Alladi Ramakrishnan Hall

Mathematical modeling of some infectious diseases: Transmission dynamics and control

Indrajit Ghosh

Agricultural and Ecological Research Unit, ISI, Kolkata

Infectious diseases have a large impact on society, as they are responsible for a quarter of all deaths in the world annually. Examining such diseases through mathematical modeling and relevant case studies is of great importance, as the outcomes of such studies are key elements in the management of infectious diseases through proper interaction and control strategies. Using appropriate mathematical one can also predict future disease cases which is another important domain in infectious disease modelling. In this talk, I will present three different infectious disease models relevant to their transmission dynamics and control. At first, a general mosquito borne disease model will be presented. Despite centuries of enormous control efforts, mosquito-borne diseases continue to show upward trend of morbidity. To control these diseases, it is necessary to understand the transmission dynamics of them among mosquitoes. There are some vertically transmitted mosquito-borne diseases which can also be spread among mosquitoes through sexual contact (e.g., dengue, zika, chikungunya). Recent experimental observations indicate that for virus persistence in mosquito population, the role of venereal transmission cannot be ignored. It is therefore important to investigate which transmission route is more responsible for the persistence of the virus when there is no host. To this aim, we propose and analyze a novel compartmental model considering mosquito population only. We found that vertical transmission pathway is more effective than venereal transmission for the persistence of the virus. However, in absence of either one of the transmission mechanisms, the infected populations will eventually die out. Furthermore, when both transmission pathways are active, a variety of parameters indicate threshold like behavior of the infection. Next, I will present a compartmental model of dengue to assess the impact of active case finding (ACF) on dengue disease transmission. Currently, primary prevention of dengue is possible only with vector control and personal protection from the bites of infected mosquitoes. We calibrate our model to the yearly dengue cases in eight dengue endemic states of India. The results of our study show that ACF of symptomatic individuals will have significant effect on dengue case reduction as compared to ACF of asymptomatic individuals. Another closely related emerging disease is Zika virus which is spread by the same mosquitoes as dengue fever. We formulate and analyze five compartmental models of Zika transmission considering both vector-borne and sexual transmission. We fitted the proposed models to Zika case data from Colombia. The analysis revealed that the sexual transmission contribution to $R_0$ is [$15.36\%$ ($95\%$ CI $12.83–17.4$)] for the best fitted model. From this study, we concluded that sexual transmission may increase the risk of Zika, but it is not sufficient to sustain an outbreak by itself. Finally, I will talk about my ongoing research works and future directions.