Optimal control of a multi-patch Dengue model under the influence of Wolbachia bacterium

Role of immigration and emigration on the spread of COVID-19 in a multipatch environment: a case study of India

Human mobility has played a critical role in the spread of COVID-19. The understanding of mobility helps in getting information on the acceleration or control of the spread of disease. The COVID-19 virus has been spreading among several locations despite all the best efforts related to its isolation. To comprehend this, a multi-patch mathematical model of COVID-19 is proposed and analysed in this work, where-in limited medical resources, quarantining, and inhibitory behaviour of healthy individuals are incorporated into the model. Furthermore, as an example, the impact of mobility in a three-patch model is studied considering the three worst-hit states of India, i.e. Kerala, Maharashtra and Tamil Nadu, as three patches. Key parameters and the basic reproduction number are estimated from the available data. Through results and analyses, it is seen that Kerala has a higher effective contact rate and has the highest prevalence. Moreover, if Kerala is isolated from Maharashtra or Tamil Nadu, the number of active cases will increase in Kerala but reduce in the other two states. Our findings indicate that the number of active cases will decrease in the high prevalence state and increase in the lower prevalence states if the emigration rate is higher than the immigration rate in the high prevalence state. Overall, proper travel restrictions are to be implemented to reduce or control the spread of disease from the high-prevalence state to other states with lower prevalence rates.

The impact of vaccination on human papillomavirus infection with disassortative geographical mixing: a two-patch modeling study

Human papillomavirus (HPV) infection can spread between regions. What is the impact of disassortative geographical mixing on the dynamics of HPV transmission? Vaccination is effective in preventing HPV infection. How to allocate HPV vaccines between genders within each region and between regions to reduce the total infection? Here we develop a two-patch two-sex model to address these questions. The control reproduction number [Formula: see text] under vaccination is obtained and shown to provide a critical threshold for disease elimination. Both analytical and numerical results reveal that disassortative geographical mixing does not affect [Formula: see text] and only has a minor impact on the disease prevalence in the total population given the vaccine uptake proportional to the population size for each gender in the two patches. When the vaccine uptake is not proportional to the population size, sexual mixing between the two patches can reduce [Formula: see text] and mitigate the consequence of disproportionate vaccine coverage. Using parameters calibrated from the data of a case study, we find that if the two patches have the same or similar sex ratios, allocating vaccines proportionally according to the new recruits in two patches and giving priority to the gender with a smaller recruit rate within each patch will bring the maximum benefit in reducing the total prevalence. We also show that a time-variable vaccination strategy between the two patches can further reduce the disease prevalence. This study provides some quantitative information that may help to develop vaccine distribution strategies in multiple regions with disassortative mixing.

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.

Stochastic dynamics of the transmission of Dengue fever virus between mosquitoes and humans

Considering the impact of environmental white noise on the quantity and behavior of vector of disease, a stochastic differential model describing the transmission of Dengue fever between mosquitoes and humans, in this paper, is proposed. By using Lyapunov methods and Itô’s formula, we first prove the existence and uniqueness of a global positive solution for this model. Further, some sufficient conditions for the extinction and persistence in the mean of this stochastic model are obtained by using the techniques of a series of stochastic inequalities. In addition, we also discuss the existence of a unique stationary distribution which leads to the stochastic persistence of this disease. Finally, several numerical simulations are carried to illustrate the main results of this contribution.

Dengue infection modeling and its optimal control analysis in East Java, Indonesia

In this study, we present a mathematical model of dengue fever transmission with hospitalization to describe the dynamics of the infection. We estimated the basic reproduction number for the infected cases in East Java Province for the year 2018 is R0≈1.1138. The parameters of the dengue model are estimated by using the confirmed notified cases of East Java province, Indonesia for the year 2018. We formulated the model for dengue with hospitalization and present its dynamics in details. Initially, we present the basic mathematical results and then show briefly the stability results for the model. Further, we formulate an optimal control problem with control functions and obtain the optimal control characterization. The optimal control problem is solved numerically and the results comprised of controls system for different strategies. The controls such as prevention and insecticide could use the best role in the disease eradication from the community. Our results suggest that the prevention of humans from the mosquitoes and the insecticide spray on mosquitoes can significantly reduce the infection of dengue fever and may reduce further spread of infection in the community.

Analysis and forecast of dengue incidence in urban Colombo, Sri Lanka

BACKGROUND

Understanding the dynamical behavior of dengue transmission is essential in designing control strategies. Mathematical models have become an important tool in describing the dynamics of a vector borne disease. Classical compartmental models are well-known method used to identify the dynamical behavior of spread of a vector borne disease. Due to use of fixed model parameters, the results of classical compartmental models do not match realistic nature. The aim of this study is to introduce time in varying model parameters, modify the classical compartmental model by improving its predictability power.

RESULTS

In this study, per-capita vector density has been chosen as the time in varying model parameter. The dengue incidences, rainfall and temperature data in urban Colombo are analyzed using Fourier mathematical analysis tool. Further, periodic pattern of the reported dengue incidences and meteorological data and correlation of dengue incidences with meteorological data are identified to determine climate data-driven per-capita vector density parameter function. By considering that the vector dynamics occurs in faster time scale compares to host dynamics, a two dimensional data-driven compartmental model is derived with aid of classical compartmental models. Moreover, a function for per-capita vector density is introduced to capture the seasonal pattern of the disease according to the effect of climate factors in urban Colombo.

CONCLUSIONS

The two dimensional data-driven compartmental model can be used to predict weekly dengue incidences upto 4 weeks. Accuracy of the model is evaluated using relative error function and the model can be used to predict more than 75% accurate data.