector and pathogen to test the latest IPCC predictions on warmer-than-average winters and hotter-than-average summers. We report three key findings. First, the R0 formulation commonly used to investigate warming effects on disease spread violates the assumptions underlying its derivation as the dominant eigenvalue of a linearized host-vector model. As a result, it overestimates disease spread in cooler environments and underestimates it in warmer environments, proving its predictions to be unreliable even in a constant thermal environment. Second, hotter-than-average summers both narrow the thermal limits for disease prevalence, and reduce prevalence within those limits, to a much greater degree than warmer-than-average winters, highlighting the importance of hot extremes in driving disease burden. Third, while warming reduces infected vector populations through the compounding effects of adult mortality, and infected host populations through the interactive effects of mortality and transmission, uninfected vector populations prove surprisingly robust to warming. This suggests that ecological predictions of warming-induced reductions in disease burden should be tempered by the evolutionary possibility of vector adaptation to both cooler and warmer climates.

Impact of incubation delay and stochastic perturbation on Dengue fever virus transmission model

Consider the fluctuation of environmental noise and the incubation period of virus, a stochastic vector-host model with incubation delay is proposed to describe the transmission of Dengue fever virus (DFVs) between humans and mosquitoes. By constructing suitable stochastic Lyapunov functional, the existence and uniqueness of global positive solutions of this model are proved. Furthermore, some sufficient conditions are obtained for the asymptotic pathwise estimation of solutions. In addition, we also consider the asymptotic pathwise estimation of solutions, the existence and uniqueness of stationary distribution of this model without delay, which imply that disease is stochastic persistent. Finally, numerical simulations explain the theoretical results and discuss the effects of stochastic perturbations and delays on DFVs transmission. Our results imply that the spread of DFVs presents many unpredictability under the influence of stochastic perturbation, and the reproduction number can no longer be used as a threshold condition for the extinction or persistence of disease. Moreover, ignoring the incubation delay will not only overestimate the risk of disease outbreaks but also underestimate the duration of diseases. Rational application of stochastic perturbations on disease transmission and incubation periods will play a very important role in vector-borne disease control.

Mathematical models for dengue fever epidemiology: A 10-year systematic review.

Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading.Mathematical models describing dengue fever epidemiological dynamics are found back from 1970. Dengue fever is a viral mosquito-borne infection caused by four antigenically related but distinct serotypes (DENV-1 to DENV-4). With 2.5 billion people at risk of acquiring the infection, it is a major international public health concern. Although most of the cases are asymptomatic or mild, the disease immunological response is complex, with severe disease linked to the antibody-dependent enhancement (ADE) - a disease augmentation phenomenon where pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection. Here, we present a 10-year systematic review on mathematical models for dengue fever epidemiology. Specifically, we review multi-strain frameworks describing host-to-host and vector-host transmission models and within-host models describing viral replication and the respective immune response.Following a detailed literature search in standard scientific databases, different mathematical models in terms of their scope, analytical approach and structural form, including model validation and parameter estimation using empirical data, are described and analyzed.Aiming to identify a consensus on infectious diseases modeling aspects that can contribute to public health authorities for disease control, we revise the current understanding of epidemiological and immunological factors influencing the transmission dynamics of dengue. This review provide insights on general features to be considered to model aspects of real-world public health problems, such as the current epidemiological scenario we are living in.

Sensitivity Analysis in an Immuno-Epidemiological Vector-Host Model.

Sensitivity Analysis (SA) is a useful tool to measure the impact of changes in model parameters on the infection dynamics, particularly to quantify the expected efficacy of disease control strategies. SA has only been applied to epidemic models at the population level, ignoring the effect of within-host virus-with-immune-system interactions on the disease spread. Connecting the scales from individual to population can help inform drug and vaccine development. Thus the value of understanding the impact of immunological parameters on epidemiological quantities. Here we consider an age-since-infection structured vector-host model, in which epidemiological parameters are formulated as functions of within-host virus and antibody densities, governed by an ODE system. We then use SA for these immuno-epidemiological models to investigate the impact of immunological parameters on population-level disease dynamics such as basic reproduction number, final size of the epidemic or the infectiousness at different phases of an outbreak. As a case study, we consider Rift Valley Fever Disease utilizing parameter estimations from prior studies. SA indicates that 1% increase in within-host pathogen growth rate can lead up to 8% increase in mathcal R_0, up to 1 % increase in steady-state infected host abundance, and up to 4% increase in infectiousness of hosts when the reproduction number mathcal R_0 is larger than one. These significant increases in population-scale disease quantities suggest that control strategies that reduce the within-host pathogen growth can be important in reducing disease prevalence.

