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

Mathematical model of Ehrlichia chaffeensis transmission dynamics in dogs

Ehrlichia chaffeensis is a tick-borne disease transmitted by ticks to dogs. Few studies have mathematical modelled such tick-borne disease in dogs, and none have developed models that incorporate different ticks' developmental stages (discrete variable) as well as the duration of infection (continuous variable). In this study, we develop and analyze a model that considers these two structural variables using integrated semigroups theory. We address the well-posedness of the model and investigate the existence of steady states. The model exhibits a disease-free equilibrium and an endemic equilibrium. We calculate the reproduction number (T 0 ). We establish a necessary and sufficient condition for the bifurcation of an endemic equilibrium. Specifically, we demonstrate that a bifurcation, either backward or forward, can occur at T 0 = 1 , leading to the existence, or not, of an endemic equilibrium even when T 0 < 1 . Finally, numerical simulations are employed to illustrate these theoretical findings.

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.

COVID-19 and Chikungunya: an optimal control model with consideration of social and environmental factors

Chikungunya is one of the Aedes aegypti diseases that mosquito transmits to humans and that are common in tropical countries like Yemen. In this work, we formulated a novel dynamic mathematical model framework, which integrates COVID-19 and Chikungunya outbreaks. The proposed model is governed by a system of dynamic ordinary differential equations (ODEs). Particle swarm optimization was employed to solve the parameters estimation problem of the outbreaks of COVID-19 and Chikungunya in Yemen (March 1, 2020, to May 30, 2020). Besides, a bi-objective optimal control model was formulated, which minimizes the number of affected individuals and minimizes the total cost associated with the intervention strategies. The bi-objective optimal control was also solved using PSO. Five preventive measures were considered to curb the environmental and social factors that trigger the emergence of these viruses. Several strategies were simulated to evaluate the best possible strategy under the conditions and available resources in Yemen. The results obtained confirm that the strategy, which provides resources to prevent the transmission of Chikungunya and provides sufficient resources for testing, applying average social distancing, and quarrying the affected individuals, has a significant effect on flattening the epidemic curves and is the most suitable strategy in Yemen.

To isolate or not to isolate: the impact of changing behavior on COVID-19 transmission

Background

The COVID-19 pandemic has caused more than 25 million cases and 800 thousand deaths worldwide to date. In early days of the pandemic, neither vaccines nor therapeutic drugs were available for this novel coronavirus. All measures to prevent the spread of COVID-19 are thus based on reducing contact between infected and susceptible individuals. Most of these measures such as quarantine and self-isolation require voluntary compliance by the population. However, humans may act in their (perceived) self-interest only.

Methods

We construct a mathematical model of COVID-19 transmission with quarantine and hospitalization coupled with a dynamic game model of adaptive human behavior. Susceptible and infected individuals adopt various behavioral strategies based on perceived prevalence and burden of the disease and sensitivity to isolation measures, and they evolve their strategies using a social learning algorithm (imitation dynamics).

Results

This results in complex interplay between the epidemiological model, which affects success of different strategies, and the game-theoretic behavioral model, which in turn affects the spread of the disease. We found that the second wave of the pandemic, which has been observed in the US, can be attributed to rational behavior of susceptible individuals, and that multiple waves of the pandemic are possible if the rate of social learning of infected individuals is sufficiently high.

Conclusions

To reduce the burden of the disease on the society, it is necessary to incentivize such altruistic behavior by infected individuals as voluntary self-isolation.

