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<p>This study deals with a thirteen-dimensional co-infected two serotype dengue model, considering cross immunity in deterministic as well as stochastic environment. Besides basic properties of the model, here we have discussed the stability of different types of equilibria. The system experiences transcritical bifurcation when the basic reproduction number crosses the critical value unity through generation of the single serotype endemic equilibrium point depending on the reproduction number of the corresponding serotype. The persistence of particular serotype infection is verified here through the study of the competitive exclusive principle using numerical simulation. Using optimal control theory we found the optimal path of the controls minimizing the implementation cost for disease eradication. Also, we have shown the effect of seasonal variation on dengue transmission dynamics. In the stochastic sense, we have found the condition of extinction and persistence of disease. Besides, we have computed the condition for stationary distribution. All the theoretical results are being verified by numerical simulations. We think that this paper will give some insights for health planners to control the burden of dengue.</p>

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Effect of cross-immunity on the transmission of a two serotypes co-infected dengue model under deterministic and stochastic environments

  • 期刊论文

  • 发表日期：

    2025年5月3日

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  • Gopal Chandra Sikdar,
  • Pritam Saha,
  • Uttam Ghosh

摘要

This study deals with a thirteen-dimensional co-infected two serotype dengue model, considering cross immunity in deterministic as well as stochastic environment. Besides basic properties of the model, here we have discussed the stability of different types of equilibria. The system experiences transcritical bifurcation when the basic reproduction number crosses the critical value unity through generation of the single serotype endemic equilibrium point depending on the reproduction number of the corresponding serotype. The persistence of particular serotype infection is verified here through the study of the competitive exclusive principle using numerical simulation. Using optimal control theory we found the optimal path of the controls minimizing the implementation cost for disease eradication. Also, we have shown the effect of seasonal variation on dengue transmission dynamics. In the stochastic sense, we have found the condition of extinction and persistence of disease. Besides, we have computed the condition for stationary distribution. All the theoretical results are being verified by numerical simulations. We think that this paper will give some insights for health planners to control the burden of dengue.