Analysis of Zika virus dynamics with sexual transmission route using multiple optimal controls

Exploring Zika's dynamics: A scoping review journey from epidemic to equations through mathematical modelling

Zika virus (ZIKV) infection, along with the concurrent circulation of other arboviruses, presents a great public health challenge, reminding the utilization of mathematical modelling as a crucial tool for explaining its intricate dynamics and interactions with co-circulating pathogens. Through a scoping review, we aimed to discern current mathematical models investigating ZIKV dynamics, focusing on its interplay with other pathogens, and to identify underlying assumptions and deficiencies supporting attention, particularly regarding the epidemiological attributes characterizing Zika outbreaks. Following the PRISMA-Sc guidelines, a systematic search across PubMed, Web of Science, and MathSciNet provided 137 pertinent studies from an initial pool of 2446 papers, showing a diversity of modelling approaches, predominantly centered on vector-host compartmental models, with a notable concentration on the epidemiological landscapes of Colombia and Brazil during the 2015-2016 Zika epidemic. While modelling studies have been important in explaining Zika transmission dynamics and their intersections with diseases such as Dengue, Chikungunya, and COVID-19 so far, future Zika models should prioritize robust data integration and rigorous validation against diverse datasets to improve the accuracy and reliability of epidemic prediction. In addition, models could benefit from adaptable frameworks incorporating human behavior, environmental factors, and stochastic parameters, with an emphasis on open-access tools to foster transparency and research collaboration.

Optimal control and cost-effectiveness analysis for leptospirosis epidemic

This paper aims to apply an optimal control theory for the autonomous model of the leptospirosis epidemic to examine the effect of four time-dependent control measures on the model dynamics with cost-effectiveness. Pontryagin's Maximum Principle was used to derive the optimality system associated with the optimal control problem. Numerical simulations of the optimality system were performed for different control strategies and the results were presented graphically with and without controls. The optimality system was simulated using the Forward-Backward Sweep method in the Matlab programme. The numerical results revealed that the combination of all optimal control measures is the most effective strategy for minimizing the spread and impact of disease in the community. Furthermore, a cost-effectiveness analysis was performed to determine the most cost-effective strategy using the incremental cost-effectiveness ratio approach and we observed that the rodenticide control-only strategy is most effective to combat the spread of disease when available resources are limited.

Modelling the transmission of dengue, zika and chikungunya: a scoping review protocol

INTRODUCTION

Aedes mosquitoes are the primary vectors for the spread of viruses like dengue (DENV), zika (ZIKV) and chikungunya (CHIKV), all of which affect humans. Those diseases contribute to global public health issues because of their great dispersion in rural and urban areas. Mathematical and statistical models have become helpful in understanding these diseases' epidemiological dynamics. However, modelling the complexity of a real phenomenon, such as a viral disease, should consider several factors. This scoping review aims to document, identify and classify the most important factors as well as the modelling strategies for the spread of DENV, ZIKV and CHIKV.

METHODS AND ANALYSIS

We will conduct searches in electronic bibliographic databases such as PubMed, MathSciNet and the Web of Science for full-text peer-reviewed articles written in English, French and Spanish. These articles should use mathematical and statistical modelling frameworks to study dengue, zika and chikungunya, and their cocirculation/coinfection with other diseases, with a publication date between 1 January 2011 and 31 July 2023. Eligible studies should employ deterministic, stochastic or statistical modelling approaches, consider control measures and incorporate parameters' estimation or considering calibration/validation approaches. We will exclude articles focusing on clinical/laboratory experiments or theoretical articles that do not include any case study. Two reviewers specialised in zoonotic diseases and mathematical/statistical modelling will independently screen and retain relevant studies. Data extraction will be performed using a structured form, and the findings of the study will be summarised through classification and descriptive analysis. Three scoping reviews will be published, each focusing on one disease and its cocirculation/co-infection with other diseases.

ETHICS AND DISSEMINATION

This protocol is exempt from ethics approval because it is carried out on published manuscripts and without the participation of humans and/or animals. The results will be disseminated through peer-reviewed publications and presentations in conferences.

Dynamics and optimal control of a Zika model with sexual and vertical transmissions

A new transmission model of Zika virus with three transmission routes including human transmission by mosquito bites, sexual transmission between males and females and vertical transmission is established. The basic reproduction number $ R_{0} $ is derived. When $ R_{0} < 1 $, it is proved that the disease-free equilibrium is globally stable. Furthermore, the optimal control and mitigation methods for transmission of Zika virus are deduced and explored. The MCMC method is used to estimate the parameters and the reasons for the deviation between the actual infection cases and the simulated data are discussed. In addition, different strategies for controlling the spread of Zika virus are simulated and studied. The combination of mosquito control strategies and internal human control strategies is the most effective way in reducing the risk of Zika virus infection.

Sensitivity assessment and optimal economic evaluation of a new COVID-19 compartmental epidemic model with control interventions

Optimal economic evaluation is pivotal in prioritising the implementation of non-pharmaceutical and pharmaceutical interventions in the control of diseases. Governments, decision-makers and policy-makers broadly need information about the effectiveness of a control intervention concerning its cost-benefit to evaluate whether a control intervention offers the best value for money. The outbreak of COVID-19 in December 2019, and the eventual spread to other parts of the world, have pushed governments and health authorities to take drastic socioeconomic, sociocultural and sociopolitical measures to curb the spread of the virus, SARS-CoV-2. To help policy-makers, health authorities and governments, we propose a Susceptible, Exposed, Asymptomatic, Quarantined asymptomatic, Severely infected, Hospitalized, Recovered, Recovered asymptomatic, Deceased, and Protective susceptible (individuals who observe health protocols) compartmental structure to describe the dynamics of COVID-19. We fit the model to real data from Ghana and Egypt to estimate model parameters using standard incidence rate. Projections for disease control and sensitivity analysis are presented using MATLAB. We noticed that multiple peaks (waves) of COVID-19 for Ghana and Egypt can be prevented if stringent health protocols are implemented for a long time and/or the reluctant behaviour on the use of protective equipment by individuals are minimized. The sensitivity analysis suggests that: the rate of diagnoses and testing, the rate of quarantine through doubling enhanced contact tracing, adhering to physical distancing, adhering to wearing of nose masks, sanitizing-washing hands, media education remains the most effective measures in reducing the control reproduction numberR c , to less than unity in the absence of vaccines and therapeutic drugs in Ghana and Egypt. Optimal control and cost-effectiveness analysis are rigorously studied. The main finding is that having two controls (transmission reduction and case isolation) is better than having one control, but is economically expensive. In case only one control is affordable, then transmission reduction is better than case isolation. Hopefully, the results of this research should help policy-makers when dealing with multiple waves of COVID-19.