Mathematical Models for Chikungunya Virus: Effects of Heterogeneity and Periodic Environmental Variations

Abstract

In recent years, chikungunya, a mosquito-borne viral disease has spread globally and invaded new habitats and, as such, it is now regarded as one of the global threats to humanity because of its highly debilitating nature and unprecedented magnitude of its spread. Precisely, there is inadequate mechanistic understanding of how environmental factors, socioeconomic factors and disease intervention strategies, combined, affects epidemic magnitude and duration. In this study, we developed four mechanistic models for Aedes aegypti mosquitoes and chikungunya virus transmission that incorporates relevant ecological and biological factors, socio-economic factors and disease intervention strategies. The first model quantifies the effects of biological control and temperature on the growth of Aedes aegypti mosquito population in the environment. Utilising empirically derived temperature functions in literature, we observed that temperature ranges from 29^0 C to 35^0 C supports maximum egg hatching as well as development of larva and pupa. We also computed the vector reproduction number and examined the influence of entomological parameters on its magnitude. In addition, results also revealed that the attack rate of aquatic predators has higher impact to reduce mosquito population compared to the size of the predator population in the environment. In the second model, we developed a mathematical model to determine optimum timing of rolling out intervention strategies during a chikungunya virus outbreak. The proposed model incorporates three intervention strategies, physical barriers, larvicide and insecticide. Making use of optimal control theory, parameter sensitivity analysis, and numerical simulations, we performed a cost-effective analysis of the aforementioned intervention strategies. Findings from the proposed model offer a framework for designing cost-effective strategies for chikungunya with multiple intervention methods. Temperature and heterogeneous biting exposure are known to be integral factor capable of altering the spread of chikungunya during an outbreak. To quantify the role of these factors, we developed two mechanistic models, an autonomous and a non-autonomous. In a non-autonomous model temperature varies with time while in the autonomous it is regarded to be constant. In all scenarios, analysis of the model showed that both temperature and heterogeneous biting exposure have a substantial influence on shaping the transmission of the disease during an outbreak. Besides, temperature and heterogeneous biting exposure, the non-autonomous model incorporated mass media campaigns. Upon evaluating the implications of mass media campaigns during chikungunya outbreak, we observed that if 20% of infections are detected and reported, with mass media campaigns at 90% efficient, then the new infections produced may decrease by 68.8% over a four-year period. Overall, our results showed that temperature, predation, heterogeneous biting exposure and mass media campaigns play an essential component in determining both the short and long chikungunya virus dynamics.