Simulation and prediction of dengue outbreaks based on an SIR model with a time-dependent transmission rate including meteorological data. An example for Colombo and Jakarta

Vector-borne diseases can usually be examined with a vector–host model like the [Formula: see text] model. This, however, depends on parameters that contain detailed information about the mosquito population that we usually do not know. For this reason, in this article, we reduce the [Formula: see text] model to an [Formula: see text] model with a time-dependent and periodic transmission rate [Formula: see text]. Since the living conditions of the mosquitos depend on the local weather conditions, meteorological data sets flow into the model in order to achieve a more realistic behavior. The developed [Formula: see text] model is adapted to existing data sets of hospitalized dengue cases in Jakarta (Indonesia) and Colombo (Sri Lanka) using numerical optimization based on Pontryagin’s maximum principle. A previous data analysis shows that the results of this parameter fit are within a realistic range and thus allow further investigations. Based on this, various simulations are carried out and the prediction quality of the model is examined.

Analysis of Strategies for Preventing and Controlling the Chikungunya Virus


 
 
 
 Alternatives to stop chikungunya outbreaks are oriented to vector control and developing a specific treatment and a preventive vaccine. Environmental control and mosquito bite prevention are undoubtedly essential to decrease the disease burden, but Aedes vectors continue to expand geographically and re-emerge. So, vaccination is proposed to respond to this etiology and recognized as a pressing need for affected countries. A mathematical host-vector model, including asymptomatic population, vector control, and vaccination (assuming the existence of a safe protective vaccine against the chikungunya virus), is suggested to analyze the effects of these efforts. Poisson distribution is applied to interpret the basic reproduction number. Then vaccination and vector control thresholds are established to prescribe the most effective protection measures against exposure to the chikungunya virus. In conclusion, it is advisable to continue with integrated control to reduce the economic impact of relevant public health responses and mitigate other infections since Aedes is a transmitter of other arboviruses such as dengue, Zika, and Mayaro. Furthermore, vaccinating all individuals in a community could be a costly and gradual process.
 
 
 

Towards a Semi-Automatic Early Warning System for Vector-Borne Diseases.

The emergence and spread of vector-borne diseases (VBDs) is a function of biotic, abiotic and socio-economic drivers of disease while their economic and societal burden depends upon a number of time-varying factors. This work is concerned with the development of an early warning system that can act as a predictive tool for public health preparedness and response. We employ a host-vector model that combines entomological (mosquito data), social (immigration rate, demographic data), environmental (temperature) and geographical data (risk areas). The output consists of appropriate maps depicting suitable risk measures such as the basic reproduction number, R0, and the probability of getting infected by the disease. These tools consist of the backbone of a semi-automatic early warning system tool which can potentially aid the monitoring and control of VBDs in different settings. In addition, it can be used for optimizing the cost-effectiveness of distinct control measures and the integration of open geospatial and climatological data. The R code used to generate the risk indicators and the corresponding spatial maps along with the data is made available.

Dynamics of a vector-host model under switching environments

<p style='text-indent:20px;'>In this paper, the stochastic vector-host model has been proposed and analysed using nice properties of piecewise deterministic Markov processes (PDMPs). A threshold for the stochastic model is derived whose sign determines whether the disease will eventually disappear or persist. We show mathematically the existence of scenarios where switching plays a significant role in surprisingly reversing the long-term properties of deterministic systems.</p>

Climate-based dengue model in Semarang, Indonesia: Predictions and descriptive analysis.

