Complex behaviour in a dengue model with a seasonally varying vector population

Temporary Cross-Immunity as a Plausible Driver of Asynchronous Cycles of Dengue Serotypes

Many infectious diseases exist as multiple variants, with interactions between variants potentially driving epidemiological dynamics. These diseases include dengue, which infects hundreds of millions of people every year and exhibits complex multi-serotype dynamics. Antibodies produced in response to primary infection by one of the four dengue serotypes can produce a period of temporary cross-immunity (TCI) to infection by other serotypes. After this period, the remaining antibodies can facilitate the entry of heterologous serotypes into target cells, thus enhancing severity of secondary infection by a heterologous serotype. This represents antibody-dependent enhancement (ADE). In this study, we analyze an epidemiological model to provide novel insights into the importance of TCI and ADE in producing cyclic outbreaks of dengue serotypes. Our analyses reveal that without TCI, such cyclic outbreaks are synchronous across serotypes and only occur when ADE produces high transmission rates. In contrast, the presence of TCI allows asynchronous cycles of serotypes by inducing a time lag between recovery from primary infection by one serotype and secondary infection by another, with such cycles able to occur without ADE. Our results suggest that TCI is a fundamental driver of asynchronous cycles of dengue serotypes and possibly other multi-variant diseases.

Spatial dynamics of dengue fever spreading for the coexistence of two serotypes with an application to the city of São Paulo, Brazil

BACKGROUND AND OBJECTIVE

Dengue fever is a disease in which individuals' spatial distribution and Aedes aegypti mosquitoes breeding places are important factors for the disease dynamics. Typically urban, dengue is a problem for least developed countries due to the ineffectiveness in controlling the vector and disorderly urbanization processes. The result is a composition of urban sanitation problems and areas with high demographic densities and intense flows of people. This paper explores the spatial distribution of vector breeding places to evaluate introducing a new dengue serotype to a population at equilibrium for a pre-existing serotype. The paper's objective is to analyze the spatial dynamics of dengue using variations of the basic reproduction number.

METHODS

A model based on probabilistic cellular automata is proposed to permitting the necessary flexibility to consider some spatial distributions of vector breeding places. Then, ordinary differential equations are used as a mean-field approach of the model, and the basic reproduction number (R₀) is derived considering the next-generation matrix method. A spatial approach for R₀ is also proposed, and the model is tested in a neighbourhood from the city of São Paulo, Brazil, to examine the potential risks of vector breeding cells distribution.

RESULTS

The results indicated that the more spread out these places, the higher are the values of R₀. When the model is applied to a neighbourhood in São Paulo, residential areas may boost the infections and must be under public vigilance to combat vector breeding sites.

CONCLUSIONS

Considering the mean-field approximation of the cellular automata model by ordinary differential equations, the basic reproduction number derived returned an estimative of the disease dynamics in the population. However, the spatial basic reproduction number was more assertive in showing areas with a higher disease incidence. Moreover, the model could be easily adapted to be used in real maps enabling simulations closer to real problems.

Is fractional-order chaos theory the new tool to model chaotic pandemics as Covid-19?

The deadly outbreak of the second wave of Covid-19, especially in worst hit lower-middle-income countries like India, and the drastic rise of another growing epidemic of Mucormycosis, call for an efficient mathematical tool to model pandemics, analyse their course of outbreak and help in adopting quicker control strategies to converge to an infection-free equilibrium. This review paper on prominent pandemics reveals that their dispersion is chaotic in nature having long-range memory effects and features which the existing integer-order models fail to capture. This paper thus puts forward the use of fractional-order (FO) chaos theory that has memory capacity and hereditary properties, as a potential tool to model the pandemics with more accuracy and closeness to their real physical dynamics. We investigate eight FO models of Bombay plague, Cancer and Covid-19 pandemics through phase portraits, time series, Lyapunov exponents and bifurcation analysis. FO controllers (FOCs) on the concepts of fuzzy logic, adaptive sliding mode and active backstepping control are designed to stabilise chaos. Also, FOCs based on adaptive sliding mode and active backstepping synchronisation are designed to synchronise a chaotic epidemic with a non-chaotic one, to mitigate the unpredictability due to chaos during transmission. It is found that severity and complexity of the models increase as the memory fades, indicating that FO can be used as a crucial parameter to analyse the progression of a pandemic. To sum it up, this paper will help researchers to have an overview of using fractional calculus in modelling pandemics more precisely and also to approximate, choose, stabilise and synchronise the chaos control parameter that will eliminate the extreme sensitivity and irregularity of the models.

The effect of demographic and environmental variability on disease outbreak for a dengue model with a seasonally varying vector population

Seasonal changes in temperature, humidity, and rainfall affect vector survival and emergence of mosquitoes and thus impact the dynamics of vector-borne disease outbreaks. Recent studies of deterministic and stochastic epidemic models with periodic environments have shown that the average basic reproduction number is not sufficient to predict an outbreak. We extend these studies to time-nonhomogeneous stochastic dengue models with demographic variability wherein the adult vectors emerge from the larval stage vary periodically. The combined effects of variability and periodicity provide a better understanding of the risk of dengue outbreaks. A multitype branching process approximation of the stochastic dengue model near the disease-free periodic solution is used to calculate the probability of a disease outbreak. The approximation follows from the solution of a system of differential equations derived from the backward Kolmogorov differential equation. This approximation shows that the risk of a disease outbreak is also periodic and depends on the particular time and the number of the initial infected individuals. Numerical examples are explored to demonstrate that the estimates of the probability of an outbreak from that of branching process approximations agree well with that of the continuous-time Markov chain. In addition, we propose a simple stochastic model to account for the effects of environmental variability on the emergence of adult vectors from the larval stage.