Quantifying Positive Health Externalities of Disease Control Interventions: Modeling Chikungunya and Dengue

Purpose. Health interventions can generate positive externalities not captured in traditional, single-disease cost-effectiveness analyses (CEAs), potentially biasing results. We illustrate this with the example of mosquito-borne diseases. When a particular mosquito species can transmit multiple diseases, a single-disease CEA comparing disease-specific interventions (e.g., vaccination) with interventions targeting the mosquito population (e.g., insecticide) would underestimate the insecticide's full benefits (i.e., preventing other diseases). Methods. We developed three dynamic transmission models: chikungunya, dengue, and combined chikungunya and dengue, each calibrated to disease-specific incidence and deaths in Colombia (June 2014 to December 2017). We compared the models' predictions of the incremental benefits and cost-effectiveness of an insecticide (10% efficacy), hypothetical chikungunya and dengue vaccines (40% coverage, 95% efficacy), and combinations of these interventions. Results. Model calibration yielded realistic parameters that produced close matches to disease-specific incidence and deaths. The chikungunya model predicted that vaccine would decrease the incidence of chikungunya and avert more total deaths than insecticide. The dengue model predicted that insecticide and the dengue vaccine would reduce dengue incidence and deaths, with no effect for the chikungunya vaccine. In the combined model, insecticide was more effective than either vaccine in reducing the incidence of and deaths from both diseases. In all models, the combined strategy was at least as effective as the most effective single strategy. In an illustrative CEA, the most frequently preferred strategy was vaccine in the chikungunya model, the status quo in the dengue model, and insecticide in the combined model. Limitations. There is uncertainty in the target calibration data. Conclusions. Failure to capture positive externalities can bias CEA results, especially when evaluating interventions that affect multiple diseases. Multidisease modeling is a reasonable alternative for addressing such biases.

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.

Optimal control strategies for dengue transmission in pakistan

This paper presents a deterministic model for dengue virus transmission. The model is parameterized using data from the 2017 dengue outbreak in Pakistan. We estimated the basic reproduction number (R₀) without any interventions for the 2017 dengue outbreak in Peshawar district of Pakistan as R₀≈2.64, the distribution of the reproduction number lies in the range R₀∈[1.21,5.24] (with a mean R₀≈2.64). Optimal control theory is then applied to investigate the optimal strategy for curtailing the spread of the disease using two time-dependent control variables determined from sensitivity analysis. These control variables are insecticide use and vaccination. The results show that the two controls avert the same number of infections in the district regardless of the weights on the costs this is due to the reciprocal relationship between the cost of insecticide use and vaccination. A strong reciprocal relationship exists between the use of insecticide and vaccination; as the cost of insecticide increases the use of vaccination increases. The use of insecticide on the other hand slightly increases when vaccination level decreases due to increase in cost.

sPop: Age-structured discrete-time population dynamics model in C, Python, and R

This article describes the sPop packages implementing the deterministic and stochastic versions of an age-structured discrete-time population dynamics model. The packages enable mechanistic modelling of a population by monitoring the age and development stage of each individual. Survival and development are included as the main effectors and they progress at a user-defined pace: follow a fixed rate, delay for a given time, or progress at an age-dependent manner. The model is implemented in C, Python, and R with a uniform design to ease usage and facilitate adoption. Early versions of the model were previously employed for investigating climate-driven population dynamics of the tiger mosquito and the chikungunya disease spread by this vector. The sPop packages presented in this article enable the use of the model in a range of applications extending from vector-borne diseases towards any age-structured population including plant and animal populations, microbial dynamics, host-pathogen interactions, infectious diseases, and other time-dependent epidemiological processes.

Computational and Mathematical Methods to Estimate the Basic Reproduction Number and Final Size for Single-Stage and Multistage Progression Disease Models for Zika with Preventative Measures

We present new mathematical models that include the impact of using selected preventative measures such as insecticide treated nets (ITN) in controlling or ameliorating the spread of the Zika virus. For these models, we derive the basic reproduction number and sharp estimates for the final size relation. We first present a single-stage model which is later extended to a new multistage model for Zika that incorporates more realistic incubation stages for both the humans and vectors. For each of these models, we derive a basic reproduction number and a final size relation estimate. We observe that the basic reproduction number for the multistage model converges to expected values for a standard Zika epidemic model with fixed incubation periods in both hosts and vectors. Finally, we also perform several computational experiments to validate the theoretical results obtained in this work and study the influence of various parameters on the models.