BackgroundDengue is one of the most rapidly spreading vector-borne diseases, which is considered to be a major health concern in tropical and sub-tropical countries. It is strongly believed that the spread and abundance of vectors are related to climate. Construction of climate-based mathematical model that integrates meteorological factors into disease infection model becomes compelling challenge since the climate is positively associated with both incidence and vector existence.MethodsA host-vector model is constructed to simulate the dynamic of transmission. The infection rate parameter is replaced with the time-dependent coefficient obtained by optimization to approximate the daily dengue data. Further, the optimized infection rate is denoted as a function of climate variables using the Autoregressive Distributed Lag (ARDL) model.ResultsThe infection parameter can be extended when updated daily climates are known, and it can be useful to forecast dengue incidence. This approach provides proper prediction, even when tested in increasing or decreasing prediction windows. In addition, associations between climate and dengue are presented as a reversed slide-shaped curve for dengue-humidity and a reversed U-shaped curves for dengue-temperature and dengue-precipitation. The range of optimal temperature for infection is 24.3–30.5 °C. Humidity and precipitation are positively associated with dengue upper the threshold 70% at lag 38 days and below 50 mm at lag 50 days, respectively.ConclusionIdentification of association between climate and dengue is potentially useful to counter the high risk of dengue and strengthen the public health system and reduce the increase of the dengue burden.

Complexity of host-vector dynamics in a two-strain dengue model

We introduce a compartmental host-vector model for dengue with two viral strains, temporary cross-immunity for the hosts, and possible secondary infections. We study the conditions on existence of endemic equilibria where one strain displaces the other or the two virus strains co-exist. Since the host and vector epidemiology follow different time scales, the model is described as a slow-fast system. We use the geometric singular perturbation technique to reduce the model dimension. We compare the behaviour of the full model with that of the model with a quasi-steady approximation for the vector dynamics. We also perform numerical bifurcation analysis with parameter values from the literature and compare the bifurcation structure to that of previous two-strain host-only models.

Optimal control analysis of vector-host model with saturated treatment.

Vector-host infectious diseases remain a challenging issue and cause millions of deaths each year globally. In such outbreaks, many countries especially developing or underdevelopment faces a situation where the number of infected individuals is getting larger and the medical facilities are limited. In this paper, we construct an epidemic model to explore the transmission dynamics of vector-borne diseases with nonlinear saturated incidence rate and saturated treatment function. This type of incidence rate, as well as the saturated treatment function, is also known as the Holling type II form and describes the effect of delayed treatment. Initially, we formulate a mathematical model and then present the basic analysis of the model including the positivity and boundedness of the solution. The threshold quantity {mathcal {R}}_{0} is presented and the stability analysis of the system is carried out for the model equilibria. The global stability results are shown using the Lyapunov function of Goh–Voltera type. The existence of backward bifurcation is discussed using the central manifold theory. Further, the global sensitivity analysis of the model is carried out using the Latin Hypercube sampling and the partial rank correlation coefficient techniques. Moreover, an optimal control problem is formulated and the necessary optimality conditions are investigated in order to eradicate the disease in a community. Four strategies are presented by choosing different set of controls combination for the disease minimization. Finally, the numerical simulations of each strategy are depicted to demonstrate the importance of suggesting control interventions on the disease dynamics and eradication.

A theoretical assessment of the effects of vectors genetics on a host-vector disease

A host-vector disease model with insecticide resistance genes is proposed as a system of differential equations. The resistance-induced reproduction number $${\mathcal {R}}_e$$ is determined and qualitative stabilities analysis are provided. We use the model to study the effects of insecticide resistance of vectors on the spread of the disease. The resistance-induced reproduction number $${\mathcal {R}}_e$$ is compared with the basic reproduction number $$({\mathcal {R}}_0)$$ in the absence of resistant strain to assess the effects of insecticide resistance.

Equilibrium and sensitivity analysis of a spatio-temporal host-vector epidemic model

Insect-borne diseases are diseases carried by insects affecting humans, animals or plants. They have the potential to generate massive outbreaks such as the Zika epidemic in 2015–2016 mostly distributed in the Americas, the Pacific and Southeast Asia, and the multi-foci outbreak caused by the bacterium Xylella fastidiosa in Europe in the 2010s. In this article, we propose and analyze the behavior of a spatially-explicit compartmental model adapted to pathosystems with fixed hosts and mobile vectors disseminating the disease. The behavior of this model based on a system of partial differential equations is complementarily characterized via a theoretical study of its equilibrium states and a numerical study of its transient phase using global sensitivity analysis. The results are discussed in terms of implications concerning the surveillance and control of the disease over a medium-to-long temporal horizon.