Disease Emergence in Multi-Patch Stochastic Epidemic Models with Demographic and Seasonal Variability

Factors such as seasonality and spatial connectivity affect the spread of an infectious disease. Accounting for these factors in infectious disease models provides useful information on the times and locations of greatest risk for disease outbreaks. In this investigation, stochastic multi-patch epidemic models are formulated with seasonal and demographic variability. The stochastic models are used to investigate the probability of a disease outbreak when infected individuals are introduced into one or more of the patches. Seasonal variation is included through periodic transmission and dispersal rates. Multi-type branching process approximation and application of the backward Kolmogorov differential equation lead to an estimate for the probability of a disease outbreak. This estimate is also periodic and depends on the time, the location, and the number of initial infected individuals introduced into the patch system as well as the magnitude of the transmission and dispersal rates and the connectivity between patches. Examples are given for seasonal transmission and dispersal in two and three patches.

Quantification of Voice Type Components Present in Human Phonation Using a Modified Diffusive Chaos Technique

Purpose:

Signal typing has been used to categorize healthy and disordered voices; however, human voices are likely comprised of differing proportions of periodic type 1 elements, type 2 elements that are periodic with modulations, aperiodic type 3 elements, and stochastic type 4 elements. A novel diffusive chaos method is presented to detect the distribution of voice types within a signal with the goal of providing an objective and clinically useful tool for evaluating the voice. It was predicted that continuous calculation of the diffusive chaos parameter throughout the voice sample would allow for construction of comprehensive voice type component profiles (VTCP).

Methods:

One hundred thirty-five voice samples of sustained /a/ vowels were randomly selected from the Disordered Voice Database Model 4337. All samples were classified according to the voice type paradigm using spectrogram analysis, yielding 34 type 1, 35 type 2, 42 type 3, and 24 type 4 voice samples. All samples were then analyzed using the diffusive chaos method, and VTCPs were generated to show the distribution of the 4 voice type components (VTC).

Results:

The proportions of VTC1 varied significantly between the majority of the traditional voice types ( P < .001). Three of the 4 VTCs of type 3 voices were significantly different from the VTCs of type 4 voices ( P < .001). These results were compared to calculations of spectrum convergence ratio, which did not vary significantly between voice types 1 and 2 or 2 and 3.

Conclusion:

The diffusive chaos method demonstrates proficiency in generating comprehensive VTCPs for disordered voices with varying severity. In contrast to acoustic parameters that provide a single measure of disorder, VTCPs can be used to detect subtler changes by observing variations in each VTC over time. This method also provides the advantage of quantifying stochastic noise components that are due to breathiness in the voice.

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.

Exploring the dynamics of respiratory syncytial virus (RSV) transmission in children

Respiratory syncytial virus (RSV) is the main cause of lower respiratory tract infections in children. Whilst highly seasonal, RSV dynamics can have either one-year (annual) or two-year (biennial) cycles. Furthermore, some countries show a 'delayed biennial' pattern, where the epidemic peak in low incidence years is delayed. We develop a compartmental model for RSV infection, driven by a seasonal forcing function, and conduct parameter space and bifurcation analyses to document parameter ranges that give rise to these different seasonal patterns. The model is sensitive to the birth rate, transmission rate, and seasonality parameters, and can replicate RSV dynamics observed in different countries. The seasonality parameter must exceed a threshold for the model to produce biennial cycles. Intermediate values of the birth rate produce the greatest delay in these biennial cycles, while the model reverts to annual cycles if the duration of immunity is too short. Finally, the existence of period doubling and period halving bifurcations suggests robust model dynamics, in agreement with the known regularity of RSV outbreaks. These findings help explain observed RSV data, such as regular biennial dynamics in Western Australia, and delayed biennial dynamics in Finland. From a public health perspective, our findings provide insight into the drivers of RSV transmission, and a foundation for exploring RSV interventions.

Modelling the transmission dynamics of dengue in the presence of Wolbachia

Use of the bacterium Wolbachia is an innovative new strategy designed to break the cycle of dengue transmission. There are two main mechanisms by which Wolbachia could achieve this: by reducing the level of dengue virus in the mosquito and/or by shortening the host mosquito's lifespan. However, although Wolbachia shortens the lifespan, it also gives a breeding advantage which results in complex population dynamics. This study focuses on the development of a mathematical model to quantify the effect on human dengue cases of introducing Wolbachia into the mosquito population. The model consists of a compartment-based system of first-order differential equations; seasonal forcing in the mosquito population is introduced through the adult mosquito death rate. The analysis focuses on a single dengue outbreak typical of a region with a strong seasonally-varying mosquito population. We found that a significant reduction in human dengue cases can be obtained provided that Wolbachia-carrying mosquitoes persist when competing with mosquitoes without Wolbachia. Furthermore, using the Wolbachia strain WMel reduces the mosquito lifespan by at most 10% and allows them to persist in competition with non-Wolbachia-carrying mosquitoes. Mosquitoes carrying the WMelPop strain, however, are not likely to persist as it reduces the mosquito lifespan by up to 50%. When all other effects of Wolbachia on the mosquito physiology are ignored, cytoplasmic incompatibility alone results in a reduction in the number of human dengue cases. A sensitivity analysis of the parameters in the model shows that the transmission probability, the biting rate and the average adult mosquito death rate are the most important parameters for the outcome of the cumulative proportion of human individuals infected with dengue.