Behavioral and game-theoretic modeling of dengue epidemic: Comment on “Mathematical models for dengue fever epidemiology: A 10-year systematic review” by M. Aguiar et al.

During the last few decades, we have seen outbreaks of various epidemics e.g., SARS epidemic in $2002-2003$ [4], H5N1 influenza in 2005 [12], H1N1 influenza in 2009 [21], Ebola in 2014 [17], dengue outbreaks [13], and currently, COVID-19 since the end of 2019. Mathematical models have helped in understanding the spreading pattern of the epidemic and validating the effectiveness of relevant control measures [9].

People from various countries have been suffering from the dengue epidemic, which is a vector borne disease, for centuries. The first case of dengue was possibly reported in a Chinese medical encyclopedia [16]. Now dengue has become a common epidemic in more than 120 countries [2]. As per the estimates provided in 2013 [6], there are around 390 million cases of dengue infection per year (95% credible interval $284-528$ million), of which 96 million people manifest clinically. Regarding the prevalence of dengue virus infection, another study in 2012 [8] estimates that 3.9 billion people are at risk of dengue epidemic every year. The worldwide distribution of dengue infected individuals and death due to dengue is depicted in Fig. 1 . On the other hand, there is no universally acceptable vaccine that can prevent its recurrent outbreaks, and the available vaccines are not affordable for many developing countries [24], [26]. A wide range of mathematical models is proposed and analyzed for dengue epidemic that has played a crucial role in decision making and design of public health policies to fight against the dengue epidemic [28].

Fig. 1.

(a) A. aegypti and distribution of dengue in 2006; (b) Death caused by dengue fever per million in 2012 (Figure source–[1]).

We strongly believe that the last 10 years review on mathematical modeling of dengue fever infection by M. Aguiar et al. [3], is a very important and timely review article which will help researchers to have clear picture and proceed for further developments regarding dengue epidemic modeling and its effective control. In the said review article, the authors mainly focused on a systemic review of multi-strain modeling frameworks as the secondary infection with heterogeneous serotype is the main risk factor behind the severity of dengue fever. This detailed and systemic review specifically considers three types of multi-strain modeling approaches, namely vector-to-host transmission, host-to-host transmission, and within-host dynamics, with the help of deterministic, stochastic, and spatial models. The said article appropriately highlights several immunological aspects of dengue infection, e.g., temporary cross-immunity, antibody-dependent enhancement, co-infection etc. as well as the effect of these factors on the possibility of recurrent dengue infection to an individual and towards the risk of severity.

Unlike to initial mathematical models of dengue epidemic, the multi-strain models can capture the complex oscillatory nature of the sizes of the recurrent outbreaks. The multi-strain model helps to capture the uneven sizes of recurrent outbreaks, as different strains of dengue viruses appear in an irregular manner. Apart from the epidemic aspects of mathematical modeling, the authors have reported that torus bifurcation is responsible for the onset of complex oscillation (namely chaos), which is a dynamic feature of the multi-strain dengue epidemic models [23]. Various optimal strategies regarding vector control and vaccination campaign are reviewed in this article. Nowadays, researchers are using immuno-epidemic models to understand the epidemic progression more accurately [7], [18]. Recent developments of immuno-epidemic models of dengue epidemic are reviewed in this article.

Simultaneous infection of a host by multiple pathogens producing similar clinical symptoms is difficult to detect clinically, whereas this co-infection may affect the condition of the patients poorly. Especially, in the current scenario, for a patient with co-infection by dengue and COVID-19, it is challenging to clinically identify the co-infection as some of the symptoms of the two diseases are identical. This scenario is also covered in the review article.

Undoubtedly, this review work deserves appreciation from all aspects; still we want to highlight some other modeling approaches that might be worthy of investigation in the days to come. It is a matter of fact that human behavior during the spread of dengue like epidemics can significantly influence the spreading pattern of the epidemic up to a certain extent. During the rainy seasons, the mosquito population grows rapidly in the waterlogged areas, mainly in the developing countries, then people start using mosquito nets at night, spray insecticides in their surroundings, clean the garbage around their habitat etc., which can reduce the rapid growth of the vector. These measures taken by common people, irrespective of the public health policies, have significant impact to reduce the intensity of disease spread. These measures come into action only when the number of infected becomes prominent, and no measures are usually initiated by the competent authorities mainly in the developing countries, which may be due to financial burden. This behavioral change of human beings can influence the dengue epidemic spreading pattern [10], [11], [19], [25]. It is important to mention here that the major behavioral changes due to human activity like, reducing risky behaviors and avoiding the places with high risk of infection, can be captured with the help of non-linear incidence rates and density dependent dispersal of susceptible and infected [14]. The behavioral change of human individuals during the season of dengue epidemic spread can also be modeled with the help of game-theoretic approach by taking into account an individual's action that can maximize their personal payoff. As a result, these will account for the reduction of risk factor of getting infection and finally contribute to the slowing down of epidemic spread at the population level. This approach is known as ‘effect of individual's decision making on global regulation’ [5]. Some preliminary game-theoretic models for dengue are available in literature [15], [22]. Finally, we want to mention that it is really challenging to collect appropriate real data in order to come up with a reliable data-driven model formulation of human behavior based dengue epidemic, however, some initiatives can be taken up to build an efficient mathematical model based upon human behavior. The mathematical modeling of dengue epidemic using neural networks [27] and machine learning techniques [20] also has the potential impact on understanding the spreading pattern of the epidemic and designing effective control measures.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Communicated by M. Frank-Kamenetskii