An epidemic model highlighting humane social awareness and vector–host lifespan ratio variation

Many vector-borne disease epidemic models neglect the fact that in modern human civilization, social awareness as well as self-defence systems are overwhelming against advanced propagation of the disease. News is becoming more effortlessly accessible through social media and mobile apps, while apparatuses for disease prevention are inclined to be more abundant and affordable. Here we study a simple host–vector model in which media-triggered social awareness and seasonality in vector breeding are taken into account. There appears a certain threshold indicating the alarming outbreak; the number of infective human individuals above which shall actuate the self-defence systems for the susceptible subpopulation. A model where the infection rate revolves in the likelihood of limited medical access, perceiving the disease as being easily curable, and overwhelming hungrier vectors is proposed. Further discoveries are made from undertaking disparate time scales in human and vector population. The resulting slow–fast system discloses notable dynamics in which solution trajectories confine to a slow manifold and the critical manifold, before finally ending up at stable equilibria. How coinciding the slow manifold with the critical manifold enhances periodic forcing is also studied. The finding on hysteresis loops gives insights into how defining an alarming outbreak critically perturbs the basic reproductive number, which later helps keep the incidence cycle on small magnitudes.

THE IMPACT OF VACCINATION ON MALARIA PREVALENCE: A VACCINE-AGE-STRUCTURED MODELING APPROACH

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

Modelling Dengue Fever Epidemics in Jakarta

This article thematizes the qualitative estimation of transmission dynamics of Dengue fever. At first, a single-compartment vector-host model for the total infective cases in one homogeneous area has been set up and simplified using a steady-state approximation. Seasonality has been considered in the transmission parameter which is modelled by a Fourier sum. The equilibria of the model and their stability as well as the computation of the basic reproductive number are presented. As a modification, models considering a segmenting of the area in separate districts and their inter-district mobility have been set up, both with and without dependence of the disease transmission parameters on the district. Those have also been analysed in terms of equilibria and stability. Parameter estimation on available Dengue data from Jakarta in the time interval of 2008–2016 using the Metropolis algorithm has been done. $${\mathscr {L}}_1$$ and $${\mathscr {L}}_2$$ comparisons show that using the multi-patch model with district-dependent parameters a decent approximation to the infection data is possible.

Modelling the effective reproduction number of vector-borne diseases: the yellow fever outbreak in Luanda, Angola 2015-2016 as an example.

The burden of vector-borne diseases (Dengue, Zika virus, yellow fever, etc.) gradually increased in the past decade across the globe. Mathematical modelling on infectious diseases helps to study the transmission dynamics of the pathogens. Theoretically, the diseases can be controlled and eventually eradicated by maintaining the effective reproduction number, (n}{}{mathcal{R}}_{mathrm{eff}}), strictly less than 1. We established a vector-host compartmental model, and derived (n}{}{mathcal{R}}_{mathrm{eff}}) for vector-borne diseases. The analytic form of the (n}{}{mathcal{R}}_{mathrm{eff}}) was found to be the product of the basic reproduction number and the geometric average of the susceptibilities of the host and vector populations. The (n}{}{mathcal{R}}_{mathrm{eff}}) formula was demonstrated to be consistent with the estimates of the 2015–2016 yellow fever outbreak in Luanda, and distinguished the second minor epidemic wave. For those using the compartmental model to study the vector-borne infectious disease epidemics, we further remark that it is important to be aware of whether one or two generations is considered for the transition “from host to vector to host” in reproduction number calculation.

Parameter estimation and fractional derivatives of dengue transmission model

In this paper, we propose a parameter estimation of dengue fever transmission model using a particle swarm optimization method. This method is applied to estimate the parameters of the host-vector and SIR type dengue transmission models by using cumulative data of dengue patient in East Java province, Indonesia. Based on the parameter values, the basic reproduction number of both models are greater than one and obtained their value for SIR is $\mathcal{R}_0 = 1.4159$ and for vector host is $\mathcal{R}_0 = 1.1474$. We then formulate the models in fractional Atangana-Baleanu derivative that possess the property of nonlocal and nonsingular kernel that has been remained effective to many real-life problems. A numerical procedure for the solution of the model SIR model is shown. Some specific numerical values are considered to obtain the graphical results for both the SIR and Vector Host model. We show that the model vector host provide good results for data fitting than that of the SIR model.